Stable emotional adaptive neuro-control of uncertain affine nonlinear systems with input saturation

Emotional controllers have been successfully pursued toward various control objectives in the past two decades, but there remain considerable challenges in exploiting their theoretical and cognitive aspects. This paper addresses these two challenges by proposing a modified thalamic connection based on an averaging operator using a radial basis emotional network (RBEN-ATC). From a theoretical perspective, we prove that the resulting RBEN-ATC mapping has the universal function approximation property. It also becomes continuous and differentiable with respect to the network weights. We then incorporate this structure to approximate the unknown dynamics of a nonlinear affine system with nonsymmetric input saturation and develop a stable adaptive radial basis emotional controller (ARBEC). From a cognitive perspective, we stay committed to the fundamental laws of the emotional brain. While this standpoint considerably complicates the design process, the resulting control system becomes interpretable from a biological perspective. For these purposes, a two-prong approach is employed here. Firstly, we incorporate a first-order compensator that handles the errors due to the nonsymmetric actuator saturation with unknown bounds. Secondly, we use a robust adaptive compensator that lessens the effect of uncertainties. Lyapunov stability analysis shows the overall ARBEC closed-loop stability of the nonlinear system. Furthermore, comparisons with other competing neuro- and fuzzy approaches show that ARBEC has better noise rejection and steady-state tracking while having comparable control energy consumption.