A Robust Optimal Nonlinear Control for Uncertain Systems: Application to a Robot Manipulator

The aim of the paper is twofold. Firstly, in this paper we are interested in control design for a class of uncertain MIMO linear systems. Specifically, we deal with trajectory tracking problems. Using the explicit nonlinear control law developed by Leitmann and co-authors during 1980s, the contribution of this paper is to elaborate upon useful closed-loop properties: (i) robustness, namely how to dominate the negative effect of the uncertainty; (ii) optimality with respect to an infinite time-horizon cost function; (iii) state estimation, ensuring uniform boundedness of the error between real and estimated states. Towards practical implementation, the control designer can choose to tune the nonlinear control law parameters based on robustness or optimality requirements. This flexibility distinguishes this article from others in the literature. The second aim of this paper is to apply, in particular, the aforementioned theoretical results on a two degree-of-freedom, rigid link, robot manipulator. Our intention is to contribute to the need for advanced model-based robot control.