Neural Dynamic Surface Approach to Output of MIMO 

We report an adaptive output feedback dynamic surface control (DSC), maintaining the prescribed performance, for a class of uncertain nonlinear systems with multiinput and multioutput. Designing neuralnetwork observers and modifying the DSC method achieves several control objectives. First, to achieve output feedback control, the finite-time echo state networks (ESN) observer with fast convergence is designed to obtain the online system states. Thus, the immeasurable states in traditional state feedback control are estimated and the unknown functions are approximated by ESN.

Then, a modified DSC approach is developed by introducing a high-order sliding mode differentiator to replace the first-order filter in each step. Thus, the effect of filter performance on closed-loop stability is reduced. Furthermore, the input to state stability guarantees that all signals of the whole closed-loop system are semiglobally uniformly ultimately bounded. Specifically, the performance functions make the tracking errors converge to a compact set around equilibrium. Two numerical examples illustrated the proposed control scheme with satisfactory results