A Globally Stable Adaptive Controller for the Human Shank Dynamics

Abstract

In this paper, we propose a globally stable adaptive controller for the human shank motion tracking problem that appears in neuromuscular electrical stimulation systems. The control problem is complicated by the fact that the mathematical model of the human shank dynamics is nonlinear and the parameters enter in a nonlinear and nonseparable form. To solve the problem, we first derive a nonlinearly parameterized regressor equation (NLPRE) that is used with a new parameter estimator specifically tailored for this NLPRE. This estimator is then combined with a classical feedback linearizing controller to ensure the tracking objective is globally achieved. A further contribution of the paper is the proof that parameter convergence, and consequent global tracking, is guaranteed with an extremely weak interval excitation requirement. A simulation study comparing the proposed adaptive controller with existing ones in the literature shows comparable human shank tracking performance but with fewer parameter estimates and without requiring knowledge of bounds for the unknown parameters.