Dynamic Sliding Mode Control of Nonlinear Systems Using Neural Networks

Dynamic sliding mode control (DSMC) of nonlinear systems using neural networks is proposed. In DSMC the chattering is removed due to the integrator which is placed before the input control signal of the plant. However, in DSMC the augmented system is one dimension bigger than the actual system i.e. the states number of augmented system is more than the actual system and then to control of such a system, we must to know and to 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 observer error is not proved to converge to zero. The advantageous of the second training law is only using of the system output and the observer error converges to zero based on the Lyapunov stability theorem. To verify these approaches Duffing-Holmes chaotic systems (DHC) is used.