Direct Learning Control of Trajectories Subject to Second-Order Internal Model for a Class of Nonlinear Systems

In this paper, we focus on the direct learning control method for a class of continuous-time nonlinear systems with parametric uncertainties. First, the definitions of direct learning control are introduced. Second-order internal model is used to define the structure of non-repeatable reference trajectories. Then, a direct learning control algorithm is proposed to achieve control objective without iterations. By means of historical control data, direct learning control technique operates in a direct way. In order to achieve a satisfactory tracking performance, the second-order internal model is applied and embedded into the direct learning control law. Finally, the efficacy of the proposed direct learning control algorithm is demonstrated by a single-link robotic manipulator with desired trajectory matching second-order internal model.