Dynamic Sliding Mode Control of Nonlinear Systems Using Neural Networks

In this paper, dynamic sliding mode control (DSMC) of nonlinear systems using neural networks is proposed. In DSMC, the chattering is removed due to the integrator placed before the input control signal of the plant. However, in DSMC, the augmented system has higher order than the actual system, i.e. the states number of the augmented system is higher than the actual system and then to control of such a system, we must know and identify the new states, or the plant model should be completely known. To solve this problem, we suggest two online neural networks to identify and to obtain a model for the unknown nonlinear system. In the first approach, the neural network training law is based on the available system states and the bound of the observer error is not proved to converge to zero. The advantage of the second training law is only using the system’s output and the observer error converges to zero based on the Lyapunov stability theorem. To verify these approaches, Duffing-Holmes chaotic systems (DHC) are used.