Robust H-infinity control and worst-case search in constrained parametric space
Ervan Kassarian, Francesco Sanfedino, Daniel Alazard, Andrea Marrazza
TL;DR
This work addresses robust control under nonlinear constraints in the uncertain-parameter space by leveraging upper-C1 function theory to justify using smooth optimization (SQP) for nonsmooth worst-case problems. It integrates a global exploration stage (PSO or Monte-Carlo) with local SQP-based exploitation, iteratively building an active set of worst-case configurations for robust controller synthesis. The approach is demonstrated on a large flexible spacecraft benchmark with 43 uncertain parameters, showing the method can detect rare worst-case configurations and produce robust controllers with manageable active configuration counts. Overall, the paper provides a scalable, practical framework for constrained robust control that complements traditional methods like μ-analysis and gridding.
Abstract
Standard H-infinity/H2 robust control and analysis tools operate on uncertain parameters assumed to vary independently within prescribed bounds. This paper extends their capabilities in the presence of constraints coupling these parameters and restricting the parametric space. Focusing on the worst-case search, we demonstrate - based on the theory of upper-C1 functions - the validity of using standard, readily available smooth optimization algorithms to address this nonsmooth constrained optimization problem. In particular, we prove that the sequential quadratic programming algorithm converges to Karush-Kuhn-Tucker points, and that such conditions are satisfied by any subgradient at a local minimum. This worst-case search then enables robust controller synthesis: as in the state-of-art algorithm for standard robust control, identified worst-case configurations are iteratively added to an active set on which a non-smooth multi-models optimization of the controller is performed. The methodology is illustrated on a satellite benchmark with flexible appendages, of order 50 with 43 uncertain parameters. From a practical point of view, we combine the local exploitation proposed above with a global exploration using either Monte-Carlo sampling or particle swarm optimization. We show that the proposed constrained optimization effectively complements Monte-Carlo sampling by enabling fast detection of rare worst-case configurations, and that the robust controller optimization converges with less than 10 active configurations.