Ellipsoidal Calculus for Estimation and Control / Edition 1

Ellipsoidal Calculus for Estimation and Control / Edition 1

by Alexander Kurzhanski, Istvan Valyi
     
 

ISBN-10: 0817636994

ISBN-13: 9780817636999

Pub. Date: 09/01/1996

Publisher: Birkhauser Verlag

The investigation of control and estimation problems under unknown but bounded errors and disturbances, as well as those of differential games and related issues, may lead to solutions and procedures formulated in terms of sets and set-valued functions. However the relevant mathematical tools are usually complicated and not easy to apply, even in the linear-convex

Overview

The investigation of control and estimation problems under unknown but bounded errors and disturbances, as well as those of differential games and related issues, may lead to solutions and procedures formulated in terms of sets and set-valued functions. However the relevant mathematical tools are usually complicated and not easy to apply, even in the linear-convex case. This book gives an account of an ellipsoidal calculus and ellipsoidal techniques, developed by the authors, that allows presentation of the set-valued solutions to these problems in terms of approximating ellipsoidal-valued functions. Such an attack leads to effective computation schemes and opens the way to applications and implementations with computer animation, particularly in decision support systems. The problems treated here are those that involve calculation of attainability domains, of control synthesis under bounded controls, state constraints and unknown input disturbances, as well as those of "viability" and of the "bounding approach" to state estimation. The text ranges from a specially developed theory of exact set-valued solutions to the description of ellipsoidal calculus, related ellipsoidal-based methods and examples worked out with computer graphics.

Product Details

ISBN-13:
9780817636999
Publisher:
Birkhauser Verlag
Publication date:
09/01/1996
Series:
Systems & Control: Foundations & Applications Series
Edition description:
1994
Pages:
344
Product dimensions:
6.10(w) x 9.25(h) x 0.24(d)

Table of Contents

I. Evolution and Control: The Exact Theory.- 1.1 The System.- 1.2 Attainability and the Solution Tubes.- 1.3 The Evolution Equation.- 1.4 The Problem of Control Synthesis: A Solution Through Set-Valued Techniques.- 1.5 Control Synthesis Through Dynamic Programming Techniques.- 1.6 Uncertain Systems: Attainability Under Uncertainty.- 1.7 Uncertain Systems: The Solvability Tubes.- 1.8 Control Synthesis Under Uncertainty.- 1.9 State Constraints and Viability.- 1.10 Control Synthesis Under State Constraints.- 1.11 State Constrained Uncertain Systems: Viability Under Counteraction.- 1.12 Guaranteed State Estimation: The Bounding Approach.- 1.13 Synopsis.- 1.14 Why Ellipsoids.- II. The Ellipsoidal Calculus.- 2.1 Basic Notions: The Ellipsoids.- 2.2 External Approximations: The Sums Internal Approximations: The Differences.- 2.3 Internal Approximations: The Sums External Approximations: The Differences.- 2.4 Sums and Differences: The Exact Representation.- 2.5 The Selection of Optimal Ellipsoids.- 2.6 Intersections of Ellipsoids.- 2.7 Finite Sums and Integrals: External Approximations.- 2.8 Finite Sums and Integrals: Internal Approximations.- III. Ellipsoidal Dynamics: Evolution and Control Synthesis.- 3.1 Ellipsoidal-Valued Constraints.- 3.2 Attainability Sets and Attainability Tubes: The External and Internal Approximations.- 3.3 Evolution Equations with Ellipsoidal-Valued Solutions.- 3.4 Solvability in Absence of Uncertainty.- 3.5 Solvability Under Uncertainty.- 3.6 Control Synthesis Through Ellipsoidal Techniques.- 3.7 Control Synthesis: Numerical Examples.- 3.8 Ellipsoidal Control Synthesis for Uncertain Systems.- 3.9 Control Synthesis for Uncertain Systems: Numerical Examples.- 3.10 Target Control Synthesis Within Free Time Interval.- IV. Ellipsoidal Dynamics: State Estimation and Viability Problems.- 4.1 Guaranteed State Estimation: A Dynamic Programming Perspective.- 4.2 From Dynamic Programming to Ellipsoidal State Estimates.- 4.3 The State Estimates, Error Bounds, and Error Sets.- 4.4 Attainability Revisited: Viability Through Ellipsoids.- 4.5 The Dynamics of Information Domains: State Estimation as a Tracking Problem.- 4.6 Discontinuous Measurements and the Singular Perturbation Technique.

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