This paper proposes a wavelet based adaptive backstepping control strategy for a class of uncertain nonlinear systems having composite delay in input. A novel strategy utilizing the delayed wavelet networks is presented to convert a nonlinear system with composite input delay to input delay free system. Delayed Wavelet Neural Networks (DWNN), are also having the similar learning capabilities like their conventional counterparts. 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. The fact that the uncertain time delayed system with the proposed control scheme converges to the small neighborhood of the origin is established through Lyapunov-Krasovskii functional. A numerical example is provided to verify the effectiveness of theoretical development.
Adaptive backstepping control, delayed wavelet networks, time delay systems, Lyapunov - Krasovskii functional
