Feedback Refinement Relations for the Synthesis of Symbolic Controllers
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This work builds on a general notion of system with set-valued dynamics and possibly non-deterministic quantizers to permit the synthesis of controllers that robustly, and provably, enforce the specification in the presence of various types of uncertainties and disturbances.Abstract:
We present an abstraction and refinement methodology for the automated controller synthesis to enforce general predefined specifications. The designed controllers require quantized (or symbolic) state information only and can be interfaced with the system via a static quantizer. Both features are particularly important with regard to any practical implementation of the designed controllers and, as we prove, are characterized by the existence of a feedback refinement relation between plant and abstraction. Feedback refinement relations are a novel concept introduced in this paper. Our work builds on a general notion of system with set-valued dynamics and possibly non-deterministic quantizers to permit the synthesis of controllers that robustly, and provably, enforce the specification in the presence of various types of uncertainties and disturbances. We identify a class of abstractions that is canonical in a well-defined sense, and provide a method to efficiently compute canonical abstractions. We demonstrate the practicality of our approach on two examples.read more
Citations
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Proceedings ArticleDOI
Abstraction-based solution of optimal stopping problems under uncertainty
Gunther Reissig,Matthias Rungger +1 more
TL;DR: This paper presents novel results on the solution of optimal control problems with the help of finite-state approximations (“symbolic models”) of infinite-state plants and proves that the computed bounds converge to the value function as the discretization errors approach zero.