Robust Control of Uncertain Systems With Nonlinearities Using Model-Based Online Robustness Measure

In this contribution, the dynamics of linear dynamical systems with nonlinearities or of nonlinear systems with structured uncertainties is controlled based on the stability analysis using the interval-analysis set-theoretic approach and combining the approach with online-optimization of the control parameters. For the online-analysis approach, a high-gain Proportional-Integral-Observer (PI-Observer) is used to estimate the model uncertainty. The estimation can be used as an online-measure of the actual model uncertainty bound which is assumed as known for the online interval analysis. Explicit expressions are given for computing the uncertain linear system stability margin in parameter space, which provides a measure of maximal parameter uncertainties preserving stability of uncertain system around known stable nominal system equilibrium. The robust PI-Observer model-based estimations are used as bounds to evaluate the system stability. The optimization of varied control gains can be used for the optimization of the introduced robustness measure, controlling uncertain nonlinear systems. The results show that the introduced new approach gives better results with respect to robustness and control performance than the classical nonlinear control method and the usual robust control method.