SYNTHESIS OF SUBOPTIMAL H-INFINITY CONTROLLERS OVER A FINITE-HORIZON

In this paper a finite horizon H(infinity) optimal control problem is posed and solved. It is shown by way of examples that the finite horizon performance is useful for the fast computation of the infimal H(infinite) norm in the infinite interval case. Also, a differential equation is derived for the measure of performance. A general suboptimal control problem is then posed and an expression for a suboptimal controller is derived solving the saddle point conditions. An expression for a feedback controller can be derived by solving a dynamic Riccati equation. In the time-invariant case, the finite horizon controller converges to a static controller as the final time becomes large. Examples are given to illustrate the usefulness of the theory.