Ellipsoidal Calculus for Estimation and Control

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 in this volume 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 may also be interpreted as a generalized technique of the "interval analysis" type with an impact on scientific computation