Design of adaptive block backstepping controllers for uncertain nonlinear dynamic systems with n blocks

Abstract

Based on the Lyapunov stability theorem, a design methodology of adaptive block backstepping control is proposed in this article for a class of multi-input systems with matched and mismatched perturbations to solve regulation problems. The systems to be controlled contain n blocks' dynamic equations, hence n − 1 virtual input controllers are firstly designed so that the state variables of first n − 1 blocks are asymptotically stable if each virtual control input is equal to the state variable of next block. Then the control input is designed in the last nth block to ensure asymptotic stability for the whole state variables even if the perturbations exist. In addition, adaptive mechanisms are embedded in each virtual input function and control input, so that the upper bound of perturbations is not required to be known beforehand. Finally, a numerical example is given for demonstrating the feasibility of the proposed control scheme.

Keywords:

• block backstepping control
• adaptive control
• Lyapunov stability theorem

Acknowledgements

The authors thank the editor, associate editor, and the anonymous reviewers for their many helpful comments and suggestions that have helped to improve the quality of this article. The authors are grateful to the National Science Council of ROC for financial support for this research (NSC 99-2221-E-110-042).