Journal ArticleDOI
Infinite horizon quadratic control of linear singularly perturbed systems with small state delays: an asymptotic solution of Riccati-type equations
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An infinite horizon linear-quadratic optimal control problem for a singularly perturbed system with multiple point-wise and distributed small delays in the state variable is considered and the zero-order asymptotic solution is constructed.Abstract:
An infinite horizon linear-quadratic optimal control problem for a singularly perturbed system with multiple point-wise and distributed small delays in the state variable is considered. The set of Riccati-type equations, associated with this problem by the control optimality conditions, is studied. Since the system in the control problem is singularly perturbed, the equations of this set are also perturbed by a small parameter of the singular perturbations. The zero-order asymptotic solution to this set of equations is constructed and justified. Based on this asymptotic solution, parameter-free sufficient conditions for the existence and uniqueness of solution to the original optimal control problem are established.read more
Citations
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Book
Complex Analysis and Dynamical Systems V
TL;DR: Agarovsky and Agranovsky as mentioned in this paper gave a generalization of the Cauchy-Szego integral in the unit ball of the Zalcman space.
Book ChapterDOI
A Turnpike Result for Discrete-Time Optimal Control Systems
TL;DR: In this paper, the authors studied the turnpike property of approximate solutions for a general class of discrete-time control systems without discounting and with a compact metric space of states.
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Stability of a Turnpike Phenomenon for a Discrete-Time Optimal Control System
TL;DR: In this paper, the authors study the structure of solutions of a discrete-time control system with a compact metric space of states X which arises in economic dynamics and show that these turnpike properties are stable under perturbations of the objective function v.
Journal ArticleDOI
Robust sampled-data H∞ control of uncertain singularly perturbed systems using time-dependent Lyapunov functionals
TL;DR: In this paper, the robust sampled-data H∞ control of linear uncertain singularly perturbed systems is investigated, where parametric uncertainties are assumed to be time-varying and norm-bounded.
Journal ArticleDOI
Stability of singularly perturbed functional-differential systems: spectrum analysis and LMI approaches
Valery Y. Glizer,Emilia Fridman +1 more
TL;DR: Two approaches to the study of the exponential stability of the singularly perturbed linear functional-differential system are suggested and a direct Lyapunov–Krasovskii method is developed for systems with time-varying delays leading to stability conditions in terms of linear matrix inequalities.
References
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Differential Equations: Stability, Oscillations, Time Lags
H. A. Antosiewicz,A. Halanay +1 more
Singular perturbations and time scales in control theory and applications: An overview
TL;DR: This paper presents an overview of singular perturbations and time scales (SPaTS) in control theory and applications during the period 1984-2001 and is not intended to be an exhaustive survey on the topic.
Journal ArticleDOI
Singular perturbation of linear regulators: Basic theorems
Petar V. Kokotovic,R. Yackel +1 more
TL;DR: The behavior of the Riccati equation for the linear regulator problem with a parameter whose perturbation changes the order of the system is analyzed in this article, where sufficient conditions are given under which the original problem tends to the solution of a low-order problem.
Journal ArticleDOI
Singular Perturbation Analysis of Boundary Value Problems for Differential-Difference Equations. V. Small Shifts with Layer Behavior
Charles G. Lange,Robert M. Miura +1 more
TL;DR: It is shown that the layer behavior can change its character and even be destroyed as the shifts increase but remain small, and the analyses of the layer equations using Laplace transforms lead to novel results.
Book
Perturbations, Approximations and Sensitivity Analysis of Optimal Control Systems
TL;DR: In this article, estimates of the solutions of abstract optimization problems are derived for regular perturbations, singular perturbation and finite difference approximations, and sensitivity analysis of the open-loop control structure with constrained controls.
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