Journal ArticleDOI
A boundary layer method for the matrix Riccati equation
R. Yackel,Petar V. Kokotovic +1 more
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TLDR
In this paper, an asymptotic expansion method was developed for a singularly perturbed matrix Riccati equation, which can be used in the design of regulator and estimator systems with small parameters.Abstract:
An asymptotic expansion method is developed for a singularly perturbed matrix Riccati equation. The method reduces the system order and avoids difficulties with numerically stiff problems. It can be used in the design of regulator and estimator systems with small parameters.read more
Citations
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Journal ArticleDOI
Survey of decentralized control methods for large scale systems
TL;DR: In this article, the authors survey the control theoretic literature on decentralized and hierarchical control, and methods of analysis of large scale systems, and present a survey of the control theory of large-scale systems.
Journal ArticleDOI
Singular perturbations and order reduction in control theory - An overview
TL;DR: The content of main theorems is presented in a tutorial form aimed at a broad audience of engineers and applied mathematicians interested in control, estimation and optimization of dynamic systems.
Proceedings ArticleDOI
A decomposition of near-optimum regulators for systems with slow and fast modes
Joe H. Chow,Petar V. Kokotovic +1 more
TL;DR: In this article, conditions for complete separation of slow and fast regulator designs are formulated and a second order approximation of the optimal performance is achieved without the knowledge of the small singular perturbation parameter.
Journal ArticleDOI
Singular Perturbations and Order Reduction in Control Theory - An Overview
TL;DR: The content of main theorems on singular perturbations is presented in a tutorial form aimed at a broad audience of engineers and applied mathematicians interested in control, estimation and optimization of dynamic systems.
Journal ArticleDOI
A note on the derivation and use of reduced-order models
R. Genesio,M. Milanese +1 more
TL;DR: In view of the particular interest in the problem of reduced-order modeling in recent years, some considerations not sufficiently investigated in current literature are pointed out and a comprehensive set of references is given.
References
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Contributions to the theory of optimal control
TL;DR: In this article, the authors considered the problem of least square feedback control in a linear time-invariant system with n states, and proposed a solution based on the concept of controllability.
Journal ArticleDOI
Asymptotic behaviour of solutions to certain problems involving non-linear differential equations containing a?small parameter multiplying the highest derivatives
TL;DR: In this paper, the authors investigated problems that can be investigated on the basis of the asymptotic behaviour of the solution to the Cauchy problem and showed that these problems can be solved by periodic and periodic solutions.
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
Boundary Layer Methods for Nonlinear Initial Value Problems
TL;DR: In this paper, a simple expansion procedure for the fundamental initial value problem is presented, which can be extended to analogous problems for systems with two small parameters and for differential-difference equations with small delays.