Stability regions for constrained nonlinear systems and their functional characterization via support-vector-machine learning

Abstract

This paper develops a computational approach for characterizing the stability regions of constrained nonlinear systems. A decision function is constructed that allows arbitrary initial states to be queried for inclusion within the stability region. Data essential to the construction process are generated by simulating the nonlinear system with multiple initial states. Using special procedures based on known properties of the stability region, the state data are randomly selected so that they are concentrated in desirable locations near the boundary of the stability region. Selected states belong either to the stability region or do not, thus producing a two-class pattern recognition problem. Support vector machine learning, applied to this problem, determines the decision function. Special techniques are introduced that significantly improve the accuracy and efficiency of the learning process. Numerical examples illustrate the effectiveness of the overall approach.