Ellipsoidal Calculus for Estimation and Control [Paperback]

This book gives an account of an ellipsoidal calculus and ellipsoidal techniques developed by the authors. 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.

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.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: Tl³V