Improving the performance of stabilizing controls for nonlinear systems

There are a variety of tools for computing stabilizing feedback control laws for nonlinear systems. The difficulty is that these tools usually do not take into account the performance of the control, and therefore systematic improvement of an arbitrary stabilizing control law is extremely difficult and often impossible. The objective of this article is to present a design algorithm that addresses this problem. The algorithm that we present iteratively computes a sequence of control laws with increasingly improved performance. We also consider implementation issues and discuss some of the successes and difficulties that we have encountered. Finally, we present a number of illustrative examples and compare our algorithm with perturbation methods