Optimization-Based Robust Nonlinear Control

摘要

New control algorithms were developed for robust stabilization of nonlinear dynamical systems. Novel, linear matrix inequality-based synthesis algorithms were developed for the anti-windup problem. Results were extended so that they are applicable to all stabilizable linear systems with input saturation. New insights into the closed-loop behavior of model predictive control were discovered. It was shown that certain model predictive control algorithms induce stability without any robustness. Then it was shown how these algorithms can be modified to guarantee robustness. Formulas for horizon length to guarantee robust stabilization were given, and in the process it was shown that many of the standard assumptions in model predictive control could be relaxed. Extremum seeking control algorithms were advanced, and developed for systems with constraints and with nonsmooth response maps. Finally, some initial progress was made on the use of logical elements in nonlinear control algorithms and the understanding of hybrid control systems in general.