A Further Result of the Nonlinear Mixed H_2/H_∞ Tracking Control Problem for Robotic Systems

摘要

The design objective of a mixed H_2/H_∞ control is to find the H_2 optimal tracking control law under a prescribed disturbance attenuation level. With the help of the technique of completing the squares, a further result of the mixed H_2/H_∞ optimal tracking control problem is presented, by combining it with standard LQ optimal control technique. In this paper, only a nonlinear time-varying Riccati equation is required to solve the problem in the design procedure―instead of two coupled nonlinear time-varying Riccati equations, or two coupled linear algebraic Riccati-Iike equations―with some assumptions made regarding the weighting matrices in the existing results. A closed-form controller for the mixed H_2/H_∞ robotic tracking problem is simply constructed with a matrix inequality check. Moreover, it shows that the existing results are the special cases of these results. Finally, detailed comparison is performed by numerical simulation of a two-link robotic manipulator.