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Hybrid Systems Theory



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Hybrid Systems Theory presented by Tom Henzinger 1 Robust hybrid systems 2 Stochastic hybrid systems 3 Compositional hybrid systems 4 Computational hybrid systems Program Review May 10 2004 Berkeley CA NSF UC Berkeley Chess Vanderbilt University ISIS University of Memphis MSI Foundations of Hybrid and Embedded Software Systems A Formal Foundation for Embedded Systems needs to combine Computatio n Theories of composition hierarchy computability complexity B Physicality R Theories of robustness approximation probabilities discounting CHESS Program Review May 10 2004 2 Continuous Dynamical Systems State space Rn Dynamics initial condition differential equations Room temperature x 0 x0 x t K x t x x0 t Analytic complexity CHESS Program Review May 10 2004 3 Discrete Transition Systems State space Bm Dynamics initial condition transition relation Heater heat of on of on t Combinatorial complexity CHESS Program Review May 10 2004 4 Hybrid Automata State space Bm Rn Dynamics initial condition transition relation differential equations Thermosta t x0 of x K x x L x l on of on x u x K Hx U x t CHESS Program Review May 10 2004 5 The Robustness Issue Hybrid Automaton Property slightly perturbed automaton CHESS Program Review May 10 2004 6 The Robustness Issue Hybrid Automaton Safe x 3 CHESS Program Review May 10 2004 7 The Robustness Issue Hybrid Automaton Unsafe x 3 CHESS Program Review May 10 2004 8 Towards Robust Hybrid Automata value Model Property States B value Model Property States R CHESS Program Review May 10 2004 9 Towards Robust Hybrid Automata value Model Property States B value m T X T pre X discountedValue Model Property States R discountedValue m T X max T pre X discount factor 0 1 CHESS Program Review May 10 2004 10 Reachability coSafety a F pre T T pre 1 max 0 b T 1 c T 2 c undiscounted property c discounted property CHESS Program Review May 10 2004 11 Main Result so far only for discrete systems Robustness Theorem de Alfaro Henzinger Majumdar If



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