Solution of the stochastic H ∞-optimization problem for discrete time linear systems under parametric uncertainty

Kurdyukov, Alexander P.; Maximov, E.A.

doi:10.1134/s0005117906080078

Cited by 17 publications

(2 citation statements)

References 18 publications

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“…This implies that design problem of anisotropy-based controllers includes classical problems of H 2 -and H 1 -optimization as limiting cases. [100] shows that H 2 -and H 1 -controllers are limiting cases of anisotropy-based controller. This monograph introduces reader to the solutions of the anisotropy-based analysis and design for linear stationary descriptor systems.…”

Section: • For Arbitrary Bounded Initial Conditions Generalized Funct...mentioning

confidence: 99%

Control of Discrete-Time Descriptor Systems

Belov

Andrianova

Kurdyukov

2018

Studies in Systems, Decision and Control

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The series "Studies in Systems, Decision and Control" (SSDC) covers both new developments and advances, as well as the state of the art, in the various areas of broadly perceived systems, decision making and control-quickly, up to date and with a high quality. The intent is to cover the theory, applications, and perspectives on the state of the art and future developments relevant to systems, decision making, control, complex processes and related areas, as embedded in the fields of engineering, computer science, physics, economics, social and life sciences, as well as the paradigms and methodologies behind them. The series contains monographs, textbooks, lecture notes and edited volumes in systems, decision making and control spanning the areas of Cyber-

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Section: • For Arbitrary Bounded Initial Conditions Generalized Funct...mentioning

confidence: 99%

Control of Discrete-Time Descriptor Systems

Belov

Andrianova

Kurdyukov

2018

Studies in Systems, Decision and Control

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“…The resulted optimal full-order estimator-based (central) controller is a unique one. An extension of these results to the systems with parametric uncertainties was given in [46,47]. But solving these complex systems of equations requires special developing of homotopy-like numerical algorithms [48].…”

Section: Introductionmentioning

confidence: 99%

Synthesis of anisotropic suboptimal controllers by convex optimization

Tchaikovsky,

Kurdyukov,

Timin

2011

Preprint

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This paper considers a disturbance attenuation problem for a linear discrete time invariant system under random disturbances with imprecisely known distributions. The statistical uncertainty is measured in terms of the mean anisotropy functional. The disturbance attenuation capabilities of the system are quantified by the anisotropic norm which is a stochastic counterpart of the H ∞ norm. The designed anisotropic suboptimal controller generally is a dynamic fixed-order output-feedback compensator which is required to stabilize the closed-loop system and keep its anisotropic norm below a prescribed threshold value. Rather than resulting in a unique controller, the suboptimal design procedure yields a family of controllers, thus providing freedom to impose some additional performance specifications on the closed-loop system. The general fixed-order synthesis procedure employs solving a convex inequality on the determinant of a positive definite matrix and two linear matrix inequalities in reciprocal matrices which make the general optimization problem nonconvex. By applying the known standard convexification procedures it is shown that the resulting optimization problem is convex for the full-information state-feedback, output-feedback full-order controllers, and static outputfeedback controller for some specific classes of plants defined by certain structural properties. In the convex cases, the anisotropic γ-optimal controllers are obtained by minimizing the squared norm threshold value subject to convex constraints. In a sense, the anisotropic controller seems to offer a promising and flexible trade-off between H 2 and H ∞ controllers which are its limiting cases. In comparison with the state-space solution to the anisotropic optimal controller synthesis problem presented before which results in a unique full-order estimator-based controller defined by a complex system of cross-coupled nonlinear matrix algebraic equations, the proposed optimization-based approach is novel and does not require developing specific homotopy-like computational algorithms.

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Normalizing Random Vector Anisotropy Magnitude

Chernyshov

2022

Lecture Notes in Control and Information Sciences - Proceedings

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Solution of the stochastic H ∞-optimization problem for discrete time linear systems under parametric uncertainty

Cited by 17 publications

References 18 publications

Control of Discrete-Time Descriptor Systems

Control of Discrete-Time Descriptor Systems

Synthesis of anisotropic suboptimal controllers by convex optimization

Normalizing Random Vector Anisotropy Magnitude

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