Symbolic models for nonlinear control systems without stability assumptions

2010/02/03 by Zamani, Majid, Pola, Giordano, Mazo, Manuel +1 · 4 citations
#93C57 #FOS: Mathematics #Optimization and Control (math.OC)

paper · doi:10.48550/arxiv.1002.0822

Abstract

Finite-state models of control systems were proposed by several researchers as a convenient mechanism to synthesize controllers enforcing complex specifications. Most techniques for the construction of such symbolic models have two main drawbacks: either they can only be applied to restrictive classes of systems, or they require the exact computation of reachable sets. In this paper, we propose a new abstraction technique that is applicable to any smooth control system as long as we are only interested in its behavior in a compact set. Moreover, the exact computation of reachable sets is not required. The effectiveness of the proposed results is illustrated by synthesizing a controller to steer a vehicle.

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• Scalable and Approximation-free Symbolic Control for Unknown Euler-Lagrange Systems
• Existence and Synthesis of Multi-Resolution Approximate Bisimulations for Continuous-State Dynamical Systems
• AP-observation Automata for Abstraction-based Verification of Continuous-time Systems (Extended Version)
• Symbolic Control: Unveiling Free Robustness Margins

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