An application of on-line parametric optimization to task-level learning control

This paper considers a novel statement of task-level learning control problem, which is formulated as an online nonlinear least square parametric optimization problem. The input of the optimized system is the feedforward control sequence, the output is a sampled deviation from the reference motion. In addition to the input vectors, the system output depends on the task parameter vector, which includes initial and desired final coordinates for the system. The task parameter vector changes in the course of the optimization (learning) iterations and is not controlled by the algorithm. The paper surveys the online parametric optimization algorithm and demonstrates its application to the point-to-point vibration-free control of a two-link flexible manipulator arm. The learning is performed in the course of normal operation of the arm, which is simulated to move through a sequence of randomly generated goal configurations. Without any prior knowledge of the system dynamics, the algorithm achieves high-performance control of arbitrary arm motion in about 500 iterations. Residual vibrations are very small for the motion time being only 50% longer than the main mode oscillation period.