Improved robust gain-scheduling static output-feedback control for discrete-time LPV systems

Peixoto, Márcia L. C.; Coutinho, Pedro Henrique Silva; Palhares, Reinaldo M.

doi:10.1016/j.ejcon.2020.12.006

Cited by 17 publications

(14 citation statements)

References 16 publications

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“…where d = 1 V ⊗ d, d ∈ R n×n , has a unique solution. Therefore, we take a large fixed μ > 0 and solve (20) for (a, b, c, d, e, L k , K k ) to obtain…”

Section: Lemma 2 ([41]mentioning

confidence: 99%

See 1 more Smart Citation

Robust Recursive Regulator for Systems Subject to Polytopic Uncertainties

2021

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We present a robust recursive framework for the regulation of discrete-time linear systems subject to polytopic uncertainties. Based on regularized least-squares with a penalty parameter, we formulate a convex optimization problem and weight the polytope vertices altogether. In this sense, the main contribution of this paper consists of a robust recursive framework for the computation of stabilizing feedback gains. The solution does not require numerical optimization packages and relies ultimately on a single penalty parameter which is easily tuned. Moreover, the gains are obtained recursively through algebraic expressions, as opposed to related works which employ linear matrix inequalities. Under observability and controllability conditions, we demonstrate convergence and stability of the closed-loop system in terms of an algebraic Riccati equation. We provide numerical and real-world examples to validate the proposed approach and for comparison with a robust H ∞ controller.

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“…where d = 1 V ⊗ d, d ∈ R n×n , has a unique solution. Therefore, we take a large fixed μ > 0 and solve (20) for (a, b, c, d, e, L k , K k ) to obtain…”

Section: Lemma 2 ([41]mentioning

confidence: 99%

“…Different methods contributed with significant advances in robust control theory for the treatment of structured uncertainties varying inside convex hulls. In this regard, recently published results include H 2 and H ∞ synthesis [14], [15], [16]; model predictive control [17], [18], [19]; and gain-scheduled control [20], [21], [22].…”

Section: Introductionmentioning

confidence: 99%

Robust Recursive Regulator for Systems Subject to Polytopic Uncertainties

2021

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show abstract

“…More recently, a linear SOF controller for discrete‐time LPV systems based on augmenting the matrices related to the control input and control gain has been proposed in Reference 8, and SOF

ℋ_{\infty}

gain‐scheduling control design conditions have been derived for discrete‐time LPV systems 9 . In particular, the conditions introduced in Reference 9 are not based on iterative methods and do not require constraints over the system's structure nor the gain‐scheduled control law.…”

Section: Introductionmentioning

confidence: 99%

“…Several studies have been carried out attempting to provide numerically tractable solutions for SOF control design, 3 such as two‐step and iterative methods, 4‐6 and the use of slack variables with a lower‐triangular structure 7 . More recently, a linear SOF controller for discrete‐time LPV systems based on augmenting the matrices related to the control input and control gain has been proposed in Reference 8, and SOF

ℋ_{\infty}

Section: Introductionmentioning

confidence: 99%

Static output‐feedback stabilization of discrete‐time linear parameter‐varying systems under actuator saturation

Peixoto

Coutinho

Bessa

et al. 2022

Intl J Robust & Nonlinear

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This paper introduces a novel local synthesis condition for gain‐scheduling static output‐feedback control of discrete‐time linear parameter‐varying (LPV) systems under actuator saturation and state constraints. The proposed condition is formulated as a set of parameter‐dependent linear matrix inequalities that are incorporated into a convex optimization procedure to provide an enlarged estimate of the region of attraction of the closed‐loop equilibrium. In contrast with related works, the proposed approach allows handling a wider class of LPV systems since no rank condition is required to employ the so‐called equality constraints.

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“…Recently, [17] proposes a novel method to compute the L 2 -gain for rational LPV systems, however no control law is designed. Many solutions to the gain-scheduled static output feedback design for discrete-time LPV systems have also been recently developed [18]- [21]. However, none of them consider rational dependence on the parameter Dissipativity theory was introduced some decades ago and has been extensively used in stability analysis and control systems design [22], [23].…”

Section: Introductionmentioning

confidence: 99%

Dissipativity-based $\mathcal{L}_2$ gain-scheduled static output feedback design for rational LPV systems

Viana¹,

Madeira²,

Lima³

2021

Preprint

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This paper proposes the design of gainscheduled static output feedback controllers for the stabilization of continuous-time linear parameter-varying systems with L 2 -gain performance. The system is transformed into the form of a differential-algebraic representation which allows dealing with the broad class of systems whose matrices can present rational or polynomial dependence on the parameter. The proposed approach uses the definition of strict QSR-dissipativity, Finsler's Lemma, and the notion of linear annihilators to formulate conditions expressed in the form of polytopic linear matrix inequalities for determining the gain-scheduled static output feedback control for system stabilization. One of the main advantages of the strategy is that it provides a simple design solution in a non-interactive manner. Furthermore, no restriction on the plant output matrix is imposed. Numerical examples highlight the effectiveness of the proposed method.

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Improved robust gain-scheduling static output-feedback control for discrete-time LPV systems

Cited by 17 publications

References 16 publications

Robust Recursive Regulator for Systems Subject to Polytopic Uncertainties

Robust Recursive Regulator for Systems Subject to Polytopic Uncertainties

Static output‐feedback stabilization of discrete‐time linear parameter‐varying systems under actuator saturation

Dissipativity-based $\mathcal{L}_2$ gain-scheduled static output feedback design for rational LPV systems

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