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Engineering - Control Engineering | Set-Theoretic Methods in Control

Set-Theoretic Methods in Control

Blanchini, Franco, Miani, Stefano

2008, XV, 487 p.

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  • A self-contained monograph focused on the area of set-theoretic methods for control, which has recently seen a resurgence of interest
  • Several established and potentially new applications are presented
  • Includes exercises, numerical examples, and case studies
  • Numerical algorithms for the solution of the proposed problems are described in detail; some are available online in MATLAB and C++
  • Provides a solid foundation of mathematical techniques and applications and also features avenues for further theoretical study
  • Contains extensive references to the literature and supplies many recipes for solving significant control problems
  • For a broad audience of graduate students, researchers, and pratitioners in applied mathematics and engineering

This self-contained monograph describes basic set-theoretic methods for control and provides a discussion of their links to fundamental problems in Lyapunov stability analysis and stabilization, optimal control, control under constraints, persistent disturbance rejection, and uncertain systems analysis and synthesis. New computer technology has catalyzed a resurgence of research in this area, particularly in the development of set-theoretic techniques, many of which are computationally demanding.

The work presents several established and potentially new applications, along with numerical examples and case studies. A key theme of the presentation is the trade-off between exact (but computationally intensive) and approximate (but conservative) solutions to problems. Mathematical language is kept to the minimum necessary for the adequate formulation and statement of main concepts. Numerical algorithms for the solution of the proposed problems are described in detail.

Set-Theoretic Methods in Control is accessible to readers familiar with the basics of systems and control theory; prerequisites such as convexity theory are included. The text provides a solid foundation of mathematical techniques and applications and also features avenues for further theoretical study. Aimed primarily at graduate students and researchers in applied mathematics and engineering, the book will also appeal to practitioners since it contains extensive references to the literature and supplies many recipes for solving significant control problems.

Content Level » Research

Keywords » Lyapunov stability - Optimal control - algorithm - algorithms - calculus - control under constraints - convex sets - invariant sets - parameter-varying systems - persistent disturbance rejection - programming - set-theoretic methods - stability - time-domain constraints - uncertain systems analysis and synthesis

Related subjects » Birkhäuser Engineering - Birkhäuser Mathematics

Table of contents 

Preface Introduction Lyapunov and Lyapunov-like Functions Convex Sets and Their Representation Invariant Sets Dynamic Programming Set-Theoretic Analysis of Dynamic Systems Control of Parameter-Varying Systems Control with Time-Domain Constraints (Sub-)Optimal Control Set-Theoretic Estimation Related Topics Appendix References Index

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