A novel approach to neuro-sliding mode controllers for systems with unknown dynamics

In this paper we propose a neural network controller, which has a single neuron with a linear activation function, namely adaline, which uses backpropagation algorithm for online training and works as a sliding mode controller which pushes the system to a certain sliding manifold. We prove that the controller is robust to parameter changes and to the uncertainties in the disturbance and the system is always stable with zero steady state error for bounded disturbance. Different from the works done until now, in this work we do not deal with the estimation of the equivalent control but instead, feeding an appropriate error function to the network and using backpropagation, i.e. gradient descent algorithm, we directly calculate the necessary control input. Initially a controller structure is proposed and in the proceeding sections an improved version is added. Simulation results are provided that verifies the success of the algorithm.