SLIDE 1 WSC7 – 7th Online World Conference on Soft Computing in
Industrial Applications
Cooperative Particle Swarm Optimization for Robust Control System Design
Renato A. Krohling
Federal University of Espírito Santo, Electrical Engineering Department Campus de Goiabeiras, C.P. 01-9001, 29060-970, Vitória, ES BRAZIL, E-mail: renato@ele.ufes.br
Leandro dos Santos Coelho
Pontifícia Universidade Católica do Paraná, Laboratório de Automação e Sistemas Rua Imaculada Conceição, 1155, 80215-030 Curitiba, PR, BRAZIL, E-mail: lscoelho@rla01.pucpr.br
Yuhui Shi
EDS Embedded Systems Group 1401 E. Hoffer Street Kokomo, IN 46902 USA E-mail: Yuhui.Shi@EDS.com
SLIDE 2
Abstract
!
novel design method for robust controllers based on Cooperative Particle Swarm Optimization (PSO) is proposed
! design is formulated as a constrained optimization problem,
i.e., the minimization of a nominal H2 performance index subject to a H-infinite robust stability constraint
! the method focuses on two (PSOs): one for minimizing the
performance index, and the other for maximizing the robust stability constraint
! simulation results are given to illustrate the effectiveness and
validity of the approach
SLIDE 3
Literature review of H2/Hinfinite control problem
! theoretical viewpoint of design methods
(Bernstein and Haddad, 1994), (Doyle et al., 1994), (Snaizer, 1995)
! practical design method
(Chen et al., 1995), (Lo Bianco, and Piazzi, 1997), (Krohling, 1998), (Krohling et al., 1999)
SLIDE 4 Problem description
! The mixed H2/Hinfinite optimal control problem can be
stated as follows
! The problem of the synthesis of the controller is now one of
how to solve the constrained minimization problem above. We investigate a very promising technique of evolutionary computation, i.e., particle swarm optimization to solve the
- ptimization problem given by the expression above.
SLIDE 5
Particle swarm optimization (PSO)
! evolutionary computation technique ! originally developed by Kennedy and Eberhart in 1995 ! motivated from the simulation of social behavior
instead of the evolution of nature as in the other evolutionary algorithms
SLIDE 6
! each potential solution (individual) in PSO is also
assigned a randomized velocity, and the potential solutions, called particles, are then “flown” through the problem space
! each particle keeps track of its coordinates in the
problem space, which are associated with the best solution (fitness) it has achieved so far. (The fitness value is also stored.) This value is called pbest.
! another “best” value that is tracked by the global
version of the particle swarm optimizer is the overall best value, and its location, obtained so far by any particle in the population. This location is called gbest.
Particle swarm optimization (PSO)
SLIDE 7
!
the particle swarm optimization concept consists of, at each time step, changing the velocity (accelerating) each particle toward its pbest and gbest locations (global version of PSO)
! acceleration is weighted by a random term, with
separate random numbers being generated for acceleration toward pbest and gbest locations
Particle swarm optimization (PSO)
SLIDE 8
! 1) Initialize a population (array) of particles with random
positions and velocities in the n dimensional problem space.
! 2) For each particle, evaluate its fitness value. ! 3) Compare each particle’s fitness evaluation with the
particle’s pbest. If current value is better than pbest, then set pbest value equal to the current value, and the pbest location equal to the current location in n-dimensional space.
Procedure of PSO – List 1
SLIDE 9
Procedure of PSO
! 4) Compare fitness evaluation with the population’s overall
previous best. If current value is better than gbest, then reset gbest to the current particle’s array index and value.
! 5) Change the velocity and position of the particle according
to equations:
SLIDE 10
Procedure of PSO
! 6) Loop to step 2) until a criterion is met, usually a
sufficiently good fitness or a maximum number of iterations (generations).
SLIDE 11
Design parameters design
!
acceleration constants
c1 = c2 = 2
!
Vmax
set at about 10-20% of the dynamic range of the variable on each dimension
! population size selected was problem-dependent
population sizes of 20-50 were probably most common.
SLIDE 12
Proposed method
Optimization with two cooperative PSOs
SLIDE 13
PSO – List 2
SLIDE 14
PSO
SLIDE 15
PSO
SLIDE 16
Design example
SLIDE 17
Design example
SLIDE 18
Design example
SLIDE 19
Conclusion
