On the stabilization of forking and cyclic trajectories for nonlinear systems⋆

Abstract

Stabilizing a reference trajectory for a nonlinear system is a common, non-trivial task in control theory. An approach to solve this problem is to approximate the nonlinear system along the trajectory as an uncertain linear time-varying one, and to solve an optimization problem featuring Linear Matrix Inequality (LMI) constraints to derive a stabilizing, smooth, gain-scheduled control law. Such an approach is extended here by considering a set of reference trajectories instead of a single one, such that switching among them is permitted. These switching events are commonly encountered in industrial plants, such as energy generation systems, and are of high relevance in practice. The approach allows one to derive a gain-scheduled control law guaranteeing asymptotic stability also during the switching and accounting for the linearization errors. Simulation results on a chemical system highlight the effectiveness of the method.