Adaptive wavelet sliding mode control of uncertain multivariable nonlinear systems

This paper will address the control problem of unknown, multivariable nonlinear affined systems. We consider integrating the robustness and self-adjustment advantages of sliding mode control (SMC) into the adaptive wavelet controller. The SMC technique is designed such that all the wavelet parameters can be automatically tuned thereby reducing the effect of the approximation errors and disturbances, and to achieve the desired control objective. Then, an adaptive wavelet sliding mode controller (AWSMC) is used to approximate the equivalent control in the neighborhood of the sliding hyperplane with on-line wavelet self-tuning parameters subject to parameter variations in the control object. This approach retains the positive property of the SMC and the wavelet series expansion can be determined systematically by the reaching condition of the SMC. As a result, we simultaneously guarantee the global stability of the closed-loop system and obtain a suitable equivalent control when the nominal mathematical model is unknown in advance. It is shown that the effects of approximation errors and external disturbances can be attenuated to a desired attenuation level by the proposed AWSMC scheme. The simulations of applying the proposed method to a two-link robotic manipulator subject to uncertainties are performed to demonstrate the properties of the developed AWSMC.