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Global optimal control of quantized systems
Lars Grüne,Florian Müller +1 more
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The article was published on 2010-01-01 and is currently open access. It has received 5 citations till now.read more
Citations
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Journal ArticleDOI
ISS-Lyapunov Functions for Discontinuous Discrete-Time Systems
TL;DR: A stronger implication-form ISS- Lyapunov function is proposed and a complete characterization of ISS-Lyapunv functions for discrete-time systems with discontinuous dynamics is provided.
Journal ArticleDOI
Finite abstraction of mixed monotone systems with discrete and continuous inputs
Samuel Coogan,Murat Arcak +1 more
TL;DR: In this paper, the authors present an efficient computational procedure for finite abstraction of discrete-time mixed monotone systems by considering a rectangular partition of the state space, and apply their results to verify the dynamical behavior of a model for insect population dynamics and to synthesize a signaling strategy for a traffic network.
Strong implication-form ISS-Lyapunov functions for discontinuous discrete-time systems
TL;DR: In this article, a stronger implication-form version of the ISS-Lyapunov function for discontinuous systems is proposed, which re-establishes the equivalence between dissipation-form and input-to-state stability.
Journal ArticleDOI
Subdivision algorithm for optimal control
TL;DR: The main contribution of the paper is understanding how cost function improves with further subdivision of state space and smaller memory footprint of the final solution in comparison with set‐oriented approach.
Book ChapterDOI
From Bellman to Dijkstra: Set oriented construction of globally optimal controllers
Lars Grüne,Oliver Junge +1 more
TL;DR: An approach for discretizing Bellman's optimality principle based on piecewise constant functions is reviewed and a discrete feedback can be constructed which robustly stabilizes a given nonlinear control system.
References
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Journal ArticleDOI
Hybrid feedback stabilization of systems with quantized signals
TL;DR: This paper is concerned with global asymptotic stabilization of continuous-time systems subject to quantization and involves merging tools from Lyapunov stability, hybrid systems, and input-to-state stability.
Journal ArticleDOI
A set oriented approach to global optimal control
Oliver Junge,Hinke M. Osinga +1 more
TL;DR: An algorithm for computing the value function for "all source, single desti- nation" discrete-time nonlinear optimal control problems together with approximations of associated globally optimal control strategies based on a set oriented approach in combination with graph-theoretic techniques.
Journal ArticleDOI
Global Optimal Control of Perturbed Systems
Lars Grüne,Oliver Junge +1 more
TL;DR: The method is based on a set-oriented discretization of the state space in combination with a new algorithm for the computation of shortest paths in weighted directed hypergraphs and it is proved the convergence of the scheme as the discretized parameter goes to zero.
Proceedings ArticleDOI
An algorithm for event-based optimal feedback control
Lars Grüne,Florian Müller +1 more
TL;DR: An algorithm for an event based approach to the global optimal control of nonlinear systems with coarsely quantized state measurement with theoretical properties and a numerical example is presented.
Proceedings ArticleDOI
Approximately optimal nonlinear stabilization with preservation of the Lyapunov function property
Lars Grüne,Oliver Junge +1 more
TL;DR: By including the discretization errors into the optimal control formulation the authors are able to compute approximate optimal value functions which preserve the Lyapunov function property and corresponding optimally stabilizing feedback laws which are constant on each partition element.