Multistep Guaranteed Cost Control of Linear Systems with Uncertain Parameters

Vinkler, Aharon; Wood, Lincoln J.

doi:10.2514/3.55908

Cited by 44 publications

(7 citation statements)

References 12 publications

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“…Equation (LO) was solved by backwards integration, but no guarantee of convergence could be given. A more efficient iterative technique suggested by Vinkler and Wood (1979) also missed the convergence guarantee. Kosmidou and Bertrand (1987) used a different choice for U(P(t)) that was linear in P(t).…”

Section: Previous Work-choices Of Bounding Functionsmentioning

confidence: 99%

“…Among them, the guaranteed cost control approach, introduced by Chang and Peng (1972), has the advantage of providing an upper bound on the performance index and thus the system performance degradation due to the uncertainties is known to be less than this bound. Some other methods have then been proposed, based on this idea (Vinkler and Wood 1979, Kosmidou and Bertrand 1987, Liou and Yang 1987. All these methods considered models with uncertain parameters in the systems dynamics matrix only.…”

Section: Introductionmentioning

confidence: 99%

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Robust stability and performance of systems with structured and bounded uncertainties: an extension of the guaranteed cost control approach

Kosmidou

1990

International Journal of Control

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Robust stability and performance of systems with structured and bounded uncertainties: an extension of the guaranteed cost control approach O. I. KOSMIDOUt A method is presented for designing a full state feedback linear control law that will ensure the robust stability and performance of a given linear uncertain system. The systems under consideration are described by state equations that depend on uncertain parameters. These uncertain parameters may be time varying. Their values are constrained to lie within known compact bounding sets. The method is based on the guaranteed cost control concept of Chang and Peng (1972). The controller gains result from the solution of a Riccati equation in which the weighting matrices depend on the uncertainty bounds. Sufficient conditions for the existence of a solution arise from the standard LQG control theory.(I)

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Section: Previous Work-choices Of Bounding Functionsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Robust stability and performance of systems with structured and bounded uncertainties: an extension of the guaranteed cost control approach

Kosmidou

1990

International Journal of Control

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“…The bound f(. utilized in [9] and [12] for full-state-feedback design was chosen to be (1. 12) ft(Q)=611A1Q+QAr l, where a is an arbitrary positive scalar.…”

mentioning

confidence: 99%

“…utilized in [9] and [12] for full-state-feedback design was chosen to be (1. 12) ft(Q)=611A1Q+QAr l, where a is an arbitrary positive scalar. As shown in [33], bound (1.14) arises from a multiplicative white noise model with exponential disturbance weighting.…”

mentioning

confidence: 99%

Robust Stability and Performance Analysis for State-Space Systems via Quadratic Lyapunov Bounds

Bernstein¹,

Haddad²

1990

SIAM J. Matrix Anal. & Appl.

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Abstract. For a given asymptotically stable linear dynamic system it is often of interest to determine whether stability is preserved as the system varies within a specified class of uncertainties. If, in addition, there also exist associated performance measures (such as the steady-state variances of selected state variables), it is desirable to assess the worst-case performance over a class of plant variations. These are problems of robust stability and performance analysis. In the present paper, quadratic Lyapunov bounds used to obtain a simultaneous treatment of both robust stability and performance are considered. The approach is based on the construction of modified Lyapunov equations, which provide sufficient conditions for robust stability along with robust performance bounds. In this paper, a wide variety of quadratic Lyapunov bounds are systematically developed and a unified treatment of several bounds developed previously for feedback control design is provided.

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“…Thus, it is desirable to obtain robust state estimators which provide acceptable performance over the range of parametric uncertainty. The approach of the present paper is related to the guaranteed cost approach developed for control in [4,16] and applied to estimation in [11]. Specifically, the main idea is to bound the effect of the uncertain parameters on',the estimation error over the uncertainty range and then choose estimator gains to minimize the estimation bound.…”

Section: Introductionmentioning

confidence: 99%

Robust, reduced-order, nonstrictly proper state estimation via the optimal projection equations with Petersen—Hollot bounds

Haddad¹,

Bernstein²

1987

Systems & Control Letters

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A state-estimation design problem involving parametric plant uncertainties is considered. An error bound suggested by recent work of Petersen and Hollot is utilized for guaranteeing robust estimation. Necessary conditions which generalize the optimal projection equations for reduced-order state estimation are used to characterize the estimator which minimizes the error bound. The design equations thus effectively serve as sufficient conditions for synthesizing robust estimators. An additional feature is the presence of a static estimation gain in conjunction with the dynamic (Kalman) estimator, i.e., a nonstrictly proper estimator.

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Multistep Guaranteed Cost Control of Linear Systems with Uncertain Parameters

Cited by 44 publications

References 12 publications

Robust stability and performance of systems with structured and bounded uncertainties: an extension of the guaranteed cost control approach

Robust stability and performance of systems with structured and bounded uncertainties: an extension of the guaranteed cost control approach

Robust Stability and Performance Analysis for State-Space Systems via Quadratic Lyapunov Bounds

Robust, reduced-order, nonstrictly proper state estimation via the optimal projection equations with Petersen—Hollot bounds

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