Static output feedback controller design for uncertain polynomial systems: an iterative sums of squares approach

Nguang, Sing Kiong; Saat, Shakir; Krug, Matthias

doi:10.1049/iet-cta.2010.0468

Cited by 28 publications

(14 citation statements)

References 14 publications

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“…The condition in [19] is less efficient than (19), in view of the fact that the following result is used in [19]: (12) is relaxed to…”

Section: Remark 2: a Nondecreasing Sequence Of Solutionsρ I To Optimimentioning

confidence: 99%

“…The work can be seen as an extension of [5] to polynomial nonlinear systems. It has to be underlined that an extension in this direction was done in [19], with the main differences that we adopt a more efficient sum-of-square decomposition, and furthermore we investigate local stabilization problem, which is relevant for nonlinear systems, where global stabilization cannot always be achieved.…”

Section: Introductionmentioning

confidence: 99%

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An iterative Sum-of-Squares optimization for static output feedback of polynomial systems

Baldi

2016

2016 IEEE 55th Conference on Decision and Control (CDC)

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Abstract-This work proposes an iterative procedure for static output feedback of polynomial systems based on Sum-ofSquares optimization. Necessary and sufficient conditions for static output feedback stabilization of polynomial systems are formulated, both for the global and for the local stabilization case. Since the proposed conditions are bilinear with respect to the decision variables, an iterative procedure is proposed for the solution of the stabilization problem. Every iteration is shown to improve the performance with respect to the previous one, even if convergence to a local minimum might occur. Since polynomial Lyapunov functions and control laws are considered, a Sum-of-Squares optimization approach is adopted. A numerical example illustrates the results.

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“…The condition in [19] is less efficient than (19), in view of the fact that the following result is used in [19]: (12) is relaxed to…”

Section: Remark 2: a Nondecreasing Sequence Of Solutionsρ I To Optimimentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

An iterative Sum-of-Squares optimization for static output feedback of polynomial systems

Baldi

2016

2016 IEEE 55th Conference on Decision and Control (CDC)

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“…Assumption 1 is a quite mild limitation imposed on the uncertainties, and thus is widely adopted in the robust control field (e.g. Asemani and Majd, 2013; Nguang, 1996; Nguang et al, 2011).…”

Section: Problem Description and Preliminariesmentioning

confidence: 99%

“…Apart from the applications mentioned above, SOS theory was also used to study other control problems, such as optimal control (Ichihara, 2009), mixed H 2 / H ∞ control (Ma et al, 2012) and non-linear robust control of a hypersonic aircraft (Ataei and Wang, 2012). Generally, the output feedback approaches based on SOS technique are non-convex (Chae et al, 2014; Nguang et al, 2011; Zheng and Wu, 2009, 2011) and thus the computational difficulties are unavoidable. As a result, most of the existing results adopt the state feedback to design controllers.…”

Section: Introductionmentioning

confidence: 99%

Observer-based robust stabilization for a class of uncertain polynomial systems

Zhou

Zeng

2015

Transactions of the Institute of Measurement and Control

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This paper focuses on the observer-based robust stabilization problem for a class of polynomial systems with norm-bounded time-varying uncertainties. The structural features of such systems guarantee the fulfilment of the separation principle between the reduced-order observer and the state feedback. The existence conditions of the observer-based robust stabilization controller are obtained by using Lyapunov stability theory. Furthermore, based on the polynomial sum of squares (SOS) theory, the above conditions are transformed into the corresponding SOS convex optimization constraints, for the avoidance of computing difficulties that exist widely in the control of non-linear systems. Finally, two numerical examples are given to illustrate the feasibility and effectiveness of the proposed approach.

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“…Therefore, the crucial property of SOS technique has effectively promoted the development of the research on polynomial nonlinear systems (e.g. Gußneraba et al, 2012; Nguang et al, 2011; Prajna et al, 2004; Xu et al, 2009).…”

Section: Introductionmentioning

confidence: 99%

Robust nonlinear H_∞ output-feedback control for flexible spacecraft attitude manoeuvring

Bai

Huang

Zeng

2019

Transactions of the Institute of Measurement and Control

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This paper presents a robust nonlinear H∞ output-feedback control approach for attitude manoeuvring of flexible spacecraft with external disturbances, inertia matrix perturbation and input constraints. By applying Lyapunov stability theory and using the generalized S-procedure and sum of squares (SOS) techniques, the robust H∞ output-feedback attitude control problem is converted into a convex optimization problem with SOS constraints when the flexible spacecraft is modelled as a polynomial state-space equation with polytope uncertainties. As a result, it overcomes the difficulty in constructing Lyapunov function and implementing numerical computation caused by the non-convexity of output-feedback H∞ control design for nonlinear systems. Moreover, it enables the state-observer and the controller to be designed independently and hence the complexity of the control algorithm is reduced remarkably. A numerical example illustrates the effectiveness and feasibility of the proposed approach.

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Static output feedback controller design for uncertain polynomial systems: an iterative sums of squares approach

Cited by 28 publications

References 14 publications

An iterative Sum-of-Squares optimization for static output feedback of polynomial systems

An iterative Sum-of-Squares optimization for static output feedback of polynomial systems

Observer-based robust stabilization for a class of uncertain polynomial systems

Robust nonlinear H_∞ output-feedback control for flexible spacecraft attitude manoeuvring

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Static output feedback controller design for uncertain polynomial systems: an iterative sums of squares approach

Cited by 28 publications

References 14 publications

An iterative Sum-of-Squares optimization for static output feedback of polynomial systems

An iterative Sum-of-Squares optimization for static output feedback of polynomial systems

Observer-based robust stabilization for a class of uncertain polynomial systems

Robust nonlinear H∞ output-feedback control for flexible spacecraft attitude manoeuvring

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Product

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Robust nonlinear H_∞ output-feedback control for flexible spacecraft attitude manoeuvring