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Theses

Verification and Synthesis of Hybrid Systems

Abstract : This thesis proposes a practical framework for the verification and synthesis of hybrid systems, that is, systems combining continuous and discrete dynamics. The lack of methods for computing reachable sets of continuous dynamics has been the main obstacle towards an algorithmic verification methodology for hybrid systems. We develop two effective approximate reachability techniques for continuous systems based on an efficient representation of sets and a combination of techniques from simulation, computational geometry, optimization, and optimal control. One is specialized for linear systems and extended to systems with uncertain input, and the other can be applied for non-linear systems. Using these reachability techniques we develop a safety verification algorithm which can work for a broad class of hybrid systems with arbitrary continuous dynamics and rather general switching behavior. We next study the problem of synthesizing switching controllers for hybrid systems with respect to a safety property. We present an effective synthesis algorithm based on the calculation of the maximal invariant set and the approximate reachability techniques. Finally, we describe the experimental tool "d/dt" which provides automatic safety verification and controller synthesis for hybrid systems with linear differential inclusions. Besides numerous academic examples, we have successfully applied the tool to verify some practical systems.
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Submitted on : Tuesday, August 24, 2004 - 3:58:15 PM
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  • HAL Id : tel-00006738, version 1

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Thi Xuan Thao Dang. Verification and Synthesis of Hybrid Systems. Other [cs.OH]. Institut National Polytechnique de Grenoble - INPG, 2000. English. ⟨tel-00006738⟩

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