Ellipsoidal Techniques: The Problem of Control Synthesis

This paper introduces a technique for solving the problem of control synthesis with constraints on the controls. Although the problem is treated here for linear systems only, the synthesized system is driven by a nonlinear control strategy and is therefore generically nonlinear. Taking a scheme based on the notion of extremal aiming strategies of N.N. Krasovski, the present paper concentrates on constructive solutions generated through ellipsoidal-valued calculus and related approximation techniques for set-valued maps. Namely, the primary problem which originally requires an application of set-valued analysis is substituted by one which is based on ellipsoidal-valued functions. This yields constructive schemes applicable to algorithmic procedures and simulation with computer graphics