H(Infinity) Optimal Control Theory Over a Finite Horizon.

In this report a finite horizon H infinity optimal control problem is treated. Results guaranteeing the existence of a unique optimal control and the worst exogenous input are derived. A criterion for the evaluation of the infimal H infinity norm is then given in terms of the least positive value for which a certain boundary value problem has a nontrivial solution. Once the infimal value is known, a noninfimal value can be selected and suboptimal H controllers can be synthesized. The problem of synthesizing suboptimal H controllers is also considered in a very general case. Without making use of any transformations, expressions for the output feedback controller are derived in terms of solutions of two dynamic Riccati equations. In the time-invariant case, the solutions of these equations usually converge to constant matrices.