Finite Horizon H^∞ Control Problems with Terminal Penalties

We generalize the standard H^∞ control problem to the finite horizon case with two (possibly singular) terminal penalties at the initial and final times. The major objective of the generalization is to increase flexibility of IF controls. Transients in the finite horizon and the terminal penalties are taken into account within the framework of H^∞ control problems. We give a complete solution, a necessary and sufficient condition, and a parameterization to the finite horizon H^∞ control problem. The solution is a natural extension of the “Riccati equation” solution. In the special case, when all the terminal penalties vanish, the solution is reduced to the existing one and to the finite horizon standard H^∞ control problem. Our approach to the problem is based on completing the square argument of a particular quadratic form, which is at least technically different from the previous ones.