A randomized approach to the H/sub 2//H/sub /spl infin// control problem via Q-parameterization

Horspool, Kenneth R.; Erwin, R. Scott; Abdallah, Chaouki T.; Dorato, P.

doi:10.1109/acc.2000.876731

Cited by 3 publications

(3 citation statements)

References 12 publications

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“…Applications of this approach to non-convex problems such as mixed H 2 /H ∞ [16] and fixed-order H ∞ design [6] have been reported recently. However, a major difficulty is illustrated by an example given in [27]: a H ∞ mixed sensitivity design for robust performance is considered, where the orders of plant and weighting filters add up to eight.…”

Section: Statistical Learning Theory and Randomized Algorithmsmentioning

confidence: 98%

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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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Section: Statistical Learning Theory and Randomized Algorithmsmentioning

confidence: 98%

“…3 can be represented in the form of the implicit system (16). Moreover, the bounds on the magnitude and rate of change of the time-varying uncertainty ∆(t) can be represented by a particular set K. If the condition of Theorem 2 is satisfied, the uncertain system in Fig.…”

Section: Robust Control Of Linear Parameter-varying Systems: Control mentioning

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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“…c°:= inf \\R; iW (Q)\\p (3)(4)(5)(6)(7)(8)(9)(10)(11)(12)(13)(14)(15)(16)(17)(18)(19) where ||.|| p denotes "Ho norm for i = 1 and i\ norm for i = 2,3,4. This set of problem can be readily solved by using G MO routine (for more details, please refer to the GMO The final resulting %2 performance of (3.18) is 0.0729 with l\ performance of 0.6026, 0.6037 and 0.0333 in other three channels.…”

Section: Bounded Suspension Deflection (Connection Goal)mentioning

confidence: 99%

Mathematical optimization and robust control synthesis

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Probabilistic Robust LPV Control

Evangelisti

Pusch

2021

2021 American Control Conference (ACC)

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A randomized approach to the H/sub 2//H/sub /spl infin// control problem via Q-parameterization

Cited by 3 publications

References 12 publications

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

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

Mathematical optimization and robust control synthesis

Probabilistic Robust LPV Control

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