The reachability problem for uncertain hybrid systems revisited: a viability theory perspective

Authors:
Yan Gao;John Lygeros;Marc Quincapoix
Affiliations:
School of Management, University of Shanghai for Science and Technology, Shanghai, China;Department of Electrical Engineering, University of Patras, Rio, Patras, Greece;Laboratoire de Mathematiques, Université de Bretagne Occidentale, Brest, France
Venue:
HSCC'06 Proceedings of the 9th international conference on Hybrid Systems: computation and control
Year:
2006

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Abstract

We revisit the problem of designing controllers to meet safety specifications for hybrid systems, whose evolution is affected by both control and disturbance inputs. The problem is formulated as a dynamic game and an appropriate notion of hybrid strategy for the control inputs is developed. The design of hybrid strategies to meet safety specifications is based on an iteration of alternating discrete and continuous safety calculations. We show that, under certain assumptions, the iteration converges to a fixed point, which turns out to be the maximal set of states for which the safety specifications can be met. The continuous part of the calculation relies on the computation of the set of winning states for one player in a two player, two target, pursuit evasion differential game. We develop a characterization of these winning states using methods from non-smooth analysis and viability theory.