Adaptive neural network observer-based filtered backstepping control for nonlinear systems with fuzzy dead-zone and uncertainty

This study proposes a high gain observer-based filtered backstepping control scheme for nonlinear systems with unknown dynamics and dead-zone constraint. Majority of the previously papers describe dead-zone by the conventional certain models, assume that all state variables are available and invoke the backstepping or conventional dynamic surface control (CDSC) approaches for controller design. This work describes the dead-zone by the fuzzy model, invokes radial basis function neural network (RBFNN) to model the unknown functions and proposes a RBFNN-based high gain observer to estimate unmeasurable states. To avoid the complexity explosion in the backstepping approach and eliminate the sensitivity to the time-constant of the first-order filters in the CDSC, a nonlinear tracking differentiator (NTD) with finite time convergence property is used instead of the first-order filters in the CDSC to obtain derivative of the virtual inputs. Moreover, the error compensation mechanism and auxiliary signal are proposed to eliminate the influence of the filtering error and input nonlinearity, respectively. Despite the fuzzy dead-zone, the proposed scheme makes the closed-loop signals uniformly ultimately bounded. In comparison with the existing results, (i) some assumptions like certain model of dead-zone and full state measurement are removed, (ii) "explosion of complexity" and sensitivity to the time constant of the first-order filters are eliminated, (iii) effect of the filtering error and input nonlinearity are compensated, (iv) number of adjustable parameters and online computational burden are decreased effectively. Simulation results on the two well-known examples verify the effectiveness and applicability of the proposed new design technique.