Control of Uncertain Plants with Unknown Deadzone via Differential Neural Networks

This paper deals with the problem of trajectory tracking for an ample class of SISO uncertain nonlinear systems subject to symmetric deadzone input. The deadzone is modeled as a combination of a linear term and a disturbance-like term. Based on this model, a differential neural network is employed in order to identify the uncertain dynamics. By using a Lyapunov-like analyses, the asymptotic converge of the identification error to a bounded zone is demonstrated. Next, by a proper control law, the state of the neural network is compelled to follow a bounded reference trajectory. We prove that the difference between the state of the neural identifier and the reference trajectory converges exponentially to zero. Thus, the asymptotical convergence of the tracking error to a bounded zone and the boundedness of all closed-loop signals are guaranteed. Since this control strategy requires the knowledge of a bound for an uncertainty/disturbance term, a systematic procedure is provided in order to find such bound. A simulation example confirms the workability of the suggested approach.