Observer-based adaptive backstepping control for Mimo nonlinear systems with unknown hysteresis: a nonlinear gain feedback approach

In this article, an adaptive neural network (NN) control problem is studied for nonstrict-feedback multi-input multi-output (MIMO) nonlinear systems with unmeasurable states and unknown hysteresis. Firstly, to estimate the unmeasurable states, a NN state observer is constructed. Additionally, the unknown nonlinear terms are online approximated by using radial basis function-neural networks (RBF-NNs). And then, the complexity problem is addressed by using the dynamic surface control (DSC), which is easy to overcome the problem of repeated differentiations for virtual control signals. Furthermore, a nonlinear gain feedback function is introduced into the backstepping design procedure to improve the dynamic performance of the closed-loop system. Meanwhile, to satisfy the practical engineering application, a prescribed performance control (PPC) technique is implemented to guarantee the tracking error can converge to a preassigned area. By using the proposed control scheme, all closed-loop signals are semi-global uniformly ultimately bounded (SGUUB). At last, the preponderance and usefulness of the proposed controller are indicated by simulation results.