Reducing the computation required to solve a standard minimax problem (Q1911281)

The author considers a minimax optimization problem involving time-dependent matrices. The inner level maximization problem is seen to have its extrema among a very large number of vertices of an uncertainty set. It is shown that this number can be significantly reduced. The outer-level minimization is convex and the problem is solved by using a sequential quadratic programming method. Then the author shows how his results can be used in considering the problem of synthesizing a robust state feedback control for a system with parameter uncertainty. Finally, an illustrative example is considered: a stabilizing state feedback compensator is found for a system depending on 15 uncertain parameters.