Stabilization of constrained uncertain systems by an off-line approach using zonotopes

Hamdi, Walid; Bey, Wissal

doi:10.1109/aset.2017.7983659

Cited by 1 publication

(2 citation statements)

References 18 publications

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“…But, due to the fact that the optimization problem is truly settled at each sampling time, it needs high computational time in online implementation. On the other hand, such problems rise appreciably with the size of the polytopic uncertainty set [16].…”

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: Introductionmentioning

confidence: 99%

“…Schur's Lemma 1 (see [16]). Let R, S, T be given matrices with appropriate sizes and assume that Q > 0; then the LMI R S S T Q > 0 (respectively, ≥ 0) is feasible if and only if the nonlinear constraint R − SQ −1 ST > 0 (respectively, ≥ 0) is feasible.…”

Section: Introductionmentioning

confidence: 99%