Singular perturbation analysis of discrete control systems
type: Item
instance of: scholarly article
title: Singular perturbation analysis of discrete control systems
zbMATH Open document ID: 0575.34002
author: B. George
published in: Lecture Notes in Mathematics
publication date: 1985-01-01T00:00:00Z
review text: This monograph presents a tutorial description of singular perturbation analysis of difference equations and its potential use in the synthesis of optimal control laws. Almost every topic is illustrated with numerical results for simple examples. The first chapter is devoted to scalar nth order difference equations with a small parameter raised to the appropriate power multiplying either the highest order coefficients or the lowest order coefficients. The second chapter is devoted to state space representations of difference equations (vector first order difference equations). Methods are presented for assessing the applicability of singular perturbation analysis, and appropriate formulations if applicable. The use of singular perturbations to simplify the computation of optimal open-loop trajectories for linear systems with quadratic cost functions is described in Chapter 3. Here it is shown how solutions may be obtained as the sum of three components, the degenerate solution, an initial boundary layer solution and a final boundary layer solution. The final chapter shows how the singular perturbation method may be applied to nonlinear equations with degenerate linear equations. The use of the singular perturbation method in solving the Riccati equation for optimal control of systems described by linear difference equations is also described in this chapter. The book contains a significant number of typographical errors, but it is easy to read and has an extensive list of references.
Mathematics Subject Classification ID: 34-02
Mathematics Subject Classification ID: 34E15
Mathematics Subject Classification ID: 34D15
Mathematics Subject Classification ID: 39A10
Mathematics Subject Classification ID: 65Q05
zbMATH DE Number: 3918822
zbMATH Keywords: singular perturbation analysis
zbMATH Keywords: numerical results
zbMATH Keywords: examples
zbMATH Keywords: quadratic cost functions
zbMATH Keywords: Riccati equation
zbMATH Keywords: optimal control
reviewed by: Harvey Cohn
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1007/bfb0074760
OpenAlex ID: W632941928
DOI: 10.1007/BFB0074760
description: scientific article; zbMATH DE number 3918822