Adaptive H₂/H_∞ tracking control for a class of uncertain robotic systems

ABSTRACT

This paper addresses the problem of designing mixed H₂/H_∞ tracking control for a large class of uncertain robotic systems. Nonlinear H_∞ control theory, H₂ control theory and intelligent adaptive control algorithm are combined to construct a hybrid adaptive/robust H₂/H_∞ tracking control scheme. One adaptive neural network system is constructed to approximate the behaviour of uncertain robot dynamics, and the other adaptive control algorithm is designed to estimate the behaviour of the modelled disturbance. Moreover, a robust H_∞ control algorithm is designed to attenuate the effects of the unmodelled disturbance. Only a set of algebraic matrix Riccati-like equations is required to implement the proposed mixed H₂/H_∞ tracking controller, and so an explicit and closed-form solution is obtained. Consequently, the mixed H₂/H_∞ adaptive/robust tracking controller developed here can be analytically computed and easily implemented. Finally, simulations are presented to illustrate the effectiveness of the proposed control algorithm.

KEYWORDS:

• Robotic system
• periodic-disturbances
• mixed H₂/H_∞ control
• hybrid adaptive/robust controller

Acknowledgments

The author would like to thank the Associate Editor and the anonymous reviewers for their valuable comments and suggestions that have improved the presentation of this paper.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work was supported by the National Science Council, Taiwan, R.O.C. [grant number Contract NSC 101-2221-E-168-031].