Ellipsoidal Calculus for Estimation and Control (Systems & Control: Foundations & Applications) - Hardcover

Kurzhanski, Alexander; Valyi, Istvan

Hardcover

ISBN 10: 0817636994 ISBN 13: 9780817636999

Publisher: Birkhäuser, 1996

Synopsis

It is well known that the emphasis of mathematical modelling on the basis of available observations is first -to use the data to specify or refine the mathematical model, then - to analyze the model through available or new mathematical tools, and further on - to use this analysis in order to predict or prescribe (control) the future course of the modelled process. This is particularly done by specifying feedback control strategies (policies) that realize the desired goals. An important component of the overall process is to verify the model and its performance over the actual course of events. The given principles are also among the objectives of modern control theory, whether directed at traditional (aerospace, mechanics, regula­ tion, technology) or relatively new applications (environment, popula­ tion, finances and economics, biomedical issues, communication, and transport) . Among the specific features of the controlled processes in the mentioned areas are usually their dynamic nature and the uncertainty in their de­ scription.

About this title

Synopsis

This text gives an account of an ellipsoidal calculus and ellipsoidal techniques that allows presentation of the set-valued solutions to these problems in terms of approximating ellipsoidal-valued functions. Such an approach leads to effective computation schemes, an dopens 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. the calculus given here may also be interpreted as a generalized technique of the "interval analysis" type with an impact on scientific computation.

Edition details

• Publisher: Birkhäuser
• Publication date: 1996
• Language: English
• ISBN 10: 0817636994
• ISBN 13: 9780817636999
• Binding: Hardcover
• Number of pages: 336