INTRODUCTION TO INTRODUCTION TO HYBRID SYSTEMS: HYBRID SYSTEMS: ORIGINS, EXAMPLES, APPLICATIONS ORIGINS, EXAMPLES, APPLICATIONS C. G. Cassandras C. G. Cassandras Dept. of Manufacturing Engineering and Center for Information and Systems Engineering (CISE) Boston University cgc@bu.edu http://vita.bu.edu/cgc CODES Lab. - Boston University Christos G. Cassandras
OUTLINE � WHAT’S A HYBRID SYSTEM… � HYBRID SYSTEMS AND COMPLEXITY: DECOMPOSITION : HYBRID SYSTEM → DES ABSTRACTION : DES → HYBRID SYSTEM � EXAMPLES, APPLICATION AREAS Christos G. Cassandras CODES Lab. - Boston University
WHAT’S A HYBRID SYSTEM? TIME-DRIVEN z = g ( z , u , t ) z = & g ( z , u , t ) & 2 2 2 2 1 1 1 1 DYNAMICS TIME x 1 x 2 x 0 x 1 EVENT-DRIVEN x = f ( x , z , u , t ) x = f ( x , z , u , t ) 2 2 1 2 2 DYNAMICS 1 1 0 1 1 ” ” E E D D O O M M “ “ W W E E More on modeling frameworks, open problems, etc: [ Proc. of IEEE Special Issue (Antsaklis, Ed.), 2000 ] N N More on modeling frameworks, open problems, etc: [ Proc. of IEEE Special Issue (Antsaklis, Ed.), 2000 ] Christos G. Cassandras CODES Lab. - Boston University
WHAT’S A HYBRID SYSTEM? CONTINUED TIME DRIVEN : i = z g ( z , u , t ) & i i i TIME TIME TIME TIME TIME x 1 x 2 x 3 x 4 x i +1 x i +1 x 0 x 1 x 2 x 3 x i EVENT - DRIVEN : = x i x f ( x , z , u , t ) + i 1 i i i i Christos G. Cassandras CODES Lab. - Boston University
WHAT’S A HYBRID SYSTEM? CONTINUED Physical State, z i = z g ( z , u , t ) & i i i hybrid … Temporal State, x x 1 x 2 x i SWITCHING TIMES SWITCHING TIMES Switching Times HAVE THEIR OWN x i +1 = f i ( x i , u i , t ) HAVE THEIR OWN DYNAMICS! DYNAMICS! Christos G. Cassandras CODES Lab. - Boston University
WHAT’S A HYBRID SYSTEM? CONTINUED PLANT REPLACE THE USUAL CONTROL LOOP BY REPLACE THE USUAL CONTROL LOOP BY CONTROLLER SUPERVISOR EVENTS PLANT PLANT CONTROLLER Christos G. Cassandras CODES Lab. - Boston University
WHAT’S A HYBRID SYSTEM? CONTINUED PLANT • Plant: time-driven + event-driven dynamics EVENT-DRIVEN DYNAMICS • Controller affects both time-driven + event-driven components TIME-DRIVEN DYNAMICS • Control may be continuous signal and/or discrete event CONTROLLER Christos G. Cassandras CODES Lab. - Boston University
DISCRETE CONTINUOUS 1980 EVENT-DRIVEN TIME-DRIVEN SYSTEMS SYSTEMS 1990 HYBRID SYSTEMS 2000 Christos G. Cassandras CODES Lab. - Boston University
DECOMPOSITION DECOMPOSITION Christos G. Cassandras CODES Lab. - Boston University
LESS COMPLEX MORE COMPLEX TIME-DRIVEN SYSTEM What exactly What exactly does that mean ? does that mean ? HYBRID SYSTEM EVENT-DRIVEN SYSTEM DECOMPOSITION DECOMPOSITION LESS COMPLEX Christos G. Cassandras CODES Lab. - Boston University
HIERARCHICAL DECOMPOSITION ??? ??? FLIGHT PLAN COMMANDS, RANDOM PLANNING PLANNING EVENTS AIRCRAFT FLIGHT DISCRETE-EVENT DISCRETE-EVENT DYNAMICS PROCESSES PROCESSES PHYSIC PHY ICAL AL PROCESSES PROCESSES Christos G. Cassandras CODES Lab. - Boston University
HIEARARCHICAL DECOMPOSITION CONTINUED MODEL TIME SCALE MODEL TIME SCALE ??? ??? Diff. Eq’s, Flows, LP Weeks - Months PLANNING PLANNING Automata, Petri nets, DISCRETE-EVENT DISCRETE-EVENT Queueing, Simulation Minutes - Weeks PROCESSES PROCESSES PHYSIC PHY ICAL AL Diff. Eq’s, Detailed Simulation m sec - Hours PROCESSES PROCESSES Christos G. Cassandras CODES Lab. - Boston University
HYBRID CONTROL SYSTEM What exactly What exactly does that mean ? does that mean ? DISCRETE-EVENT DISCRETE-EVENT PROCESSES PROCESSES CONTROL CONTROL CONTROL CONTROL PHYSICAL PHYSICAL PROCESSES PROCESSES Christos G. Cassandras CODES Lab. - Boston University
ABSTRACTION ABSTRACTION (AGGREGATION) (AGGREGATION) Christos G. Cassandras CODES Lab. - Boston University
LESS COMPLEX MORE COMPLEX TIME-DRIVEN SYSTEM ZOOM OUT HYBRID EVENT-DRIVEN SYSTEM SYSTEM ABSTRACTION ABSTRACTION LESS COMPLEX (AGGREGATION) GGREGATION) Christos G. Cassandras CODES Lab. - Boston University
LESS COMPLEX MORECOMPLEX TIME-DRIVEN SYSTEM HYBRID HYBRID SYSTEM SYSTEM EVENT-DRIVEN ABSTRACTION ABSTRACTION SYSTEM DECOMPOSITION DECOMPOSITION (AGGREGATION) GGREGATION) Christos G. Cassandras CODES Lab. - Boston University
WHAT IS THE RIGHT ABSTRACTION LEVEL ? TOO FAR… model not detailed enough TOO CLOSE… too much undesirable detail JUST RIGHT… good model CREDIT: W.B. Gong Christos G. Cassandras CODES Lab. - Boston University
EXAMPLES EXAMPLES Christos G. Cassandras CODES Lab. - Boston University
HYBRID SYSTEM EXAMPLES 1. Autonomous Switching, e.g., Hysteresis < ∆ > − ∆ x x ≥ ∆ x = + = − + x x u & x x u & ≤ − ∆ x CODES Lab. - Boston University Christos G. Cassandras
HYBRID SYSTEM EXAMPLES CONTINUED 2. External Switching, e.g., Zeno’s bouncing ball = = x v , v 0 & & x x = = − y v , v mg & & y y Switching Events CODES Lab. - Boston University Christos G. Cassandras
HYBRID SYSTEM EXAMPLES CONTINUED 3. Controlled Switching, e.g., Interconnected tanks u 1 ( t ) HIGH LOW u 2 ( t ) u 3 ( t ) HIGH HIGH LOW LOW CODES Lab. - Boston University Christos G. Cassandras
HYBRID SYSTEM EXAMPLES CONTINUED 4. Other cases of controlled switching: - Diving: control depths for decompression TRADEOFF: Safety vs. Time - Vehicle transmission: control gear switching TRADEOFF: Efficiency vs. Time - Low-power electronics: power control TRADEOFF: Power conservation vs. Time - Manufacturing: process control + operational control TRADEOFF: Product quality vs. Time CODES Lab. - Boston University Christos G. Cassandras
HYBRID SYSTEMS IN MANUFACTURING Key questions facing manufacturing system integrators: • How to integrate ‘process control’ with ‘operations control’ ? • How to improve product QUALITY within reasonable TIME ? PROCESS CONTROL OPERATIONS CONTROL • Physicists • Industrial Engineers, OR • Material Scientists • Schedulers • Chemical Engineers • Inventory Control • ... • ... Christos G. Cassandras CODES Lab. - Boston University
HYBRID SYSTEMS IN MANUFACTURING CONTINUED Throughout a manuf. process, each part is characterized by • A PHYSICAL state (e.g., size, temperature, strain) • A TEMPORAL state (e.g., total time in system, total time to due-date) NEW Time-driven PHYSICAL Dynamics PHYSICAL STATE STATE OPERATION OPERATION NEW TEMPORAL STATE TEMPORAL Event-driven STATE Dynamics Christos G. Cassandras CODES Lab. - Boston University
HYBRID SYSTEMS IN MANUFACTURING CONTINUED { } EVENT-DRIVEN = + x max x , a s ( u ) COMPONENT − i i 1 i i i Part Part Arrivals Departures a i , z i ( a i ) x i , z i ( x i ) ( ) TIME-DRIVEN = z ( t ) g z , u , t & u i COMPONENT i i i Christos G. Cassandras CODES Lab. - Boston University
EXAMPLE …and m to this state ust be processed (e.g., desired temperature ) STATE STATE Every part starts at this state z i ( u i ) s i ( u i ) PROCESS TIME PROCESS TIME Christos G. Cassandras CODES Lab. - Boston University
HYBRID SYSTEMS IN COOPERATIVE CONTROL TARGET EVENT: threat sensed THREATS TIME-DRIVEN DYNAMICS BASE EVENT: info. communicated by team member Christos G. Cassandras CODES Lab. - Boston University
HYBRID SYSTEMS IN COOP. CONTROL CONTINUED V 2 V 3 V 4 V 1 V 5 Christos G. Cassandras CODES Lab. - Boston University
HYBRID SYSTEMS IN COOP. CONTROL CONTINUED Current Control Horizon V 2 V 3 V 4 V 1 V 6 Optimal heading Over Event-Driven Receding Horizon V 5 Christos G. Cassandras CODES Lab. - Boston University
ABSTRACTION OF A DISCRETE-EVENT SYSTEM DISCRETE-EVENT SYSTEM Christos G. Cassandras CODES Lab. - Boston University
ABSTRACTION OF A DISCRETE-EVENT SYSTEM DISCRETE-EVENT SYSTEM TIME-DRIVEN EVENTS FLOW RATE DYNAMICS HYBRID SYSTEM Christos G. Cassandras CODES Lab. - Boston University
http://vita.bu.edu/cgc/hybrid Christos G. Cassandras CODES Lab. - Boston University
DESIGN, ANALYSIS, SYNTHESIS ISSUES TIME-DRIVEN EVENT-DRIVEN WORLD WORLD Automata with state transitions Differential equations dependent on diff. equations: with jumps/switches: Supervisory Control, Reachability Stability, Robustness Optimal Control, etc. Perturbation Analysis, etc. DECIDABILITY, VERIFICATION, QUANTIZATION, SIMULATION, … [ Proc. of IEEE Special Issue (Antsaklis, Ed.), 2000 ] [ Proc. of IEEE Special Issue (Antsaklis, Ed.), 2000 ] Christos G. Cassandras CODES Lab. - Boston University
Recommend
More recommend
