Congealed neural network design for uncertain nonlinear spatiotemporal control systems

This note is concerned with the approximation-based adaptive control problem for a class of uncertain nonlinear spatiotemporal systems. A congealed neural network (ConNN) is first proposed to approximate nonlinear spatiotemporal uncertainties arising from system states and time-varying parameters. Unlike conventional NN approximation structures, the ConNN explicitly decomposes the time-varying coupling weight into a congealed weight and a time-dependent perturbation. The congealed weight is estimated using a standard adaptive law for constant parameters, while the residual perturbation is handled within the network structure. To enhance robustness, smooth sliding-mode-like functions are then embedded into the control architecture, effectively attenuating bias terms, particularly in reference tracking scenarios. It is shown that the resulting ConNN-based adaptive controller guarantees adjustable, bounded-error tracking performance, thereby extending the applicability of robust adaptive control to complex spatiotemporal systems and outperforming existing NN-based approaches.