Robust Adaptive Nonlinear Controller for Robotic Systems: Linear Matrix Inequality Approach

In this paper the tracking problem of a robotic system with model uncertainty is considered via an application of the H_∞ control theory for nonlinear systems. In particular, we develop a state feedback controller which yields a global exponential stability of the underlying system and provides the closed loop system with relatively low gains. The main ingredient which facilitates our development is the choice of a particular storage function (which serves as a Lyaponov function). This particular storage function leads to certain linear matrix inequalities, the solution of which yields the desired controller. Moreover, the resulting LMIs (Linear Matrix Inequalities) turn out to be of the same form of the LMIs achieved in the analogous linear case. Simulation results and implementation of the control algorithm in a two-degree of freedom robot illustrate the controller efficiency.