A novel approach to the computation of the maximal controlled invariant set for constrained linear systems

Αθανασόπουλος, Νικόλαος; Bitsoris, George

doi:10.23919/ecc.2009.7074885

Cited by 7 publications

(10 citation statements)

References 23 publications

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“…e ellipsoidal invariant sets approach referred to in Section 2.2.1 is a semidefinite programming method. Based on the work of Athanasopoulos and Bitsoris [21], a second linear programming approach is used to enlarge polyhedral sets. Step 2.…”

Section: E Proposed Methodology As Illustrated Inmentioning

confidence: 99%

“…In fact, the obtainable difficulty is associated with the determination of controlled invariant sets [19,20]. e computation of the maximal controlled invariant set process introduced in [21] and the corresponding state feedback control laws for linear systems subject to polyhedral input and state constraints have been studied in [22,23]. Kouvaritakis et al [24] developed an advanced method to enlarge the terminal invariant set using a linear programming approach.…”

Section: Introductionmentioning

confidence: 99%

“…e contributions of this paper are twofold: firstly, to highlight the robust control of states, an RMPC algorithm [15,18] was applied. is approach is based on a computation method of maximal controlled invariant sets [21]. Secondly, the combination of MPC method and maximized invariant sets procedure is proposed in order to precisely advance the performance of the employed system.…”

Section: Introductionmentioning

confidence: 99%

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Constrained Uncertain System Stabilization with Enlargement of Invariant Sets

2020

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An enhanced method able to perform accurate stability of constrained uncertain systems is presented. The main objective of this method is to compute a sequence of feedback control laws which stabilizes the closed-loop system. The proposed approach is based on robust model predictive control (RMPC) and enhanced maximized sets algorithm (EMSA), which are applied to improve the performance of the closed-loop system and achieve less conservative results. In fact, the proposed approach is split into two parts. The first is a method of enhanced maximized ellipsoidal invariant sets (EMES) based on a semidefinite programming problem. The second is an enhanced maximized polyhedral set (EMPS) which consists of appending new vertices to their convex hull to minimize the distance between each new vertex and the polyhedral set vertices to ensure state constraints. Simulation results on two examples, an uncertain nonisothermal CSTR and an angular positioning system, demonstrate the effectiveness of the proposed methodology when compared to other works related to a similar subject. According to the performance evaluation, we recorded higher feedback gain provided by smallest maximized invariant sets compared to recently studied methods, which shows the best region of stability. Therefore, the proposed algorithm can achieve less conservative results.

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Section: E Proposed Methodology As Illustrated Inmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Constrained Uncertain System Stabilization with Enlargement of Invariant Sets

2020

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“…It is clear that the so obtained admissible domain D = C (g T 1 ) ∩ P(G * 2 , re p * ) is not unique because an asymptotically stable linear system possesses many positively invariant polyhedral sets P(G * 2 , e p * ). It is however possible to enlarge an initially determined admissible domain of attraction not by scaling but using techniques of determination of maximal positively invariant sets [22], [27] or by applying the recently established approach of enlargement of positively invariant sets with specified complexity [2], [3].…”

Section: Polyhedral Domains Of Attractionmentioning

confidence: 99%

The Linear Constrained Control Problem for Discrete-Time Systems: Regulation on the Boundaries

Bitsoris

Olaru

Vassilaki

2019

Springer Proceedings in Mathematics &Amp; Statistics

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The chapter deals with the problem of regulation of linear systems around an equilibrium lying on the boundary of a polyhedral domain where linear constraints on the control and/or the state vectors are satisfied. In the first part of the chapter, the fundamental limitations for constrained control with active constraints at equilibrium are exposed. Next, based on the invariance properties of polyhedral and semi-ellipsoidal sets, design methods for guaranteeing convergence to the equilibrium while respecting linear control constraints are proposed. To this end, Lyapunov-like polyhedral functions, LMI methods and eigenstructure assignment techniques are applied.

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“…Em geral, o conjunto de restrições nãoé invariante. Sendo assim, vários pesquisadores propuseram métodos numéricos que permitem calcular um conjunto invariante con-trolado a partir do conjunto de restrições, garantindo a satisfação das mesmas como por exemplo em (Scibilia et al, 2009), (Athanasopoulos and Bitsoris, 2009), (Athanasopoulos and Bitsoris, 2010), (Sheer and Gutman, 2016) e (Li and Liu, 2016).…”

Section: Introductionunclassified

Cálculo de Conjuntos Invariantes Controlados Robustos com Complexidade Fixa usando Otimização Bilinear

Oliveira

Júnior

Dórea

2020

Anais Do Congresso Brasileiro De Automática 2020

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Neste trabalho uma metodologia numérica para o cálculo de poliedros invariantes controlados robustos de complexidade fixa, baseado em otimização bilinear, é proposta para sistemas lineares de tempo discreto, sujeitos a restrições nos estados e nas entradas de controle e a perturbações de amplitude limitada. Um conjunto é invariante controlado robusto se qualquer trajetória do estado iniciada dentro do conjunto pode ser mantido dentro dele por meio de uma ação de controle adequada, apesar das perturbações. Métodos convencionais de cálculo destes poliedros podem resultar em conjuntos de alta complexidade, definidos por um grande número de vértices. Por meio de exemplos numéricos, verifica-se que a metodologia proposta é capaz de calcular poliedros de volume maior do que os de métodos recentes que buscam também conjuntos com complexidade reduzida.

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A novel approach to the computation of the maximal controlled invariant set for constrained linear systems

Cited by 7 publications

References 23 publications

Constrained Uncertain System Stabilization with Enlargement of Invariant Sets

Constrained Uncertain System Stabilization with Enlargement of Invariant Sets

The Linear Constrained Control Problem for Discrete-Time Systems: Regulation on the Boundaries

Cálculo de Conjuntos Invariantes Controlados Robustos com Complexidade Fixa usando Otimização Bilinear

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