Ellipsoidal techniques for the problem of control synthesis

This paper introduces a technique for solving the problem of control synthesis for linear systems with constraints on the controls. 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