Improved optimisation approach to the robust H2/H∞ control problem for linear systems

Gonçalves, Eduardo Nunes; Palhares, Reinaldo M.; Takahashi, Ricardo H. C.

doi:10.1049/ip-cta:20045041

Cited by 28 publications

(11 citation statements)

References 12 publications

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“…For this controller, and considering the whole polytope, [18] presents the following values for the H 2 and H 1 norms computed via a different approach described in [22,21]:…”

Section: Norm Computation For Uncertain Systemsmentioning

confidence: 99%

Design of mixed H2/H∞ control systems using algorithms inspired by the immune system

Guimarães

Palhares

Campelo

et al. 2007

Information Sciences

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“…For this controller, and considering the whole polytope, [18] presents the following values for the H 2 and H 1 norms computed via a different approach described in [22,21]:…”

Section: Norm Computation For Uncertain Systemsmentioning

confidence: 99%

Design of mixed H2/H∞ control systems using algorithms inspired by the immune system

Guimarães

Palhares

Campelo

et al. 2007

Information Sciences

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“…The iterative procedure continues until a convergence criterion is satisfied. Analogous procedures have been employed by the authors in several problems of system analysis and control design: robust statefeedback control synthesis (Gonc¸alves, Palhares, and Takahashi 2005), robust PID control synthesis (Gonc¸alves, Palhares, and Takahashi 2008), robust filter synthesis (Gonc¸alves, Palhares, Takahashi, and Mesquita 2006a), and robust model reduction (Gonc¸alves, Palhares, Takahashi, and Chasin 2009).…”

Section: Introductionmentioning

confidence: 99%

Robust ℋ₂/ℋ_∞/reference model dynamic output-feedback control synthesis

Gonçalves

Bachur

Palhares

et al. 2011

International Journal of Control

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This article presents a new strategy to design robust model matching dynamic output-feedback controllers that guarantee tracking response specifications, disturbance rejection and noise attenuation. The proposed synthesis methodology, based on a multi-objective optimisation problem, can be applied to uncertain continuous or discrete-time linear time-invariant systems with polytopic uncertainty, leading to both full-order and reducedorder robust-performance dynamic controllers. The objective functions represent the H 1 -norm of the difference between the closed-loop transfer function matrix, from the reference signals and the plant outputs and the reference model matrix, the H 1 -norm of the closed-loop transfer function matrix from the disturbances and the plant outputs and the H 2 -norm of the closed-loop transfer function matrix from the measurement noises and the control inputs. An integral control action is also introduced in order to achieve zero steady-state error. In the case of MIMO systems, the proposed strategy can be applied to decouple the closed-loop control system choosing an appropriated reference model matrix. Two examples are presented to illustrate both SISO and MIMO systems control synthesis.

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“…Robust stability and performance are achieved by minimizing an appropriate norm (such as · L 2 -L 2 (or · ∞ ), · L 2 -L∞ and · L∞-L∞ , which are called energy to energy, energy to peak, and peak to peak, respectively) of a transfer function. Considerable attention has been devoted to the optimal control problem, such as energy to energy (or H ∞ ) control and model reduction [4,6,25,26], H 2 (and mixed H 2 /H ∞ ) control and filtering [8,9,19,20,22,23], energy to peak (or L 2 -L ∞ ) control and filtering [7,21]. In many practical cases, the L 2 -L ∞ performance is more reasonable to achieve in system design.…”

Section: Introductionmentioning

confidence: 99%

Robust control of uncertain differential linear repetitive processes

Wang

2008

Systems & Control Letters

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For two-dimensional (2-D) systems, information propagates in two independent directions. 2-D systems are known to have both system-theoretic and applications interest, and the so-called linear repetitive processes (LRPs) are a distinct class of 2-D discrete linear systems. This paper is concerned with the problem of L 2 -L ∞ (energy to peak) control for uncertain differential LRPs, where the parameter uncertainties are assumed to be norm-bounded. For an unstable LRP, our attention is focused on the design of an L 2 -L ∞ static state feedback controller and an L 2 -L ∞ dynamic output feedback controller, both of which guarantee the corresponding closed-loop LRPs to be stable along the pass and have a prescribed L 2 -L ∞ performance. Sufficient conditions for the existence of such L 2 -L ∞ controllers are proposed in terms of linear matrix inequalities (LMIs). The desired L 2 -L ∞ dynamic output feedback controller can be found by solving a convex optimization problem. A numerical example is provided to demonstrate the effectiveness of the proposed controller design procedures.

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Improved optimisation approach to the robust H2/H∞ control problem for linear systems

Cited by 28 publications

References 12 publications

Design of mixed H2/H∞ control systems using algorithms inspired by the immune system

Design of mixed H2/H∞ control systems using algorithms inspired by the immune system

Robust ℋ₂/ℋ_∞/reference model dynamic output-feedback control synthesis

Robust control of uncertain differential linear repetitive processes

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Improved optimisation approach to the robust H2/H∞ control problem for linear systems

Cited by 28 publications

References 12 publications

Design of mixed H2/H∞ control systems using algorithms inspired by the immune system

Design of mixed H2/H∞ control systems using algorithms inspired by the immune system

Robust ℋ2/ℋ∞/reference model dynamic output-feedback control synthesis

Robust control of uncertain differential linear repetitive processes

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Robust ℋ₂/ℋ_∞/reference model dynamic output-feedback control synthesis