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
Incremental Abstraction Computation for Symbolic Controller Synthesis in a Changing Environment
TL;DR: This paper presents an incremental algorithm to locally adapt abstractions to changes in the disturbance model, and empirically shows the benefit of dynamic abstraction adaptation on two large examples: a 5-dimensional vehicle model and a 12-dimensional quadrotor model.
Book ChapterDOI
Synthesis of Symbolic Controllers: A Parallelized and Sparsity-Aware Approach
TL;DR: This paper presents a new approach to “symbolic control”, where complex physical systems are approximated by finite-state abstractions, and provably-correct digital controllers are algorithmically synthesized for concrete systems, satisfying some complex high-level requirements.
Journal ArticleDOI
Robustly Complete Synthesis of Memoryless Controllers for Nonlinear Systems With Reach-and-Stay Specifications
TL;DR: In this paper, the authors propose a finitely terminating algorithm to solve reach-and-stay control problems for nonlinear systems, which is guaranteed to return a control strategy if the specification is robustly realizable.
Proceedings ArticleDOI
Hyper-Rectangular Over-Approximations of Reachable Sets for Linear Uncertain Systems
Mohamed Serry,Gunther Reissig +1 more
TL;DR: A novel method, using the frameworks of differential inequalities and essentially nonnegative matrices, to construct hyper-rectangular over-approximations of reachable sets for a general class of linear uncertain systems whose nominal parameters and bounds on uncertainties are time-varying.
Proceedings ArticleDOI
Symbolic synthesis with average performance guarantees
TL;DR: A general quantitative controller synthesis framework to synthesize controllers that not only enforce a desired input-output behavior on the closed-loop, but additionally minimize a certain average cost function, which is used to assess the closed loop behavior.
References
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Differential Equations with Discontinuous Righthand Sides
TL;DR: The kind and level of sophistication of mathematics applied in various sciences has changed drastically in recent years: measure theory is used (non-trivially) in regional and theoretical economics, algebraic geometry interacts with physics, and such new emerging subdisciplines as "experimental mathematics", "CFD", "completely integrable systems", "chaos, synergetics and large-scale order", which are almost impossible to fit into the existing classification schemes.
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Principles of Model Checking
TL;DR: Principles of Model Checking offers a comprehensive introduction to model checking that is not only a text suitable for classroom use but also a valuable reference for researchers and practitioners in the field.
Book
Feedback Systems: An Introduction for Scientists and Engineers
TL;DR: Feedback Systems develops transfer functions through the exponential response of a system, and is accessible across a range of disciplines that utilize feedback in physical, biological, information, and economic systems.