A further result of the nonlinear mixed H2/H∞ tracking control problem for robotic systems

Abstract

AbstractThe design objective of a mixed H2/H∞ control is to find the H2 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 H2/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 H2/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. © 2002 John Wiley & Sons, Inc.