This paper focuses on the robust output precise tracking control problem of uncertain nonlinear systems in pure-feedback form with unknown input dead zone. By designing an extended state observer, the states unmeasurable problem in traditional feedback control is solved, and the lumped uncertainty, which is caused by system unknown functions and input dead zone, is estimated. In order to apply separation principle, finitetime extended state observer is designed to obtain system states and estimate the lumped uncertainty. Then, by introducing tracking differentiator, a modified dynamic surface control approach is developed to eliminate the 'explosion of complexity' problem and guarantee the tracking performance of system output. Because tracking differentiator is a fast precise signal filter, the closed-loop control performance is significantly improved when it is used in dynamic surface control instead of first-order filters. The L 1 stability of the whole closed-loop system, which guarantees both the transient and steady-state performance, is shown by the Lyapunov method and initialization technique. Numerical and experiment examples are performed to illustrate our proposed control scheme with satisfactory results.where O à 1 represents the estimation of the filter error boundary à 1 ; # 1;2 is the second state of the first employed TD (36); and  1 ; 1 ; ! are the positive constants.

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 neural network 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.

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In this brief, the problems of stability and tracking control for multimotor servomechanism with unmodeled dynamics are addressed by neural active disturbance rejection control. For realizing output feedback, an extended state observer based on high-order sliding mode (HOSM) differentiator is designed to estimate the unmeasured velocity. Moreover, HOSM differentiator is introduced to modify the traditional dynamic surface control method. The designed controller solves the contradiction between rapidness and overshoot, which comes from the traditional proportional-integral-derivative that deals with a large number of practical systems with unknown disturbances. In addition, unknown functions, including friction and disturbances, are approximated by Chebyshev neural networks (CNNs), in which adaptive laws are provided by Lyapunov method. Especially, steady state and transient performance of closed-loop system are maintained by performance function in theoretical analysis. Finally, extensive experimental results are provided to illustrate our proposed approach.Index Terms-Dynamic surface control (DSC), extended state observer (ESO), multimotor servomechanism (MMS), neural networks (NNs), output feedback.