Nonlinear Tracking and Rejection using Linear Parameter-Varying Control

The Linear Parameter-Varying (LPV) framework has been introduced with the intention to provide stability and performance guarantees for analysis and controller synthesis for Nonlinear (NL) systems via convex methods. By extending results of the Linear Time-Invariant framework, mainly based on quadratic stability and performance using dissipativity theory, it has been assumed that they generalize tracking and disturbance rejection guarantees for NL systems. However, as has been shown in literature, stability and performance through standard dissipativity is not sufficient in order to satisfy the desired guarantees in case of reference tracking and disturbance rejection for nonlinear systems. We propose to solve this problem by the application of incremental dissipativity, which does ensure these specifications. A novel approach is proposed to synthesize and realize an NL controller which is able to guarantee incremental stability and performance for NL systems via convex optimization using methods from the LPV framework. Through simulations and experiments, the presented method is compared to standard LPV controller designs, showing significant performance improvements.