Abstract
A design and verification methodology for hybrid dynamical systems, based on optimal control and game theory, is presented. The hybrid design is seen as a game between two players. One is the disturbances that enter the dynamics. The disturbances can encode the actions of other agents (in a multi-agent setting), the actions of high level controllers or the usual unmodeled environmental disturbances. The second player is the control, which is to be chosen by the designer. The two players compete over a cost function that encodes the properties that the closed loop hybrid system needs to satisfy (e.g. safety). The control “wins” the game if it can keep the system “safe” for any allowable disturbance. The solution to the game theory problem provides the designer with continuous controllers as well as sets of safe states where the control “wins” the game. The sets of safe sets can be used to construct an interface that guarantees the safe operation of the combined hybrid system.
The motivating example for our work is Automated Highway Systems. We show how to cast the lower level, multi-agent vehicle following problem in the game theoretic setting and give an algorithm that can produce a safe design.
Research supported by the Army Research Office under grant DAAH 04-95-1-0588 and the PATH program, Institute of Transportation Studies, University of California, Berkeley, under MOU-135 and MOU-238.
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Lygeros, J., Godbole, D.N., Sastry, S. (1997). Hybrid controller design for multi-agent systems. In: Stephen Morse, A. (eds) Control Using Logic-Based Switching. Lecture Notes in Control and Information Sciences, vol 222. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0036084
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DOI: https://doi.org/10.1007/BFb0036084
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