Evolving granular feedback linearization: Design, analysis, and applications

Abstract

Exact feedback linearization is a method for nonlinear control which amounts to cancel the nonlinearities of a nonlinear system such that the resulting closed-loop dynamics is linear. The effectiveness of exact feedback linearization relies on a precise description of the system nonlinearities. This paper suggests a novel robust control approach for adaptive control of nonlinear systems called robust granular feedback linearization. The approach employs an instance of evolving the participatory learning algorithm to continuously estimate unknown nonlinearities and cancel their effects in the control loop. Under mild conditions, the robust granular feedback linearization is ensured to be Lyapunov stable by using convex methods. Simulation experiments with a surge tank is used to evaluate and to compare the performance of the robust granular feedback linearization against exact feedback linearization and an adaptive controller based on bacterial foraging. The results indicate that the robust granular feedback linearization outperforms both, the exact and the adaptive foraging controllers. The effectiveness of robust granular feedback linearization is further testified in an actual surge tank control system application.