Sufficient conditions for H-infinity control on the finite time interval

Abstract

Abstract The article considers a problem of control of linear non-stationary continuous dynamical systems on a finite time interval. It is assumed that information about the linear output of the controlled system is available instead of the full state vector. The problem of the synthesis of H-infinity regulators is formulated. Based on the ideas of the extension principle, sufficient conditions for H-infinity control are formulated and proved, the best control law for an object and the worst control law for external disturbances with full state feedback are found. Since the exact implementation of the obtained control laws in the absence of complete information about the state is impossible, two approaches to the approximate solution of the problem are proposed. Both approaches are associated with finding an estimate of the state vector and using it in control. The first approach is based on the use of pseudoinverse matrices, which allow finding the estimate based on incoming measurements. The second approach utilizes the idea of using asymptotic observers that ensure that the estimation error tends to zero as well as the asymptotic stability of the closed-loop system. The solution of a model example is given, illustrating the application of the proposed approaches.