A Numerical Framework and Benchmark Case study for Muti-modal Fuel - - PowerPoint PPT Presentation
Introduction Hybrid Optimal control Case Study Summary and Future Work The end A Numerical Framework and Benchmark Case study for Muti-modal Fuel Efficient Aircraft Conflict Avoidance Manuel Soler, Maryam Kamgarpour, and John Lygeros
Introduction Hybrid Optimal control Case Study Summary and Future Work The end
Manuel Soler, Maryam Kamgarpour, and John Lygeros Presented by Manuel Soler
Department of Bioengineering and Aerospace Engineering Universidad Carlos III de Madrid
Manuel Soler ICRAT’14
Introduction Hybrid Optimal control Case Study Summary and Future Work The end
1
Introduction Motivation Description of the problem
2
Hybrid Optimal control Hybrid optimal control problem statement Solution approach
3
Case Study Problem set up Results
4
Summary and future work
Manuel Soler ICRAT’14
Introduction Hybrid Optimal control Case Study Summary and Future Work The end
1
Introduction Motivation Description of the problem
2
Hybrid Optimal control Hybrid optimal control problem statement Solution approach
3
Case Study Problem set up Results
4
Summary and future work
Manuel Soler ICRAT’14
Introduction Hybrid Optimal control Case Study Summary and Future Work The end
1
Introduction Motivation Description of the problem
2
Hybrid Optimal control Hybrid optimal control problem statement Solution approach
3
Case Study Problem set up Results
4
Summary and future work
Manuel Soler ICRAT’14
Introduction Hybrid Optimal control Case Study Summary and Future Work The end
1
Introduction Motivation Description of the problem
2
Hybrid Optimal control Hybrid optimal control problem statement Solution approach
3
Case Study Problem set up Results
4
Summary and future work
Manuel Soler ICRAT’14
Introduction Hybrid Optimal control Case Study Summary and Future Work The end Motivation
The future ATM is to be built around the so called Trajectory Based Operational (TBO) concept Trajectory Management Planning Sharing Agreeing Syncronizing Human in/over the loop Pilots Controllers Developing Human Decision Support tools for a safer, more efficient air navigation system
Manuel Soler ICRAT’14
Introduction Hybrid Optimal control Case Study Summary and Future Work The end Motivation
The future ATM is to be built around the so called Trajectory Based Operational (TBO) concept Trajectory Management Planning Sharing Agreeing Syncronizing Human in/over the loop Pilots Controllers Developing Human Decision Support tools for a safer, more efficient air navigation system
Manuel Soler ICRAT’14
Introduction Hybrid Optimal control Case Study Summary and Future Work The end Motivation
The future ATM is to be built around the so called Trajectory Based Operational (TBO) concept Trajectory Management Planning Sharing Agreeing Syncronizing Human in/over the loop Pilots Controllers Developing Human Decision Support tools for a safer, more efficient air navigation system
Manuel Soler ICRAT’14
Introduction Hybrid Optimal control Case Study Summary and Future Work The end Motivation
The future ATM is to be built around the so called Trajectory Based Operational (TBO) concept Trajectory Management Planning Sharing Agreeing Syncronizing Human in/over the loop Pilots Controllers Developing Human Decision Support tools for a safer, more efficient air navigation system
Manuel Soler ICRAT’14
Introduction Hybrid Optimal control Case Study Summary and Future Work The end Motivation
The future ATM is to be built around the so called Trajectory Based Operational (TBO) concept Trajectory Management Planning Sharing Agreeing Syncronizing Human in/over the loop Pilots Controllers Developing Human Decision Support tools for a safer, more efficient air navigation system
Manuel Soler ICRAT’14
Introduction Hybrid Optimal control Case Study Summary and Future Work The end Motivation
The future ATM is to be built around the so called Trajectory Based Operational (TBO) concept Trajectory Management Planning Sharing Agreeing Syncronizing Human in/over the loop Pilots Controllers Developing Human Decision Support tools for a safer, more efficient air navigation system
Manuel Soler ICRAT’14
Introduction Hybrid Optimal control Case Study Summary and Future Work The end Motivation
The future ATM is to be built around the so called Trajectory Based Operational (TBO) concept Trajectory Management Planning Sharing Agreeing Syncronizing Human in/over the loop Pilots Controllers Developing Human Decision Support tools for a safer, more efficient air navigation system
Manuel Soler ICRAT’14
Introduction Hybrid Optimal control Case Study Summary and Future Work The end Motivation
The future ATM is to be built around the so called Trajectory Based Operational (TBO) concept Trajectory Management Planning Sharing Agreeing Syncronizing Human in/over the loop Pilots Controllers Developing Human Decision Support tools for a safer, more efficient air navigation system
Manuel Soler ICRAT’14
Introduction Hybrid Optimal control Case Study Summary and Future Work The end Motivation
The future ATM is to be built around the so called Trajectory Based Operational (TBO) concept Trajectory Management Planning Sharing Agreeing Syncronizing Human in/over the loop Pilots Controllers Developing Human Decision Support tools for a safer, more efficient air navigation system
Manuel Soler ICRAT’14
Introduction Hybrid Optimal control Case Study Summary and Future Work The end Motivation
The future ATM is to be built around the so called Trajectory Based Operational (TBO) concept Trajectory Management Planning Sharing Agreeing Syncronizing Human in/over the loop Pilots Controllers Developing Human Decision Support tools for a safer, more efficient air navigation system
Manuel Soler ICRAT’14
Introduction Hybrid Optimal control Case Study Summary and Future Work The end Motivation
The future ATM is to be built around the so called Trajectory Based Operational (TBO) concept Trajectory Management Planning Sharing Agreeing Syncronizing Human in/over the loop Pilots Controllers Developing Human Decision Support tools for a safer, more efficient air navigation system
Manuel Soler ICRAT’14
Introduction Hybrid Optimal control Case Study Summary and Future Work The end Description of the problem
Conflict avoidance Description of the problem The goal is to find optimal trajectories at the tactical level that avoid loss of separation minima. We take into account non-linear aircraft performance in order to analyze fuel consumption;
system; The problem is formulated as a Hybrid Optimal Control Problem.
Manuel Soler ICRAT’14
Introduction Hybrid Optimal control Case Study Summary and Future Work The end Description of the problem
Conflict avoidance Description of the problem The goal is to find optimal trajectories at the tactical level that avoid loss of separation minima. We take into account non-linear aircraft performance in order to analyze fuel consumption;
system; The problem is formulated as a Hybrid Optimal Control Problem.
Manuel Soler ICRAT’14
Introduction Hybrid Optimal control Case Study Summary and Future Work The end Description of the problem
Conflict avoidance Description of the problem The goal is to find optimal trajectories at the tactical level that avoid loss of separation minima. We take into account non-linear aircraft performance in order to analyze fuel consumption;
system; The problem is formulated as a Hybrid Optimal Control Problem.
Manuel Soler ICRAT’14
Introduction Hybrid Optimal control Case Study Summary and Future Work The end Description of the problem
Conflict avoidance Description of the problem The goal is to find optimal trajectories at the tactical level that avoid loss of separation minima. We take into account non-linear aircraft performance in order to analyze fuel consumption;
system; The problem is formulated as a Hybrid Optimal Control Problem.
Manuel Soler ICRAT’14
Introduction Hybrid Optimal control Case Study Summary and Future Work The end Description of the problem
Conflict avoidance Description of the problem The goal is to find optimal trajectories at the tactical level that avoid loss of separation minima. We take into account non-linear aircraft performance in order to analyze fuel consumption;
system; The problem is formulated as a Hybrid Optimal Control Problem.
Manuel Soler ICRAT’14
Introduction Hybrid Optimal control Case Study Summary and Future Work The end Description of the problem
Conflict avoidance Description of the problem The goal is to find optimal trajectories at the tactical level that avoid loss of separation minima. We take into account non-linear aircraft performance in order to analyze fuel consumption;
system; The problem is formulated as a Hybrid Optimal Control Problem.
Manuel Soler ICRAT’14
Introduction Hybrid Optimal control Case Study Summary and Future Work The end Description of the problem
Conflict avoidance Description of the problem The goal is to find optimal trajectories at the tactical level that avoid loss of separation minima. We take into account non-linear aircraft performance in order to analyze fuel consumption;
system; The problem is formulated as a Hybrid Optimal Control Problem.
Manuel Soler ICRAT’14
Introduction Hybrid Optimal control Case Study Summary and Future Work The end Description of the problem
Conflict avoidance Description of the problem The goal is to find optimal trajectories at the tactical level that avoid loss of separation minima. We take into account non-linear aircraft performance in order to analyze fuel consumption;
system; The problem is formulated as a Hybrid Optimal Control Problem.
Manuel Soler ICRAT’14
Introduction Hybrid Optimal control Case Study Summary and Future Work The end
1
Introduction Motivation Description of the problem
2
Hybrid Optimal control Hybrid optimal control problem statement Solution approach
3
Case Study Problem set up Results
4
Summary and future work
Manuel Soler ICRAT’14
Introduction Hybrid Optimal control Case Study Summary and Future Work The end Hybrid optimal control problem statement
J(t, x(t), u(t), l) t ∈ [tI , tF] ˙ x(t) = f [x(t), u(t), l] 0 = g[x(t), u(t), l] tI ˜ tF x(tI) = xI ψ(x(tF)) = 0 x(t) u∗(t) φ[x(t), u(t), l] ≤ 0
Manuel Soler ICRAT’14
Introduction Hybrid Optimal control Case Study Summary and Future Work The end Hybrid optimal control problem statement
J(t, x(t), u(t), l) t ∈ [tI , tF]
˙ x(t) = w(t) · f1[x(t), u(t), l] + (1 − w(t)) · f2[x(t), u(t), l] 0 = w(t) · g1[x(t), u(t), l] + (1 − w(t)) · g2[x(t), u(t), l]
tI ˜ tF x(tI) = xI ψ(x(tF)) = 0 x(t) u∗(t) φ[x(t), u(t), l] ≤ 0 w(t) ∈ {0, 1}
Manuel Soler ICRAT’14
Introduction Hybrid Optimal control Case Study Summary and Future Work The end Hybrid optimal control problem statement
Problem (Hybrid Optimal Control Problem) min J(t, x(t), u(t), l) = E(tF, x(tF)) + tF
tI
L(x(t), u(t), l)dt; subject to: ˙ x(t) = w(t) · f1[x(t), u(t), l] + (1 − w(t)) · f2[x(t), u(t), l], dynamic equations; 0 = w(t) · g1[x(t), u(t), l] + (1 − w(t)) · g2[x(t), u(t), l], algebraic equations; φl ≤ φ[x(t), u(t), l] ≤ φu, path constraints. x(tI ) = xI , initial boundary conditions; ψ(x(tF)) = 0, terminal boundary conditions; w(t) ∈ {0, 1}, Binary control functions; (OCP)
Manuel Soler ICRAT’14
Introduction Hybrid Optimal control Case Study Summary and Future Work The end Hybrid optimal control problem statement
Problem (Hybrid Optimal Control Problem) min J(t, x(t), u(t), l) = E(tF, x(tF)) + tF
tI
L(x(t), u(t), l)dt; subject to: ˙ x(t) = w(t) · f1[x(t), u(t), l] + (1 − w(t)) · f2[x(t), u(t), l], dynamic equations; 0 = w(t) · g1[x(t), u(t), l] + (1 − w(t)) · g2[x(t), u(t), l], algebraic equations; φl ≤ φ[x(t), u(t), l] ≤ φu, path constraints. x(tI ) = xI , initial boundary conditions; ψ(x(tF)) = 0, terminal boundary conditions; w(t) ∈ {0, 1}, Binary control functions; (OCP)
Manuel Soler ICRAT’14
Introduction Hybrid Optimal control Case Study Summary and Future Work The end Hybrid optimal control problem statement
Problem (Hybrid Optimal Control Problem) min J(t, x(t), u(t), l) = E(tF, x(tF)) + tF
tI
L(x(t), u(t), l)dt; subject to: ˙ x(t) = w(t) · f1[x(t), u(t), l] + (1 − w(t)) · f2[x(t), u(t), l], dynamic equations; 0 = w(t) · g1[x(t), u(t), l] + (1 − w(t)) · g2[x(t), u(t), l], algebraic equations; φl ≤ φ[x(t), u(t), l] ≤ φu, path constraints. x(tI ) = xI , initial boundary conditions; ψ(x(tF)) = 0, terminal boundary conditions; w(t) ∈ {0, 1}, Binary control functions; (OCP)
Manuel Soler ICRAT’14
Introduction Hybrid Optimal control Case Study Summary and Future Work The end Hybrid optimal control problem statement
Problem (Hybrid Optimal Control Problem) min J(t, x(t), u(t), l) = E(tF, x(tF)) + tF
tI
L(x(t), u(t), l)dt; subject to: ˙ x(t) = w(t) · f1[x(t), u(t), l] + (1 − w(t)) · f2[x(t), u(t), l], dynamic equations; 0 = w(t) · g1[x(t), u(t), l] + (1 − w(t)) · g2[x(t), u(t), l], algebraic equations; φl ≤ φ[x(t), u(t), l] ≤ φu, path constraints. x(tI ) = xI , initial boundary conditions; ψ(x(tF)) = 0, terminal boundary conditions; w(t) ∈ {0, 1}, Binary control functions; (OCP)
Manuel Soler ICRAT’14
Introduction Hybrid Optimal control Case Study Summary and Future Work The end Hybrid optimal control problem statement
Problem (Hybrid Optimal Control Problem) min J(t, x(t), u(t), l) = E(tF, x(tF)) + tF
tI
L(x(t), u(t), l)dt; subject to: ˙ x(t) = w(t) · f1[x(t), u(t), l] + (1 − w(t)) · f2[x(t), u(t), l], dynamic equations; 0 = w(t) · g1[x(t), u(t), l] + (1 − w(t)) · g2[x(t), u(t), l], algebraic equations; φl ≤ φ[x(t), u(t), l] ≤ φu, path constraints. x(tI ) = xI , initial boundary conditions; ψ(x(tF)) = 0, terminal boundary conditions; w(t) ∈ {0, 1}, Binary control functions; (OCP)
Manuel Soler ICRAT’14
Introduction Hybrid Optimal control Case Study Summary and Future Work The end Hybrid optimal control problem statement
Problem (Hybrid Optimal Control Problem) min J(t, x(t), u(t), l) = E(tF, x(tF)) + tF
tI
L(x(t), u(t), l)dt; subject to: ˙ x(t) = w(t) · f1[x(t), u(t), l] + (1 − w(t)) · f2[x(t), u(t), l], dynamic equations; 0 = w(t) · g1[x(t), u(t), l] + (1 − w(t)) · g2[x(t), u(t), l], algebraic equations; φl ≤ φ[x(t), u(t), l] ≤ φu, path constraints. x(tI ) = xI , initial boundary conditions; ψ(x(tF)) = 0, terminal boundary conditions; w(t) ∈ {0, 1}, Binary control functions; (OCP)
Manuel Soler ICRAT’14
Introduction Hybrid Optimal control Case Study Summary and Future Work The end Hybrid optimal control problem statement
Problem (Hybrid Optimal Control Problem) min J(t, x(t), u(t), l) = E(tF, x(tF)) + tF
tI
L(x(t), u(t), l)dt; subject to: ˙ x(t) = w(t) · f1[x(t), u(t), l] + (1 − w(t)) · f2[x(t), u(t), l], dynamic equations; 0 = w(t) · g1[x(t), u(t), l] + (1 − w(t)) · g2[x(t), u(t), l], algebraic equations; φl ≤ φ[x(t), u(t), l] ≤ φu, path constraints. x(tI ) = xI , initial boundary conditions; ψ(x(tF)) = 0, terminal boundary conditions; w(t) ∈ {0, 1}, Binary control functions; (OCP)
Manuel Soler ICRAT’14
Introduction Hybrid Optimal control Case Study Summary and Future Work The end Hybrid optimal control problem statement
Problem (Hybrid Optimal Control Problem) min J(t, x(t), u(t), l) = E(tF, x(tF)) + tF
tI
L(x(t), u(t), l)dt; subject to: ˙ x(t) = w(t) · f1[x(t), u(t), l] + (1 − w(t)) · f2[x(t), u(t), l], dynamic equations; 0 = w(t) · g1[x(t), u(t), l] + (1 − w(t)) · g2[x(t), u(t), l], algebraic equations; φl ≤ φ[x(t), u(t), l] ≤ φu, path constraints. x(tI ) = xI , initial boundary conditions; ψ(x(tF)) = 0, terminal boundary conditions; w(t) ∈ {0, 1}, Binary control functions; (OCP)
Manuel Soler ICRAT’14
Introduction Hybrid Optimal control Case Study Summary and Future Work The end Hybrid optimal control problem statement
Problem (Hybrid Optimal Control Problem) min J(t, x(t), u(t), l) = E(tF, x(tF)) + tF
tI
L(x(t), u(t), l)dt; subject to: ˙ x(t) = w(t) · f1[x(t), u(t), l] + (1 − w(t)) · f2[x(t), u(t), l], dynamic equations; 0 = w(t) · g1[x(t), u(t), l] + (1 − w(t)) · g2[x(t), u(t), l], algebraic equations; φl ≤ φ[x(t), u(t), l] ≤ φu, path constraints. x(tI ) = xI , initial boundary conditions; ψ(x(tF)) = 0, terminal boundary conditions; w(t) ∈ {0, 1}, Binary control functions; (OCP)
Manuel Soler ICRAT’14
Introduction Hybrid Optimal control Case Study Summary and Future Work The end Solution approach
Relaxation of binary constraints through a penalty term Relax w(t) ∈ [0, 1]. Define β : [t0, tf ] → [−1, 1], with β(t) = 2w(t) − 1. We define a penalty cost as C ·
1 |β(t)|d .
The resulting problem is a continuous optimal control problem. It is solved using a direct collocation method: transforming it into a NLP and using the NLP solver IPOPT.
Manuel Soler ICRAT’14
Introduction Hybrid Optimal control Case Study Summary and Future Work The end Solution approach
Relaxation of binary constraints through a penalty term Relax w(t) ∈ [0, 1]. Define β : [t0, tf ] → [−1, 1], with β(t) = 2w(t) − 1. We define a penalty cost as C ·
1 |β(t)|d .
The resulting problem is a continuous optimal control problem. It is solved using a direct collocation method: transforming it into a NLP and using the NLP solver IPOPT.
Manuel Soler ICRAT’14
Introduction Hybrid Optimal control Case Study Summary and Future Work The end Solution approach
Relaxation of binary constraints through a penalty term Relax w(t) ∈ [0, 1]. Define β : [t0, tf ] → [−1, 1], with β(t) = 2w(t) − 1. We define a penalty cost as C ·
1 |β(t)|d .
The resulting problem is a continuous optimal control problem. It is solved using a direct collocation method: transforming it into a NLP and using the NLP solver IPOPT.
Manuel Soler ICRAT’14
Introduction Hybrid Optimal control Case Study Summary and Future Work The end Solution approach
Relaxation of binary constraints through a penalty term Relax w(t) ∈ [0, 1]. Define β : [t0, tf ] → [−1, 1], with β(t) = 2w(t) − 1. We define a penalty cost as C ·
1 |β(t)|d .
The resulting problem is a continuous optimal control problem. It is solved using a direct collocation method: transforming it into a NLP and using the NLP solver IPOPT.
Manuel Soler ICRAT’14
Introduction Hybrid Optimal control Case Study Summary and Future Work The end Solution approach
Relaxation of binary constraints through a penalty term Relax w(t) ∈ [0, 1]. Define β : [t0, tf ] → [−1, 1], with β(t) = 2w(t) − 1. We define a penalty cost as C ·
1 |β(t)|d .
The resulting problem is a continuous optimal control problem. It is solved using a direct collocation method: transforming it into a NLP and using the NLP solver IPOPT.
Manuel Soler ICRAT’14
Introduction Hybrid Optimal control Case Study Summary and Future Work The end Solution approach
Relaxation of binary constraints through a penalty term Relax w(t) ∈ [0, 1]. Define β : [t0, tf ] → [−1, 1], with β(t) = 2w(t) − 1. We define a penalty cost as C ·
1 |β(t)|d .
The resulting problem is a continuous optimal control problem. It is solved using a direct collocation method: transforming it into a NLP and using the NLP solver IPOPT.
Manuel Soler ICRAT’14
Introduction Hybrid Optimal control Case Study Summary and Future Work The end Solution approach
Relaxation of binary constraints through a penalty term Relax w(t) ∈ [0, 1]. Define β : [t0, tf ] → [−1, 1], with β(t) = 2w(t) − 1. We define a penalty cost as C ·
1 |β(t)|d .
The resulting problem is a continuous optimal control problem. It is solved using a direct collocation method: transforming it into a NLP and using the NLP solver IPOPT.
Manuel Soler ICRAT’14
Introduction Hybrid Optimal control Case Study Summary and Future Work The end Solution approach
Problem (Relaxed Hybrid Optimal Control Problem) min J(t, x(t), u(t), l) = E(tF, x(tF)) + tF
tI
1 |β(t)|d
subject to: ˙ x(t) = w(t) · f1[x(t), u(t), l] + (1 − w(t)) · f2[x(t), u(t), l], dynamic equations; 0 = w(t) · g1[x(t), u(t), l] + (1 − w(t)) · g2[x(t), u(t), l], algebraic equations; φl ≤ φ[x(t), u(t), l] ≤ φu, path constraints. x(tI ) = xI , initial boundary conditions; ψ(x(tF)) = 0, terminal boundary conditions; β(t) ∈ [−1, 1], auxiliary binary control functions; w(t) = 1 2(1 − β(t)), then w(t) ∈ [0, 1], binary control functions;
Manuel Soler ICRAT’14
Introduction Hybrid Optimal control Case Study Summary and Future Work The end Solution approach
Problem (Relaxed Hybrid Optimal Control Problem) min J(t, x(t), u(t), l) = E(tF, x(tF)) + tF
tI
1 |β(t)|d
subject to: ˙ x(t) = w(t) · f1[x(t), u(t), l] + (1 − w(t)) · f2[x(t), u(t), l], dynamic equations; 0 = w(t) · g1[x(t), u(t), l] + (1 − w(t)) · g2[x(t), u(t), l], algebraic equations; φl ≤ φ[x(t), u(t), l] ≤ φu, path constraints. x(tI ) = xI , initial boundary conditions; ψ(x(tF)) = 0, terminal boundary conditions; β(t) ∈ [−1, 1], auxiliary binary control functions; w(t) = 1 2(1 − β(t)), then w(t) ∈ [0, 1], binary control functions;
Manuel Soler ICRAT’14
Introduction Hybrid Optimal control Case Study Summary and Future Work The end Solution approach
Problem (Relaxed Hybrid Optimal Control Problem) min J(t, x(t), u(t), l) = E(tF, x(tF)) + tF
tI
1 |β(t)|d
subject to: ˙ x(t) = w(t) · f1[x(t), u(t), l] + (1 − w(t)) · f2[x(t), u(t), l], dynamic equations; 0 = w(t) · g1[x(t), u(t), l] + (1 − w(t)) · g2[x(t), u(t), l], algebraic equations; φl ≤ φ[x(t), u(t), l] ≤ φu, path constraints. x(tI ) = xI , initial boundary conditions; ψ(x(tF)) = 0, terminal boundary conditions; β(t) ∈ [−1, 1], auxiliary binary control functions; w(t) = 1 2(1 − β(t)), then w(t) ∈ [0, 1], binary control functions;
Manuel Soler ICRAT’14
Introduction Hybrid Optimal control Case Study Summary and Future Work The end Solution approach
Problem (Relaxed Hybrid Optimal Control Problem) min J(t, x(t), u(t), l) = E(tF, x(tF)) + tF
tI
1 |β(t)|d
subject to: ˙ x(t) = w(t) · f1[x(t), u(t), l] + (1 − w(t)) · f2[x(t), u(t), l], dynamic equations; 0 = w(t) · g1[x(t), u(t), l] + (1 − w(t)) · g2[x(t), u(t), l], algebraic equations; φl ≤ φ[x(t), u(t), l] ≤ φu, path constraints. x(tI ) = xI , initial boundary conditions; ψ(x(tF)) = 0, terminal boundary conditions; β(t) ∈ [−1, 1], auxiliary binary control functions; w(t) = 1 2(1 − β(t)), then w(t) ∈ [0, 1], binary control functions;
Manuel Soler ICRAT’14
Introduction Hybrid Optimal control Case Study Summary and Future Work The end Solution approach
Problem (Relaxed Hybrid Optimal Control Problem) min J(t, x(t), u(t), l) = E(tF, x(tF)) + tF
tI
1 |β(t)|d
subject to: ˙ x(t) = w(t) · f1[x(t), u(t), l] + (1 − w(t)) · f2[x(t), u(t), l], dynamic equations; 0 = w(t) · g1[x(t), u(t), l] + (1 − w(t)) · g2[x(t), u(t), l], algebraic equations; φl ≤ φ[x(t), u(t), l] ≤ φu, path constraints. x(tI ) = xI , initial boundary conditions; ψ(x(tF)) = 0, terminal boundary conditions; β(t) ∈ [−1, 1], auxiliary binary control functions; w(t) = 1 2(1 − β(t)), then w(t) ∈ [0, 1], binary control functions;
Manuel Soler ICRAT’14
Introduction Hybrid Optimal control Case Study Summary and Future Work The end Solution approach
Problem (Relaxed Hybrid Optimal Control Problem) min J(t, x(t), u(t), l) = E(tF, x(tF)) + tF
tI
1 |β(t)|d
subject to: ˙ x(t) = w(t) · f1[x(t), u(t), l] + (1 − w(t)) · f2[x(t), u(t), l], dynamic equations; 0 = w(t) · g1[x(t), u(t), l] + (1 − w(t)) · g2[x(t), u(t), l], algebraic equations; φl ≤ φ[x(t), u(t), l] ≤ φu, path constraints. x(tI ) = xI , initial boundary conditions; ψ(x(tF)) = 0, terminal boundary conditions; β(t) ∈ [−1, 1], auxiliary binary control functions; w(t) = 1 2(1 − β(t)), then w(t) ∈ [0, 1], binary control functions;
Manuel Soler ICRAT’14
Introduction Hybrid Optimal control Case Study Summary and Future Work The end Solution approach
Problem (Relaxed Hybrid Optimal Control Problem) min J(t, x(t), u(t), l) = E(tF, x(tF)) + tF
tI
1 |β(t)|d
subject to: ˙ x(t) = w(t) · f1[x(t), u(t), l] + (1 − w(t)) · f2[x(t), u(t), l], dynamic equations; 0 = w(t) · g1[x(t), u(t), l] + (1 − w(t)) · g2[x(t), u(t), l], algebraic equations; φl ≤ φ[x(t), u(t), l] ≤ φu, path constraints. x(tI ) = xI , initial boundary conditions; ψ(x(tF)) = 0, terminal boundary conditions; β(t) ∈ [−1, 1], auxiliary binary control functions; w(t) = 1 2(1 − β(t)), then w(t) ∈ [0, 1], binary control functions;
Manuel Soler ICRAT’14
Introduction Hybrid Optimal control Case Study Summary and Future Work The end Solution approach
Problem (Relaxed Hybrid Optimal Control Problem) min J(t, x(t), u(t), l) = E(tF, x(tF)) + tF
tI
1 |β(t)|d
subject to: ˙ x(t) = w(t) · f1[x(t), u(t), l] + (1 − w(t)) · f2[x(t), u(t), l], dynamic equations; 0 = w(t) · g1[x(t), u(t), l] + (1 − w(t)) · g2[x(t), u(t), l], algebraic equations; φl ≤ φ[x(t), u(t), l] ≤ φu, path constraints. x(tI ) = xI , initial boundary conditions; ψ(x(tF)) = 0, terminal boundary conditions; β(t) ∈ [−1, 1], auxiliary binary control functions; w(t) = 1 2(1 − β(t)), then w(t) ∈ [0, 1], binary control functions;
Manuel Soler ICRAT’14
Introduction Hybrid Optimal control Case Study Summary and Future Work The end Solution approach
Problem (Relaxed Hybrid Optimal Control Problem) min J(t, x(t), u(t), l) = E(tF, x(tF)) + tF
tI
1 |β(t)|d
subject to: ˙ x(t) = w(t) · f1[x(t), u(t), l] + (1 − w(t)) · f2[x(t), u(t), l], dynamic equations; 0 = w(t) · g1[x(t), u(t), l] + (1 − w(t)) · g2[x(t), u(t), l], algebraic equations; φl ≤ φ[x(t), u(t), l] ≤ φu, path constraints. x(tI ) = xI , initial boundary conditions; ψ(x(tF)) = 0, terminal boundary conditions; β(t) ∈ [−1, 1], auxiliary binary control functions; w(t) = 1 2(1 − β(t)), then w(t) ∈ [0, 1], binary control functions;
Manuel Soler ICRAT’14
Introduction Hybrid Optimal control Case Study Summary and Future Work The end Problem set up
1
Introduction Motivation Description of the problem
2
Hybrid Optimal control Hybrid optimal control problem statement Solution approach
3
Case Study Problem set up Results
4
Summary and future work
Manuel Soler ICRAT’14
Introduction Hybrid Optimal control Case Study Summary and Future Work The end Problem set up
d dt V χ γ λ θ he m =
T(t)−D(he(t),V (t),CL(t))−m(t)·g·sin γ(t) m(t) L(he(t),V (t),CL(t))·sin µ(t) m(t)·V (t)·cos γ(t) L(he(t),V (t),CL(t))·cos µ(t)−m(t)·g·cos γ(t) m(t)·V (t) V (t)·cos γ(t)·cos χ(t) R·cos θ(t) V (t)·cos γ(t)·sin χ(t) R
V (t) · sin γ(t) −T(t) · η(V (t)) . (1)
xe xw ye yw χ T D
(a) Top view
ye yw L ze zw µ mg
(b) Front view
xe xw T L D ze zw γ mg
(c) Lateral view
Figure: Aircraft state and forces
Manuel Soler ICRAT’14
Introduction Hybrid Optimal control Case Study Summary and Future Work The end Problem set up
H = 1000 [ft] H = 1000 [ft]
(a) Vertical Separation
Rc = 5 [Nm]
(b) Horizontal Separation
Figure: Minimum required separation.
Manuel Soler ICRAT’14
Introduction Hybrid Optimal control Case Study Summary and Future Work The end Problem set up
∆hi ∆hj H Ac.j Ac.i Figure: Vertical advisories through climb/descend maneuver.
Manuel Soler ICRAT’14
Introduction Hybrid Optimal control Case Study Summary and Future Work The end Problem set up
∆hi ∆hj H Ac.j Ac.i Figure: Vertical advisories through climb/descend maneuver. ∆Vj ∆χj Ac.j Ac.i ∆χi ∆Vi Rc Figure: Horizontal advisories through a turn maneuver.
Manuel Soler ICRAT’14
Introduction Hybrid Optimal control Case Study Summary and Future Work The end Problem set up
Set up
Manuel Soler ICRAT’14
Introduction Hybrid Optimal control Case Study Summary and Future Work The end Problem set up
Set up
Ac.4 Ac.6 Ac.2 Ac.8 Ac.3 Ac.5 Ac.1 Ac.7
Figure: Benchmark case study. The labeled points are initial position of the aircraft
h = 11.000; nsamples = 50 (per aircraft)
Manuel Soler ICRAT’14
Introduction Hybrid Optimal control Case Study Summary and Future Work The end Problem set up
Initial and final conditions
Table: Boundary values.
Initial values Final values m [kg] V [m/s] λe◦ θe◦ χ [deg] λe◦ θe◦
220 6 46.5 10 46.5
220 10 46.5 180 6 46.5
220 8 44.5 90 8 48.5
220 8 48.5 270 8 44.5
220 8 − 2 · √ 2/2 46.5 − 2 · √ 2/2 45 8 + 2 · √ 2/2 46.5 + 2 · √ 2/2
220 8 + 2 · √ 2/2 46.5 + 2 · √ 2/2 225 8 − 2 · √ 2/2 46.5 − 2 · √ 2/2
220 8 + 2 · √ 2/2 46.5 − 2 · √ 2/2 135 8 − 2 · √ 2/2 46.5 + 2 · √ 2/2
220 8 − 2 · √ 2/2 46.5 + 2 · √ 2/2 315 8 + 2 · √ 2/2 46.5 − 2 · √ 2/2
Manuel Soler ICRAT’14
Introduction Hybrid Optimal control Case Study Summary and Future Work The end Problem set up
Manuel Soler ICRAT’14
Introduction Hybrid Optimal control Case Study Summary and Future Work The end Problem set up
∆χj Ac.j Ac.i ∆χi Rc Figure: Horizontal advisories through a turn maneuver.
Manuel Soler ICRAT’14
Introduction Hybrid Optimal control Case Study Summary and Future Work The end Problem set up
∆Vj Ac.j Ac.i ∆χi Rc Figure: Horizontal advisories through a turn maneuver.
Manuel Soler ICRAT’14
Introduction Hybrid Optimal control Case Study Summary and Future Work The end Problem set up
∆χj Ac.j Ac.i ∆Vi Rc Figure: Horizontal advisories through a turn maneuver.
Manuel Soler ICRAT’14
Introduction Hybrid Optimal control Case Study Summary and Future Work The end Problem set up
∆Vj Ac.j Ac.i ∆Vi Rc Figure: Horizontal advisories through a turn maneuver.
Undefined number of advisories (switches) and 4 different combination of modes per aircraft pair
Manuel Soler ICRAT’14
Introduction Hybrid Optimal control Case Study Summary and Future Work The end Problem set up
∆Vj Ac.j Ac.i ∆Vi Rc Figure: Horizontal advisories through a turn maneuver.
Undefined number of advisories (switches) and 4 different combination of modes per aircraft pair
Manuel Soler ICRAT’14
Introduction Hybrid Optimal control Case Study Summary and Future Work The end Results
1
Introduction Motivation Description of the problem
2
Hybrid Optimal control Hybrid optimal control problem statement Solution approach
3
Case Study Problem set up Results
4
Summary and future work
Manuel Soler ICRAT’14
Introduction Hybrid Optimal control Case Study Summary and Future Work The end Results
Manuel Soler ICRAT’14
Introduction Hybrid Optimal control Case Study Summary and Future Work The end Results
50 0.5 1 AC 1 50 0.5 1 AC 2 50 0.5 1 AC 3 50 0.5 1 AC 4
Sampling times Sampling times Sampling times Sampling times
w(t) w(t) w(t) w(t)
(a) w(t) in Aircraft 1, 2, 3, 4
50 0.5 1 AC 5 50 0.5 1 AC 6 50 0.5 1 AC 7 50 0.5 1 AC 8
Sampling times Sampling times Sampling times Sampling times
w(t) w(t) w(t) w(t)
(b) w(t) in Aircraft 5, 6, 7, 8
Figure: Binary control functions w(t) as a function of the number of
Manuel Soler ICRAT’14
Introduction Hybrid Optimal control Case Study Summary and Future Work The end Results
10 20 30 40 50 150 200 250 AC 1 AC 2 AC 3 AC 4 AC 5 AC 6 AC 7 AC 8
Sampling times
V [m/s]
(a) V (t)
10 20 30 40 50 −50 50 100 150 200 250 300 350 AC 1 AC 2 AC 3 AC 4 AC 5 AC 6 AC 7 AC 8
Sampling times
χ [deg]
(b) T(t)
Figure: Velocity and heading at sampling times
Manuel Soler ICRAT’14
Introduction Hybrid Optimal control Case Study Summary and Future Work The end Results
10 20 30 40 50 5.38 5.4 5.42 5.44 5.46 5.48 5.5 x 10
4AC 1 AC 2 AC 3 AC 4 AC 5 AC 6 AC 7 AC 8
Sampling times
m [kg]
(a) m(t)
10 20 30 40 50 1 2 3 4 5 x 10
4AC 1 AC 2 AC 3 AC 4 AC 5 AC 6 AC 7 AC 8
Sampling times
T [N]
(b) χ(t)
10 20 30 40 50 −15 −10 −5 5 10 15 20 AC 1 AC 2 AC 3 AC 4 AC 5 AC 6 AC 7 AC 8
Sampling times
µ [deg]
(c) µ(t)
Manuel Soler ICRAT’14
Introduction Hybrid Optimal control Case Study Summary and Future Work The end Results
Table: Numerical Results.
Fuel consum. [kg] Time [s] num. advisories num. conflicts
748.9 1420.4 7
763.8 1431.8 6
1098.4 2076.1 5
1105 2053.7 5
972.7 1860 4
966 1754.7 3
948.2 1792.2 1
966.7 1772.6 2 Computational time: 6400 sec
Manuel Soler ICRAT’14
Introduction Hybrid Optimal control Case Study Summary and Future Work The end Results
Table: Numerical Results.
Fuel consum. [kg] Time [s] num. advisories num. conflicts
748.9 1420.4 7
763.8 1431.8 6
1098.4 2076.1 5
1105 2053.7 5
972.7 1860 4
966 1754.7 3
948.2 1792.2 1
966.7 1772.6 2 Computational time: 6400 sec
Manuel Soler ICRAT’14
Introduction Hybrid Optimal control Case Study Summary and Future Work The end
1
Introduction Motivation Description of the problem
2
Hybrid Optimal control Hybrid optimal control problem statement Solution approach
3
Case Study Problem set up Results
4
Summary and future work
Manuel Soler ICRAT’14
Introduction Hybrid Optimal control Case Study Summary and Future Work The end Summary and future work
Summary a) We formulated fuel optimal conflict free aircraft trajectory planning as a hybrid optimal control problem. b) This formulation allowed for inclusion of accurate aircraft dynamic models and conflict resolution maneuvers that are consistent with air traffic control procedures. c) We developed an algorithm for solving the hybrid optimal control problem through transforming it to a nonlinear program. d) Our approach was illustrated with a case study with accurate civilian aircraft model, and realistic number of aircraft.
Manuel Soler ICRAT’14
Introduction Hybrid Optimal control Case Study Summary and Future Work The end Summary and future work
Summary a) We formulated fuel optimal conflict free aircraft trajectory planning as a hybrid optimal control problem. b) This formulation allowed for inclusion of accurate aircraft dynamic models and conflict resolution maneuvers that are consistent with air traffic control procedures. c) We developed an algorithm for solving the hybrid optimal control problem through transforming it to a nonlinear program. d) Our approach was illustrated with a case study with accurate civilian aircraft model, and realistic number of aircraft.
Manuel Soler ICRAT’14
Introduction Hybrid Optimal control Case Study Summary and Future Work The end Summary and future work
Summary a) We formulated fuel optimal conflict free aircraft trajectory planning as a hybrid optimal control problem. b) This formulation allowed for inclusion of accurate aircraft dynamic models and conflict resolution maneuvers that are consistent with air traffic control procedures. c) We developed an algorithm for solving the hybrid optimal control problem through transforming it to a nonlinear program. d) Our approach was illustrated with a case study with accurate civilian aircraft model, and realistic number of aircraft.
Manuel Soler ICRAT’14
Introduction Hybrid Optimal control Case Study Summary and Future Work The end Summary and future work
Summary a) We formulated fuel optimal conflict free aircraft trajectory planning as a hybrid optimal control problem. b) This formulation allowed for inclusion of accurate aircraft dynamic models and conflict resolution maneuvers that are consistent with air traffic control procedures. c) We developed an algorithm for solving the hybrid optimal control problem through transforming it to a nonlinear program. d) Our approach was illustrated with a case study with accurate civilian aircraft model, and realistic number of aircraft.
Manuel Soler ICRAT’14
Introduction Hybrid Optimal control Case Study Summary and Future Work The end Summary and future work
Summary a) We formulated fuel optimal conflict free aircraft trajectory planning as a hybrid optimal control problem. b) This formulation allowed for inclusion of accurate aircraft dynamic models and conflict resolution maneuvers that are consistent with air traffic control procedures. c) We developed an algorithm for solving the hybrid optimal control problem through transforming it to a nonlinear program. d) Our approach was illustrated with a case study with accurate civilian aircraft model, and realistic number of aircraft.
Manuel Soler ICRAT’14
Introduction Hybrid Optimal control Case Study Summary and Future Work The end Summary and future work
The above presented work corresponds to a preliminary study that should be further explored and extended. Ongoing and future work includes: Implement the algorithm in a real air traffic control (ATC) sector, considering first a single FL and then extending it considering a vertical structure. Introduce arrival time constraints at the exit waypoints in order not to disrupt the air traffic system downwards due to aircraft flying ahead/behind schedule. Include wind forecasts into aircraft dynamics and take into account the uncertainty in the forecast and its propagation along the trajectories. Drastic reduction of the computational time in order to be able to run the algorithm in real time. Impose constraints in the maximum number of advisories. Analyzing Pareto optimality of the solution to ensure fair advisories for each aircraft. Increase the number of samples in order to improve the conflict detection sensitivity of the algorithm. Comparison of fuel savings resulting from the algorithm with respect to current conflict resolution procedures. Trust and acceptance test by pilots and air traffic controllers.
Manuel Soler ICRAT’14
Introduction Hybrid Optimal control Case Study Summary and Future Work The end Summary and future work
The above presented work corresponds to a preliminary study that should be further explored and extended. Ongoing and future work includes: Implement the algorithm in a real air traffic control (ATC) sector, considering first a single FL and then extending it considering a vertical structure. Introduce arrival time constraints at the exit waypoints in order not to disrupt the air traffic system downwards due to aircraft flying ahead/behind schedule. Include wind forecasts into aircraft dynamics and take into account the uncertainty in the forecast and its propagation along the trajectories. Drastic reduction of the computational time in order to be able to run the algorithm in real time. Impose constraints in the maximum number of advisories. Analyzing Pareto optimality of the solution to ensure fair advisories for each aircraft. Increase the number of samples in order to improve the conflict detection sensitivity of the algorithm. Comparison of fuel savings resulting from the algorithm with respect to current conflict resolution procedures. Trust and acceptance test by pilots and air traffic controllers.
Manuel Soler ICRAT’14
Introduction Hybrid Optimal control Case Study Summary and Future Work The end Summary and future work
The above presented work corresponds to a preliminary study that should be further explored and extended. Ongoing and future work includes: Implement the algorithm in a real air traffic control (ATC) sector, considering first a single FL and then extending it considering a vertical structure. Introduce arrival time constraints at the exit waypoints in order not to disrupt the air traffic system downwards due to aircraft flying ahead/behind schedule. Include wind forecasts into aircraft dynamics and take into account the uncertainty in the forecast and its propagation along the trajectories. Drastic reduction of the computational time in order to be able to run the algorithm in real time. Impose constraints in the maximum number of advisories. Analyzing Pareto optimality of the solution to ensure fair advisories for each aircraft. Increase the number of samples in order to improve the conflict detection sensitivity of the algorithm. Comparison of fuel savings resulting from the algorithm with respect to current conflict resolution procedures. Trust and acceptance test by pilots and air traffic controllers.
Manuel Soler ICRAT’14
Introduction Hybrid Optimal control Case Study Summary and Future Work The end Summary and future work
The above presented work corresponds to a preliminary study that should be further explored and extended. Ongoing and future work includes: Implement the algorithm in a real air traffic control (ATC) sector, considering first a single FL and then extending it considering a vertical structure. Introduce arrival time constraints at the exit waypoints in order not to disrupt the air traffic system downwards due to aircraft flying ahead/behind schedule. Include wind forecasts into aircraft dynamics and take into account the uncertainty in the forecast and its propagation along the trajectories. Drastic reduction of the computational time in order to be able to run the algorithm in real time. Impose constraints in the maximum number of advisories. Analyzing Pareto optimality of the solution to ensure fair advisories for each aircraft. Increase the number of samples in order to improve the conflict detection sensitivity of the algorithm. Comparison of fuel savings resulting from the algorithm with respect to current conflict resolution procedures. Trust and acceptance test by pilots and air traffic controllers.
Manuel Soler ICRAT’14
Introduction Hybrid Optimal control Case Study Summary and Future Work The end Summary and future work
The above presented work corresponds to a preliminary study that should be further explored and extended. Ongoing and future work includes: Implement the algorithm in a real air traffic control (ATC) sector, considering first a single FL and then extending it considering a vertical structure. Introduce arrival time constraints at the exit waypoints in order not to disrupt the air traffic system downwards due to aircraft flying ahead/behind schedule. Include wind forecasts into aircraft dynamics and take into account the uncertainty in the forecast and its propagation along the trajectories. Drastic reduction of the computational time in order to be able to run the algorithm in real time. Impose constraints in the maximum number of advisories. Analyzing Pareto optimality of the solution to ensure fair advisories for each aircraft. Increase the number of samples in order to improve the conflict detection sensitivity of the algorithm. Comparison of fuel savings resulting from the algorithm with respect to current conflict resolution procedures. Trust and acceptance test by pilots and air traffic controllers.
Manuel Soler ICRAT’14
Introduction Hybrid Optimal control Case Study Summary and Future Work The end Summary and future work
The above presented work corresponds to a preliminary study that should be further explored and extended. Ongoing and future work includes: Implement the algorithm in a real air traffic control (ATC) sector, considering first a single FL and then extending it considering a vertical structure. Introduce arrival time constraints at the exit waypoints in order not to disrupt the air traffic system downwards due to aircraft flying ahead/behind schedule. Include wind forecasts into aircraft dynamics and take into account the uncertainty in the forecast and its propagation along the trajectories. Drastic reduction of the computational time in order to be able to run the algorithm in real time. Impose constraints in the maximum number of advisories. Analyzing Pareto optimality of the solution to ensure fair advisories for each aircraft. Increase the number of samples in order to improve the conflict detection sensitivity of the algorithm. Comparison of fuel savings resulting from the algorithm with respect to current conflict resolution procedures. Trust and acceptance test by pilots and air traffic controllers.
Manuel Soler ICRAT’14
Introduction Hybrid Optimal control Case Study Summary and Future Work The end Summary and future work
The above presented work corresponds to a preliminary study that should be further explored and extended. Ongoing and future work includes: Implement the algorithm in a real air traffic control (ATC) sector, considering first a single FL and then extending it considering a vertical structure. Introduce arrival time constraints at the exit waypoints in order not to disrupt the air traffic system downwards due to aircraft flying ahead/behind schedule. Include wind forecasts into aircraft dynamics and take into account the uncertainty in the forecast and its propagation along the trajectories. Drastic reduction of the computational time in order to be able to run the algorithm in real time. Impose constraints in the maximum number of advisories. Analyzing Pareto optimality of the solution to ensure fair advisories for each aircraft. Increase the number of samples in order to improve the conflict detection sensitivity of the algorithm. Comparison of fuel savings resulting from the algorithm with respect to current conflict resolution procedures. Trust and acceptance test by pilots and air traffic controllers.
Manuel Soler ICRAT’14
Introduction Hybrid Optimal control Case Study Summary and Future Work The end Summary and future work
The above presented work corresponds to a preliminary study that should be further explored and extended. Ongoing and future work includes: Implement the algorithm in a real air traffic control (ATC) sector, considering first a single FL and then extending it considering a vertical structure. Introduce arrival time constraints at the exit waypoints in order not to disrupt the air traffic system downwards due to aircraft flying ahead/behind schedule. Include wind forecasts into aircraft dynamics and take into account the uncertainty in the forecast and its propagation along the trajectories. Drastic reduction of the computational time in order to be able to run the algorithm in real time. Impose constraints in the maximum number of advisories. Analyzing Pareto optimality of the solution to ensure fair advisories for each aircraft. Increase the number of samples in order to improve the conflict detection sensitivity of the algorithm. Comparison of fuel savings resulting from the algorithm with respect to current conflict resolution procedures. Trust and acceptance test by pilots and air traffic controllers.
Manuel Soler ICRAT’14
Introduction Hybrid Optimal control Case Study Summary and Future Work The end Summary and future work
The above presented work corresponds to a preliminary study that should be further explored and extended. Ongoing and future work includes: Implement the algorithm in a real air traffic control (ATC) sector, considering first a single FL and then extending it considering a vertical structure. Introduce arrival time constraints at the exit waypoints in order not to disrupt the air traffic system downwards due to aircraft flying ahead/behind schedule. Include wind forecasts into aircraft dynamics and take into account the uncertainty in the forecast and its propagation along the trajectories. Drastic reduction of the computational time in order to be able to run the algorithm in real time. Impose constraints in the maximum number of advisories. Analyzing Pareto optimality of the solution to ensure fair advisories for each aircraft. Increase the number of samples in order to improve the conflict detection sensitivity of the algorithm. Comparison of fuel savings resulting from the algorithm with respect to current conflict resolution procedures. Trust and acceptance test by pilots and air traffic controllers.
Manuel Soler ICRAT’14
Introduction Hybrid Optimal control Case Study Summary and Future Work The end Summary and future work
The above presented work corresponds to a preliminary study that should be further explored and extended. Ongoing and future work includes: Implement the algorithm in a real air traffic control (ATC) sector, considering first a single FL and then extending it considering a vertical structure. Introduce arrival time constraints at the exit waypoints in order not to disrupt the air traffic system downwards due to aircraft flying ahead/behind schedule. Include wind forecasts into aircraft dynamics and take into account the uncertainty in the forecast and its propagation along the trajectories. Drastic reduction of the computational time in order to be able to run the algorithm in real time. Impose constraints in the maximum number of advisories. Analyzing Pareto optimality of the solution to ensure fair advisories for each aircraft. Increase the number of samples in order to improve the conflict detection sensitivity of the algorithm. Comparison of fuel savings resulting from the algorithm with respect to current conflict resolution procedures. Trust and acceptance test by pilots and air traffic controllers.
Manuel Soler ICRAT’14
Introduction Hybrid Optimal control Case Study Summary and Future Work The end Summary and future work
The above presented work corresponds to a preliminary study that should be further explored and extended. Ongoing and future work includes: Implement the algorithm in a real air traffic control (ATC) sector, considering first a single FL and then extending it considering a vertical structure. Introduce arrival time constraints at the exit waypoints in order not to disrupt the air traffic system downwards due to aircraft flying ahead/behind schedule. Include wind forecasts into aircraft dynamics and take into account the uncertainty in the forecast and its propagation along the trajectories. Drastic reduction of the computational time in order to be able to run the algorithm in real time. Impose constraints in the maximum number of advisories. Analyzing Pareto optimality of the solution to ensure fair advisories for each aircraft. Increase the number of samples in order to improve the conflict detection sensitivity of the algorithm. Comparison of fuel savings resulting from the algorithm with respect to current conflict resolution procedures. Trust and acceptance test by pilots and air traffic controllers.
Manuel Soler ICRAT’14
Introduction Hybrid Optimal control Case Study Summary and Future Work The end
Contact Info Department of Bioengineering and Aerospace Engineering. Universidad Carlos III; Phone: +34 91 624 8219; mail: masolera@ing.uc3m.es Group site: http://aero.uc3m.es Personal site: http://www.aerospaceengineering.es
Manuel Soler ICRAT’14
Introduction Hybrid Optimal control Case Study Summary and Future Work The end
Contact Info Department of Bioengineering and Aerospace Engineering. Universidad Carlos III; Phone: +34 91 624 8219; mail: masolera@ing.uc3m.es Group site: http://aero.uc3m.es Personal site: http://www.aerospaceengineering.es
Manuel Soler ICRAT’14
Introduction Hybrid Optimal control Case Study Summary and Future Work The end
Contact Info Department of Bioengineering and Aerospace Engineering. Universidad Carlos III; Phone: +34 91 624 8219; mail: masolera@ing.uc3m.es Group site: http://aero.uc3m.es Personal site: http://www.aerospaceengineering.es
Manuel Soler ICRAT’14
Introduction Hybrid Optimal control Case Study Summary and Future Work The end
Contact Info Department of Bioengineering and Aerospace Engineering. Universidad Carlos III; Phone: +34 91 624 8219; mail: masolera@ing.uc3m.es Group site: http://aero.uc3m.es Personal site: http://www.aerospaceengineering.es
Manuel Soler ICRAT’14