Recursive direct learning of control efforts for trajectories with different magnitude scales

Abstract

Direct learning control (DLC) schemes have been developed recently to address non-repeatable trajectory tracking problems. Unlike conventional iterative learning schemes, DLC schemes learn a set of unknown basis function vectors which can be used to generate the desired control profile of a new trajectory. DLC schemes use al available trajectory tracking information to obtain the unknown basis function vectors in a Least Squares and pointwise manner. A drawback of DLC is that the inverse matrix calculation is inevitable, which is time consuming and may result in singularities due to the batch processing nature. A Recursive Direct Learning Control method is proposed which learns the basis function vectors meanwhile overcomes the implementation difficulties in DLC schemes. The focus of this paper is on learning the control profile of trajectories with same operation period but different magnitude scales. The recursive learning method makes use of one trajectory information at a time, thus avoids the batch processing. The scheme is first developed for a class of nonlinear time varying systems and then extended to cover more general classes of nonlinear systems including robotic manipulator dynamics. Extensive simulation results on a two-link robotic model are provided to confirm the features of the proposed algorithm.