Synthesis of Suboptimal H ∞ Controllers over a Finite Horizon

In this chapter a finite horizon H_∞ optimal control problem is posed and solved. A criterion which is useful for the evaluation of the infimal H_∞ norm in the finite horizon case is given. Also, a differential equation is derived for the measure of performance in terms of the final time. 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. Also, a criterion that yields the actual performance of the suboptimal controller is given. 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.