16. Multiobjective Robust Control Toolbox for Linear-Matrix-Inequality-Based Control

Dussy, Stephane

doi:10.1137/1.9780898719833.ch16

Cited by 6 publications

(6 citation statements)

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“…See, for instance, some examples in references . Moreover, it has been shown in that the DAR includes the linear fractional representation (LFR) of nonlinear systems introduced in , and thus we may apply the LFR modeling tools (see, e.g., ) to derive a DAR model for (nonsingular) rational control systems. Remark Although the DAR representation presents some similarity to quasi‐LPV models (see, for instance, and references therein) some key differences should be highlighted.…”

Section: Preliminariesmentioning

confidence: 99%

“…The class of systems considered in this paper covers all systems modeled by rational differential equations. The motivation to investigate rational systems is their use to model several phenomena in real life applications, in particular in systems biology, engineering, physics, and economics, and also in nonlinear system identification and realization theory , which has given rise to a large number of works on the stability analysis, control and filter design for rational nonlinear systems . We emphasize that a large class of systems can be embedded in this setup such as quadratic and polynomial systems.…”

Section: Introductionmentioning

confidence: 99%

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Static anti‐windup design for a class of nonlinear systems

Silva

Oliveira

Coutinho³

et al. 2012

Intl J Robust & Nonlinear

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This paper focuses on the problem of static anti-windup design for a class of multivariable nonlinear systems subject to actuator saturation. The considered class regards all systems that are rational on the states or that can be conveniently represented by a rational system with algebraic constraints considering some variable changes. More precisely, a method is proposed to compute a static anti-windup gain which ensures regional stability for the closed-loop system assuming that a dynamic output feedback controller is previously designed to stabilize the nonlinear system. The results are based on a differential algebraic representation of rational systems. The control saturation effects are taken into account by the application of a generalized sector bound condition. From these elements, LMI-based conditions are devised to compute an anti-windup gain with the aim of enlarging the closed-loop region of attraction. Several numerical examples are provided to illustrate the application of the proposed method.On the other hand, a key problem to characterize the stability of nonlinear systems is the determination of a nonconservative estimate of the system region of attraction. In general, the estimates are obtained from Lyapunov level sets (see, for instance, the references [17][18][19][20][21]). In this context, considering an NDI-based controller, the synthesis of a dynamic anti-windup compensator aiming at the enlargement of an estimate of the region of attraction of the closed-loop system in the subspace of the plant variables has been proposed in [22] for the class of quadratic systems. The considered architecture in this case, as in [12], can be seen as a generalization of the coprime-factorization approach (or the model recovery anti-windup) used in linear anti-windup [2,23]. This same problem has been tackled in [24] but considering rational systems and static anti-windup compensation. In particular, the multivariable case is not addressed, and the method is based on a nonconvex condition, although the problem solution is obtained from LMI relaxations. These drawbacks have been in part overcome in [25], where convex stabilizing conditions are proposed. However, it should be pointed out that in [24] and [25], only systems and controllers with linear outputs can be considered. It turns out that these approaches cannot be applied in the case of NDI controllers, for instance.In light of the aforementioned scenario, this paper aims at devising a numerical and tractable technique to design static anti-windup compensators for a class of nonlinear systems subject to actuator saturation. The class of systems considered in this paper covers all systems modeled by rational differential equations. The motivation to investigate rational systems is their use to model several phenomena in real life applications, in particular in systems biology, engineering, physics, and economics, and also in nonlinear system identification and realization theory [26,27], which has given rise to a large number of works on the stability a...

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Section: Preliminariesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Static anti‐windup design for a class of nonlinear systems

Silva

Oliveira

Coutinho³

et al. 2012

Intl J Robust & Nonlinear

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“…In addition, when the matrices B e , B p , B y and B w are constrained to be constant, the representation in (9) can be derived from the LFR of non-linear systems introduced in [9]. Thus, the computational tools for LFR modelling [17] can be applied to obtain a DAR for f e (•). In Section 5, the DAR modelling is illustrated considering the dynamics of a perfusion/chemostat bioreactor.…”

Section: Control Designmentioning

confidence: 99%

A robust non‐linear feedback control strategy for a class of bioprocesses

Coutinho¹,

Wouwer

2013

IET Control Theory & Applications

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“…A straightforward consequence from the above relations is that the LFR tools developed in [22,23] can be applied to obtain a DAR model of the nonlinear system. However, the LFR representation as well as the DAR one are not unique.…”

Section: Related Representations Of Dynamical Systemsmentioning

confidence: 99%

ℒ︁₂‐Gain analysis and control of uncertain nonlinear systems with bounded disturbance inputs

Coutinho

Trofino

et al. 2007

Intl J Robust & Nonlinear

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SUMMARYThis paper proposes a convex approach to regional stability and L 2 -gain analysis and control synthesis for a class of nonlinear systems subject to bounded disturbance signals, where the system matrices are allowed to be rational functions of the state and uncertain parameters. To derive sufficient conditions for analysing input-to-output properties, we consider polynomial Lyapunov functions of the state and uncertain parameters (assumed to be bounded) and a differential-algebraic representation of the nonlinear system. The analysis conditions are written in terms of linear matrix inequalities determining a bound on the L 2 -gain of the input-to-output operator for a class of (bounded) admissible disturbance signals. Through a suitable parametrization involving the Lyapunov and control matrices, we also propose a linear (full-order) output feedback controller with a guaranteed bound on the L 2 -gain. Numerical examples are used to illustrate the proposed approach.

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16. Multiobjective Robust Control Toolbox for Linear-Matrix-Inequality-Based Control

Cited by 6 publications

References 0 publications

Static anti‐windup design for a class of nonlinear systems

Static anti‐windup design for a class of nonlinear systems

A robust non‐linear feedback control strategy for a class of bioprocesses

ℒ︁₂‐Gain analysis and control of uncertain nonlinear systems with bounded disturbance inputs

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16. Multiobjective Robust Control Toolbox for Linear-Matrix-Inequality-Based Control

Cited by 6 publications

References 0 publications

Static anti‐windup design for a class of nonlinear systems

Static anti‐windup design for a class of nonlinear systems

A robust non‐linear feedback control strategy for a class of bioprocesses

ℒ︁2‐Gain analysis and control of uncertain nonlinear systems with bounded disturbance inputs

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ℒ︁₂‐Gain analysis and control of uncertain nonlinear systems with bounded disturbance inputs