Temporal Logic Control of Discrete-Time Piecewise Affine Systems

Yordanov, Boyan; Tůmová, Jana; Černá, Ivana; Barnat, Jǐŕı; Belta, Călin

doi:10.1109/tac.2011.2178328

Cited by 107 publications

(64 citation statements)

References 28 publications

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“…In [2], [3] a sequence of abstractions is proposed which approximates the PWA system in the sense of simulation relations. While being provably correct, the results in [3], [4] do not quantify the conservativeness of the approach in the formal verification and control design of PWA systems. Quantifying conservativeness is important to evaluate how far the solutions based on symbolic models are from the corresponding solutions in the pure hybrid domain.…”

Section: Introductionmentioning

confidence: 94%

“…An example of splitting policy is reported in Section VII. The practical computation of operators Bisim and Split is based on basic manipulations of polytopes; the interested reader can refer to [4] where similar computations are described in detail. We now have all the ingredients to introduce a sequence of abstractions approximating the PWA system .…”

Section: Sequences Of Symbolic Modelsmentioning

confidence: 99%

“…A symbolic model of a continuous or hybrid system is a finite state automaton in which a symbolic state corresponds to an aggregate of continuous states and a symbolic control label to an aggregate of continuous control inputs. Symbolic models have been employed in [2]- [4] as an effective tool to address stabilizability problems, formal verification and control design of discrete-time PWA systems. The work in [2] explores the use of symbolic models for stabilizability problems while the work in [3] for solving formal verification problems; these papers consider PWA systems with no control inputs.…”

Section: Introductionmentioning

confidence: 99%

“…The work in [2] explores the use of symbolic models for stabilizability problems while the work in [3] for solving formal verification problems; these papers consider PWA systems with no control inputs. The work in [4] instead, considers PWA systems with control inputs and uses symbolic models for solving control problems with temporal logic-types specifications. In [2], [3] a sequence of abstractions is proposed which approximates the PWA system in the sense of simulation relations.…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Symbolic Models and Control of Discrete-Time Piecewise Affine Systems: An Approximate Simulation Approach

Pola

Benedetto

2014

IEEE Trans. Automat. Contr.

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Symbolic models have been recently used as a sound mathematical formalism for the formal verification and control design of purely continuous and hybrid systems. In this note we propose a sequence of symbolic models that approximates a discrete-time Piecewise Affine (PWA) system in the sense of approximate simulation and converges to the PWA system in the so-called simulation metric. Symbolic control design is then addressed with specifications expressed in terms of non-deterministic finite automata. A sequence of symbolic control strategies is derived which converges, in the sense of simulation metric, to the maximal controller solving the given specification on the PWA system.Index Terms-Approximate simulation, piecewise affine systems, symbolic control design, symbolic models.

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Section: Introductionmentioning

confidence: 94%

Section: Sequences Of Symbolic Modelsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Symbolic Models and Control of Discrete-Time Piecewise Affine Systems: An Approximate Simulation Approach

Pola

Benedetto

2014

IEEE Trans. Automat. Contr.

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“…Given a finite abstraction of a dynamical system (see [1]- [7]) and an LTL specification, feasible control policies can be automatically created for non-deterministic systems [8]. Unfortunately, the complexity of synthesizing a control policy that ensures that a nondeterministic system satisfies an LTL formula is doublyexponential in the formula length [9].…”

Section: Introductionmentioning

confidence: 99%

Optimal control of non-deterministic systems for a computationally efficient fragment of temporal logic

Wolff

Topcu

Murray

2013

52nd IEEE Conference on Decision and Control

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We develop a framework for optimal control policy synthesis for non-deterministic transition systems subject to temporal logic specifications. We use a fragment of temporal logic to specify tasks such as safe navigation, response to the environment, persistence, and surveillance. By restricting specifications to this fragment, we avoid a potentially doublyexponential automaton construction. We compute feasible control policies for non-deterministic transition systems in time polynomial in the size of the system and specification. We also compute optimal control policies for average, minimax (bottleneck), and average cost-per-task-cycle cost functions. We highlight several interesting cases when optimal policies can be computed in time polynomial in the size of the system and specification. Additionally, we make connections between computing optimal control policies for an average cost-per-task-cycle cost function and the generalized traveling salesman problem. We give simulation results for motion planning problems.

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Duality-Based Nested Controller Synthesis from STL Specifications for Stochastic Linear Systems

Jha

Raj

Jha

et al. 2018

Lecture Notes in Computer Science

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Temporal Logic Control of Discrete-Time Piecewise Affine Systems

Cited by 107 publications

References 28 publications

Symbolic Models and Control of Discrete-Time Piecewise Affine Systems: An Approximate Simulation Approach

Symbolic Models and Control of Discrete-Time Piecewise Affine Systems: An Approximate Simulation Approach

Optimal control of non-deterministic systems for a computationally efficient fragment of temporal logic

Duality-Based Nested Controller Synthesis from STL Specifications for Stochastic Linear Systems

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