Synthesis of worst-case optimal controllers over a finite horizon

Necessary conditions are developed for a finite-horizon version of the H_∞ optimal control problem. Problems involving generalized cost functionals and nonzero initial conditions are considered. A criterion for the evaluation of the performance index is given in these cases. The author´s computational experience shows that the finite-horizon performance is useful in computing the infimal H_∞ norm in the infinite horizon case, as the final time becomes large. Also, expressions are derived for the variation in performance in terms of system parameter variations. These linear expressions are useful in the evaluation of the robustness of the proposed control strategy