Adaptive neural networks control for uncertain parabolic distributed parameter systems with nonlinear periodic time-varying parameter

This paper studies the problem of adaptive neural networks control(ANNC) for uncertain parabolic distributed parameter systems(DPSs) with nonlinear periodic time-varying parameter(NPTVP). Firstly, the uncertain nonlinear dynamic and unknown periodic TVP are represented by using neural networks(NNs) and Fourier series expansion(FSE), respectively. Secondly, based on the ANNC and reparameterization approaches, two control algorithms are designed to make the uncertain parabolic DPSs with NPTVP asymptotically stable. The sufficient conditions of the asymptotically stable for the resulting closed-loop systems are also derived. Finally, a simulation is carried out to verify the effectiveness of the two control algorithms designed in this work.