This paper investigates fuzzy adaptive actuator failure compensation control for a class of uncertain stochastic nonlinear systems in strict-feedback form. These stochastic nonlinear systems contain the actuator faults of both loss of effectiveness and lock-in-place, unmodeled dynamics, and without direct measurements of state variables. With the help of fuzzy logic systems to approximate the unknown nonlinear functions, a fuzzy state observer is established to estimate the unmeasured states. By introducing the dynamical signal and the changing supply function technique design into the backstepping control design, a robust adaptive fuzzy fault-tolerant control scheme is developed. It is proved that the proposed control approach can guarantee that all the signals of the closed-loop system are bounded in probability in the presence of the actuator failures and the unmodeled dynamics. Simulation results are provided to show the effectiveness of the control approach.

Fuzzy Adaptive Actuator Failure Compensation Control of Uncertain Stochastic Nonlinear Systems With Unmodeled Dynamics

This paper presents an adaptive output-feedback neural network (NN) control scheme for a class of stochastic nonlinear time-varying delay systems with unknown control directions. To make the controller design feasible, the unknown control coefficients are grouped together and the original system is transformed into a new system using a linear state transformation technique. Then, the Nussbaum function technique is incorporated into the backstepping recursive design technique to solve the problem of unknown control directions. Furthermore, under the assumption that the time-varying delays exist in the system output, only one NN is employed to compensate for all unknown nonlinear terms depending on the delayed output. Moreover, by estimating the maximum of NN parameters instead of the parameters themselves, the NN parameters to be estimated are greatly decreased and the online learning time is also dramatically decreased. It is shown that all the signals of the closed-loop system are bounded in probability. The effectiveness of the proposed scheme is demonstrated by the simulation results.

Output-Feedback Adaptive Neural Control for Stochastic Nonlinear Time-Varying Delay Systems With Unknown Control Directions

This paper presents a saturated Nussbaum function based approach for robotic systems with unknown actuator dynamics. To eliminate the effect of the control shock from the traditional Nussbaum function, a new type of the saturated Nussbaum function is developed with the idea of time-elongation. Moreover, by exploiting properties of the proposed Nussbaum function, a promising theorem is established to deal with unknown multiple actuator nonlinearities. In what follows, the proposed theorem is integrated with the adaptive control technique such that the stability analysis of the robotic system is completed. It thus guarantees that the state of the robotic system asymptotically converges to the desired trajectory. Finally, comparative studies are carried out to validate the effectiveness and the superiority of the proposed approach.

Saturated Nussbaum Function Based Approach for Robotic Systems With Unknown Actuator Dynamics

This paper investigates the problem of output feedback adaptive stabilization for a class of nonstrict-feedback stochastic nonlinear systems with both unknown backlashlike hysteresis and unknown control directions. A new linear state transformation is applied to the original system, and then, control design for the new system becomes feasible. By combining the neural network’s (NN’s) parameterization, variable separation technique, and Nussbaum gain function method, an input-driven observer-based adaptive NN control scheme, which involves only one parameter to be updated, is developed for such systems. All closed-loop signals are bounded in probability and the error signals remain semiglobally bounded in the fourth moment (or mean square). Finally, the effectiveness and the applicability of the proposed control design are verified by two simulation examples.

Adaptive Neural Output Feedback Control for Nonstrict-Feedback Stochastic Nonlinear Systems With Unknown Backlash-Like Hysteresis and Unknown Control Directions

Observer-based fuzzy adaptive prescribed performance tracking control for nonlinear stochastic systems with input saturation

This study focuses on the problem of adaptive neural control for a class of uncertain non-affine stochastic non-linear systems with time-varying delay. Major technical difficulties for this class of systems lie in: (i) the unknown control direction embedded in the unknown control gain functions and (ii) the unknown system function with unknown time-varying delay. A novel Razumikhin–Nussbaum lemma is proposed to overcome the mentioned difficulties. Moreover, based on the Razumikhin functional approach, an adaptive neural controller is developed for this class of systems by exploring the application of Nussbaum functions to stochastic non-linear systems. The proposed design guarantees that all the error variables in the closed-loop systems are four-moment semi-globally uniformly ultimately bounded in a compact set, while the tracking error remains in a neighbourhood of the origin. The effectiveness of the proposed design is verified by simulation results.

Adaptive neural control for a class of non-affine stochastic non-linear systems with time-varying delay: A Razumikhin-Nussbaum method

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Adaptive neural control for a class of non-affine stochastic non-linear systems with time-varying delay: A Razumikhin-Nussbaum method