Singular perturbations in optimal control problems

DOI10.1007/BF01262406zbMath0595.49019OpenAlexW2037223680MaRDI QIDQ1077702

A. B. Vasil'eva, Mikhail Dmitriev

Publication date: 1986

Published in: Journal of Soviet Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf01262406

zbMATH Keywords

regularizationchatteringRiccati equationhigh gainlinear-quadratic problemsTychonov's theorem

Mathematics Subject Classification ID

Related Items (19)

Stability and stabilisability of the singularly perturbed system with delay on time scales: a decomposition approach ⋮ Asymptotic expansion of the solution of a singularly perturbed optimal control problem with elliptical control constraints ⋮ Asymptotic expansion of a solution for the singularly perturbed optimal control problem with a convex integral quality index and smooth control constraints ⋮ On a singularly perturbed time-optimal control problem with two small parameters ⋮ Quasidifferentiability and uniform observability of linear time-varying singularly perturbed systems ⋮ Approximation of the Solution Based on the Decoupling Transformation of Linear Time-Varying Singularly Perturbed System with Delay ⋮ On the Stability of Three-Time-Scale Linear Time-Invariant Singularly Perturbed Systems with State Delay ⋮ Reduction of the optimal tracking problem in the presence of noise ⋮ Singularly perturbed problems with multi-tempo fast variables ⋮ Asymptotic analysis and solution of a finite-horizon \(H_{\infty}\) control problem for singularly-perturbed linear systems with small state delay ⋮ ASYMPTOTIC EXPANSION OF A SOLUTION FOR THE SINGULARLY PERTURBED OPTIMAL CONTROL PROBLEM WITH A CONVEX INTEGRAL QUALITY INDEX AND SMOOTH CONTROL CONSTRAINTS ⋮ Unnamed Item ⋮ Asymptotic expansion of solution to singularly perturbed optimal control problem with convex integral quality functional with terminal part depending on slow and fast variables ⋮ Asymptotic solution of a singularly perturbed optimal problem with integral constraint ⋮ Asymptotics of the optimal time in a time-optimal problem with two small parameters ⋮ Complete controllability conditions for linear singularly perturbed time-invariant systems with multiple delays via chang-type transformation ⋮ \(H_\infty\) control of linear singularly perturbed systems with small state delay ⋮ Asymptotic solution of a boundary-value problem for linear singularly-perturbed functional differential equations arising in optimal control theory ⋮ An averaging method for singularly perturbed systems of semilinear differential inclusions with analytic semigroups

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