Foundations of deterministic and stochastic control
type: Item
instance of: scholarly article
title: Foundations of deterministic and stochastic control
zbMATH Open document ID: 1002.93003
author: Jon H. Davis
published in: Systems \& Control: Foundations \& Applications
publication date: 2002-09-24T00:00:00Z
review text: This volume is a textbook on linear control systems with an emphasis on stochastic optimal control with solution methods using spectral factorization in line with the original approach of N. Wiener. Continuous-time and discrete-time versions are presented in parallel. When this is not the case, we mention it. Chapter one is an introduction to realization theory (this is where controllability and observability appear as important underlying concepts) and identification problems are tackled. Chapter two is devoted to the LQ output regulator, and a section focuses more specifically on tracking issues. Chapter three consists in a development of stability theory. Lyapunov's theory is presented first in the nonlinear case, and then several frequency-domain criteria (Nyquist criterion, circle theorem, small gain theorem) are provided for the (linear) continuous-time case. Chapter four is a short and practical introduction to probabilities and random processes with an emphasis on the discrete case. Since the book mainly deals with linear systems, it is convenient to use Gaussian variables so that they too are included at the end. The next chapter presents Kalman-Bucy filters in the discrete case. Chapter six is a pendant to chapter four for the continuous-time case. Chapter seven introduces stochastic optimal control problems in the discrete (mainly linear) case. The dynamic programming method is shown. The separation theorem is provided in both the discrete and the continuous-time cases. Chapter eight is devoted to the Luenberger observer (in the continuous-time situation). Chapter nine shifts the focus to estimation problems for nonlinear and finite state problems. A Bayesian approach for finite Markov processes is proposed. Chapter ten is devoted to Wiener filtering and spectral factorization. This is applied to the computation of optimal gains. Chapter eleven is a generalization of Wiener-Hopf factorization methods to the infinite-dimensional continuous-time case and op…
Mathematics Subject Classification ID: 93-02
Mathematics Subject Classification ID: 93E20
Mathematics Subject Classification ID: 93C80
Mathematics Subject Classification ID: 47A68
Mathematics Subject Classification ID: 93-01
zbMATH DE Number: 1805578
zbMATH Keywords: stochastic optimal control
zbMATH Keywords: spectral factorization
zbMATH Keywords: LQ output regulator
zbMATH Keywords: tracking
zbMATH Keywords: Kalman-Bucy filters
zbMATH Keywords: separation theorem
zbMATH Keywords: estimation
zbMATH Keywords: Wiener filtering
zbMATH Keywords: Riccati equation
reviewed by: A. Akutowicz
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1805578