On the Computation of Robust Control Invariant Sets for Piecewise Affine Systems

Álamo, T.; Fiacchini, Mirko; Cepeda, A.; Limón, Daniel; Bravo, José Manuel; Camacho, Eduardo F.

doi:10.1007/978-3-540-72699-9_10

Cited by 9 publications

(10 citation statements)

References 12 publications

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“…Literature exists for computing polyhedral invariant sets for discrete-time linear systems [6,7]. Computing robust control invariant sets for piecewise affine systems has been addressed by [1]. The authors in [4] use Newton's method and the secant method to find zeros for set-valued maps, and use this technique in [3] to find invariant sets for dynamical systems.…”

Section: Figure 1 Figure Showing Unit Circles For Different Normsmentioning

confidence: 99%

“…For use in Algorithm 1, the set F(•) contains such vectors (•) evaluated at discrete values that an unknown disturbance function (•) can take. However, in real-ity, such disturbances would be parametrized by time as per (1). So consider (p ij ) = f(p ij ) + (t 1 ), and (y) = f(y) + (t 2 ), where t 1 , t 2 are some time instants, and points p ij , y ∈ seg(p (i−1)k ; p i,j ).…”

Section: Mathematical Justificationmentioning

confidence: 99%

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An algorithm for computing robust forward invariant sets of two dimensional nonlinear systems

Mukhopadhyay

Zhang

2020

Asian Journal of Control

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Robustness of nonlinear systems can be analyzed by computing robust forward invariant sets (RFISs). Knowledge of the smallest RFIS of a system, can help analyze system performance under perturbations. A novel algorithm is developed to compute an approximation of the smallest RFIS for two-dimensional nonlinear systems subjected to a bounded additive disturbance. The problem of computing an RFIS is formulated as a path planning problem, and the algorithm developed plans a path which iteratively converges to the boundary of an RFIS. Rigorous mathematical analysis shows that the proposed algorithm terminates in a finite number of iterations, and that the output of the proposed algorithm is an RFIS.Simulations are presented to illustrate the proposed algorithm, and to support the mathematical results. This work may aid future development, for use with higher dimensional systems.

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Section: Figure 1 Figure Showing Unit Circles For Different Normsmentioning

confidence: 99%

Section: Mathematical Justificationmentioning

confidence: 99%

An algorithm for computing robust forward invariant sets of two dimensional nonlinear systems

Mukhopadhyay

Zhang

2020

Asian Journal of Control

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“…Since this method is finitely determined thanks to the contractiveness of the Lyapunov function, the terminal region is a polygon (Rakovic, 2005). A single polyhedral invariant set can be calculated by means of the method proposed in Alamo et al (2008). This leads to a simpler region at expense of conservativeness.…”

Section: Stabilizing Design Of Mpcmentioning

confidence: 99%

Model predictive control techniques for hybrid systems

Camacho

Ramı́rez

Limón

et al. 2010

Annual Reviews in Control

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136

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This paper describes the main issues encountered when applying model predictive control to hybrid processes. Hybrid model predictive control (HMPC) is a research field non fully developed with many open challenges. The paper describes some of the techniques proposed by the research community to overcome the main problems encountered. Issues related to the stability and the solution of the optimization problem are also discussed. The paper ends by describing the results of a benchmark exercise in which several HMPC schemes were applied to a solar air conditioning plant.

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“…We propose an alternative approach that relies on the abstraction of the nonlinear system to a PieceWise Affine (PWA) model with additive disturbance so as to exploit an efficient procedure for robust invariant set computation for PWA systems, [6]. If the abstraction is conformant (i.e., it can generate all possible trajectories of the original system), then, an inner approximation of the invariant set for the nonlinear system is obtained.…”

Section: Introductionmentioning

confidence: 99%

An abstraction and refinement computational approach to safety verification of discrete time nonlinear systems

Smeraldo

Desimini

Prandini

2022

2022 European Control Conference (ECC)

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This paper addresses safety verification of nonlinear systems through invariant set computation. More precisely, our goal is verifying if the state of a given discrete time nonlinear system will keep evolving within a safe region, starting from a given set of initial conditions. To this purpose, we introduce a conformant PieceWise Affine (PWA) abstraction of the nonlinear system, which is instrumental to computing a conservative approximation of its maximal invariant set within the safe region. If the obtained set covers the set of initial conditions, safety is proven. Otherwise, subsequent refinements of the PWA abstraction are performed, either on the whole safe region or on some appropriate subset identified through a guided refinement approach and containing the set of initial conditions. Some numerical examples demonstrate the effectiveness of the approach.

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On the Computation of Robust Control Invariant Sets for Piecewise Affine Systems

Cited by 9 publications

References 12 publications

An algorithm for computing robust forward invariant sets of two dimensional nonlinear systems

An algorithm for computing robust forward invariant sets of two dimensional nonlinear systems

Model predictive control techniques for hybrid systems

An abstraction and refinement computational approach to safety verification of discrete time nonlinear systems

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