A Riccati-genetic algorithms approach to fixed-structure controller synthesis

Farag, A.; Werner, Herbert

doi:10.23919/acc.2004.1383890

Cited by 21 publications

(18 citation statements)

References 10 publications

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“…in Farag and Werner [6] for non-convex synthesis problems involving LTI systems. In this work the fitness of controllers was evaluated by solving algebraic Riccati equations.…”

Section: B Hybrid Evolutionary-algebraic Algorithm For Controller Symentioning

confidence: 98%

Synthesis of Low-Order Controllers for LPV Systems Using LMIs and Evolutionary Search

Chughtai

Werner

2006

Proceedings of the 45th IEEE Conference on Decision and Control

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A procedure for designing robust and gainscheduled controllers for linear parameter-varying (LPV) systems is proposed that exploits known bounds on the rate of parameter variation to reduce conservatism. Recent results on stability analysis of LPV systems with known bounds on the rate of parameter change, using the concept of quadratic separators have been extended to compute a measure of worst-case performance of an LPV system by solving an LMI problem. The problem of synthesizing robust and gain-scheduled controllers leads to a bilinear matrix inequality, and a hybrid approach to solving this problem based on LMI solvers and genetic algorithms is proposed in this paper. Two design examples illustrate the efficiency of the proposed method.

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“…in Farag and Werner [6] for non-convex synthesis problems involving LTI systems. In this work the fitness of controllers was evaluated by solving algebraic Riccati equations.…”

Section: B Hybrid Evolutionary-algebraic Algorithm For Controller Symentioning

confidence: 98%

Synthesis of Low-Order Controllers for LPV Systems Using LMIs and Evolutionary Search

Chughtai

Werner

2006

Proceedings of the 45th IEEE Conference on Decision and Control

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“…An approach similar to that used in [25] but with improved efficiency and applicable to a variety of design techniques was proposed in [10] and [9]. To outline the idea, we consider again the LMI condition (2), which represents a necessary and sufficient condition for the H ∞ norm of (1) to be less than γ .…”

Section: A Hybrid Evolutionary-algebraic Algorithmmentioning

confidence: 99%

A Hybrid Evolutionary-Algebraic Approach to Optimal and Robust Controller Design (Hybride evolutionär-algebraische Verfahren für den Entwurf optimaler und robuster Regler)

Werner¹,

Farag²

2005

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Dedicated to Prof. Dr.-Ing. Heinz Unbehauen at the occasion of his 70th birthday Modern control techniques -such as H 2 or H ∞ optimal controller design -offer powerful synthesis tools, provided the controller has the same order as the plant, and there are no constraints on the information structure of the feedback loop (e. g. decentralized control). If these assumptions do not hold -as is often the case in practical applications -the synthesis problem becomes non-convex and hard to solve. A frequently encountered situation is however that a synthesis problem is intractable, whereas the corresponding analysis problem is convex and easy to solve. In this case, it is often more efficient to use the easily available analysis results to guide a stochastic search for the solution, rather than to address the hard synthesis problem directly. In this paper, such an approach -based on a combination of algebraic tools from optimal control theory and evolutionary search techniques -is presented. Four benchmark problems representing ''hard" control problems are used to illustrate the approach and to compare its efficiency with that of previously published solutions.Moderne H 2 -und H ∞ -optimale Reglerentwurfsverfahren sind nur anwendbar wenn der Regler die gleiche dynamische Ordnung wie die Strecke hat, und wenn keine Beschränkungen der Reglerstruktur (wie etwa bei dezentraler Regelung) vorliegen. Sind diese Voraussetzungen nicht erfüllt -was in der Praxis oft vorkommt -dann liegt ein nicht-konvexes Entwurfsproblem vor. Häufig ist jedoch das Analyse-Problem, das einem nicht-konvexen Entwurfsproblem entspricht, konvex und kann mit relativ geringem Rechenaufwand gelöst werden. In solchen Fällen ist es oft effizienter, Lösungen dieser Analyse-Probleme für stochastische Suchverfahren zu verwenden, als das nicht-konvexe Entwurfsproblem direkt zu lösen. In der vorliegenden Arbeit wird ein auf dieser Idee beruhender hybrider evolutionär-algebraischer Ansatz vorgestellt, der Werkzeuge aus der Theorie der optimalen Regelung kombiniert mit evolutionären Suchstrategien. Vier Benchmark-Probleme illustrieren die Vielseitigkeit und Effizienz des vorgeschlagenen Verfahrens.

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“…A hybrid evolutionary-algebraic approach for solving the non-convex problem of fixed structure and low-order controller design that was proposed in (Farag and Werner [2004]) is utilized here for this purpose. The method is based on the following assumptions (Apkarian et al [1995]):…”

Section: Discrete-time Controller Designmentioning

confidence: 99%

“…To solve the non-convex problem of finding a controller of order n k < n that minimizes the performance measure, we follow the approach in Farag and Werner [2004] and split the original problem into a convex subproblemthe minimization problem (19) -and a nonconvex onethe search for the controller parameters. The former one can be solved with LMI solvers and the latter one with evolutionary search techniques.…”

Section: Discrete-time Controller Designmentioning

confidence: 99%

Polytopic Quasi-LPV Models Based on Neural State-Space Models and Application to Air Charge Control of a SI Engine

Abbas

Werner

2008

IFAC Proceedings Volumes

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This paper is one of two joint papers, each presenting a different representation of a feedforward neural network. Here a discrete-time polytopic quasi linear parameter varying (LPV) model of a nonlinear system based on a neural state-space model is proposed, whereas in the joint paper (Abbas and Werner [2008]) a neural state-space model is transformed into a linear fractional transformation (LFT) representation to obtain a discrete-time quasi-LPV model of the nonlinear system. As a practical application, air charge control of a spark-ignition (SI) engine is used in both papers to illustrate two different synthesis methods for fixed structure low-order discrete-time LPV controllers. In the present paper, the synthesis of a fixed-structure low-order self-scheduled H ∞ controller is based on linear matrix inequality (LMIs) and evolutionary search. A controller is designed for the nonlinear system and its performance is compared with that achieved when a standard self-scheduled H ∞ controller is used.

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A Riccati-genetic algorithms approach to fixed-structure controller synthesis

Cited by 21 publications

References 10 publications

Synthesis of Low-Order Controllers for LPV Systems Using LMIs and Evolutionary Search

Synthesis of Low-Order Controllers for LPV Systems Using LMIs and Evolutionary Search

A Hybrid Evolutionary-Algebraic Approach to Optimal and Robust Controller Design (Hybride evolutionär-algebraische Verfahren für den Entwurf optimaler und robuster Regler)

Polytopic Quasi-LPV Models Based on Neural State-Space Models and Application to Air Charge Control of a SI Engine

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