Control Synthesis of Nonlinear Sampled Switched Systems using Euler's Method

Coënt, Adrien Le; Vuyst, Florian De; Chamoin, Ludovic; Fribourg, Laurent

doi:10.4204/eptcs.247.2

Cited by 15 publications

(43 citation statements)

References 21 publications

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“…These results mainly originate from collaboration with A. Le Coënt, F. De Vuyst, L. Chamoin, J. Alexandre dit Sandretto and A. Chapoutot (see [11,10]).…”

Section: Introductionmentioning

confidence: 86%

“…In order to avoid such a wrapping effect, we proposed an alternate method which, instead of using interval arithmetic [14] and higher order Taylor series, has simply recourse to the basic (forward) Euler method [11]. This is made possible through a new error analysis of the Euler method via the notion of "one-sided Lipschitz constant".…”

Section: Guaranteed Integrationmentioning

confidence: 99%

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Euler’s Method Applied to the Control of Switched Systems

Fribourg

2017

Lecture Notes in Computer Science

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Hybrid systems are a powerful formalism for modeling and reasoning about cyber-physical systems. They mix the continuous and discrete natures of the evolution of computerized systems. Switched systems are a special kind of hybrid systems, with restricted discrete behaviours: those systems only have finitely many different modes of (continuous) evolution, with isolated switches between modes. Such systems provide a good balance between expressiveness and controllability, and are thus in widespread use in large branches of industry such as power electronics and automotive control. The control law for a switched system defines the way of selecting the modes during the run of the system. Controllability is the problem of (automatically) synthezing a control law in order to satisfy a desired property, such as safety (maintaining the variables within a given zone) or stabilisation (confinement of the variables in a close neighborhood around an objective point). In order to compute the control of a switched system, we need to compute the solutions of the differential equations governing the modes. Euler's method is the most basic technique for approximating such solutions. We present here an estimation of the Euler's method local error, using the notion of "one-sided Lispchitz constant" for modes. This yields a general control synthesis approach which can encompass several features such as bounded disturbance and compositionality.

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“…These results mainly originate from collaboration with A. Le Coënt, F. De Vuyst, L. Chamoin, J. Alexandre dit Sandretto and A. Chapoutot (see [11,10]).…”

Section: Introductionmentioning

confidence: 86%

Section: Guaranteed Integrationmentioning

confidence: 99%

Euler’s Method Applied to the Control of Switched Systems

Fribourg

2017

Lecture Notes in Computer Science

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“…The main difference with previous work [27,37,19,46,47] is that our method makes use of explicit Euler's algorithm for ODE integration (cf. [32,33]) instead of sophisticated algorithms such as Lohner's algorithm [27] or interval Taylor series methods [44]. This leads us to a simple implementation of just a few hundred lines of Octave (see [31]).…”

Section: Guaranteed Optimal Controlmentioning

confidence: 99%

“…Given a point y P S of ε-representative z P X , and a pattern π ε k returned by P ROC ε k pzq, we are now going to show that the distance }Ỹ π ε k kτ,z´y f } converges to v k pyq as ε Ñ 0. We first consider the ODE: dy dt " f u pyq, and give an upper bound to the error between the exact solution of the ODE and its Euler approximation (see [33]). if λ u ă 0 : δ u t,µ "ˆµ 2 e λut`C 2 u…”

Section: Error Upper Boundmentioning

confidence: 99%

Guaranteed Optimal Reachability Control of Reaction-Diffusion Equations Using One-Sided Lipschitz Constants and Model Reduction

Coent

Fribourg

2020

Cyber Physical Systems. Model-Based Design

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We show that, for any spatially discretized system of reactiondiffusion, the approximate solution given by the explicit Euler timediscretization scheme converges to the exact time-continuous solution, provided that diffusion coefficient be sufficiently large. By "sufficiently large", we mean that the diffusion coefficient value makes the one-sided Lipschitz constant of the reaction-diffusion system negative. We apply this result to solve a finite horizon control problem for a 1D reactiondiffusion example. We also explain how to perform model reduction in order to improve the efficiency of the method.

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“…However, there was no focus on safety in this approach. In our work, the safety strategy synthesis relies on a discretization of the continuous variables, leading to a decidable problem that can be handled by Uppaal Tiga, but we furthermore provide safety guarantees for the original system with the use of a Timed Game abstraction based on a guaranteed Euler scheme [37].…”

Section: Our Contributionmentioning

confidence: 99%

SOS: Safe, Optimal and Small Strategies for Hybrid Markov Decision Processes

Ashok

Křetínský

Larsen

et al. 2019

Quantitative Evaluation of Systems

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For hybrid Markov decision processes, Uppaal Stratego can compute strategies that are safe for a given safety property and (in the limit) optimal for a given cost function. Unfortunately, these strategies cannot be exported easily since they are computed as a very long list. In this paper, we demonstrate methods to learn compact representations of the strategies in the form of decision trees. These decision trees are much smaller, more understandable, and can easily be exported as code that can be loaded into embedded systems. Despite the size compression and actual differences to the original strategy, we provide guarantees on both safety and optimality of the decision-tree strategy. On the top, we show how to obtain yet smaller representations, which are still guaranteed safe, but achieve a desired trade-off between size and optimality.

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Control Synthesis of Nonlinear Sampled Switched Systems using Euler's Method

Cited by 15 publications

References 21 publications

Euler’s Method Applied to the Control of Switched Systems

Euler’s Method Applied to the Control of Switched Systems

Guaranteed Optimal Reachability Control of Reaction-Diffusion Equations Using One-Sided Lipschitz Constants and Model Reduction

SOS: Safe, Optimal and Small Strategies for Hybrid Markov Decision Processes

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