Nonlinear robust optimization of uncertainty affine dynamic systems under the L-infinity norm

In this paper, we discuss robust optimal control techniques for dynamic systems which are affine in the uncertainty. Here, the uncertainty is assumed to be time-dependent but bounded by an L-infinity norm. We are interested in finding a tight upper bound for the worst case excitation of the inequality state constraints requiring to solve a parameterized lower-level maximization problem. In this paper, we suggest to replace this lower level maximization problem by an equivalent minimization problem using a special version of modified Lyapunov equations. This new reformulation offers advantages for robust optimal control problems where the uncertainty is time-dependent, i.e. infinite dimensional, while the inequality state constraints need to be robustly regarded on the whole time horizon.