Wavelet based adaptive backstepping controller for a class of nonregular systems with input constraints

This paper proposes a wavelet based adaptive backstepping controller for a class of nonlinear, nonregular systems i.e. the nonlinear systems lacking well defined relative degree. The controller is designed to provide the desired performance in presence of actuator constraints. Proposed controller comprises of wavelet based backstepping controller and a robust controller. Wavelet backstepping controller is the principal controller while robust controller is designed to achieve the desired performance by attenuating the effect of approximation error caused by wavelet identifier. Wavelet networks, which are having superior learning capability in comparison to conventional neural network, are used for approximation of unknown system dynamics. Also the adaptation laws are derived in the sense of Lyapunov function and Barbalat’s lemma, assuring the stability of the system. To deal with actuator constraints, the system is augmented with additional dynamics based on the error analysis so as to recover the unconstrained response rapidly while preserving the system stability.