EE291E - UC BERKELEY EE291E: Hybrid Systems T. John Koo and S. Shankar Sastry Department of EECS University of California at Berkeley Spring 2002 koo/EE291E

EE291E - UC BERKELEY

EE291E: Hybrid Systems

T. John Koo and S. Shankar Sastry

Department of EECS

University of California at Berkeley

Spring 2002

http://robotics.eecs.berkeley.edu/~koo/EE291E/


Controller Synthesis

A Game Theoretic Approach– In Church[1], solutions to digital circuits are studied by posing

the controller synthesis problem as a discrete game between the system and its environment.

– A version of the von Neumann-Morgenstern discrete game[2] is used for deriving the solution by Buchi and Landweber[3] and Rabin[4].

– Games on automata are discussed in [5].– In [6] and [7], a survey of infinite discrete games on automata is

presented.– Controller synthesis on times automata was first developed in [8]

and [9].– An algorithm for controller synthesis on linear automata is

presented in [10].– The notion of control invariance for continuous systems is

described in [11].– The notion of control invariance for hybrid systems is discussed

in [12].


Notation

Discrete and Continuous Systems


Infinite Game on Finite Automata

System Definition



Wining Condition



State Space Partition







Check union or intersection






The Value Function



The Value Function










Dynamics Games on Nonlinear Systems









The Value Function



The Value Function



The Value Function





Computation – Optimal Control Theory1.

2.

3.








Reference

Synthesizing Controllers for Nonlinear Hybrid SystemsClaire J. Tomlin, John Lygeros, and Shankar SastryVolume 1386, LNCS series, Springer-Verlag, 1998.

Documents

EE291E - UC BERKELEY EE291E: Hybrid Systems T. John Koo and S. Shankar Sastry Department of EECS University of California at Berkeley Spring 2002 koo/EE291E