Adaptive Fault-Tolerant Control for Pure-Feedback Stochastic Nonlinear Systems with Sensor and Actuator Faults

In this article, for a class of stochastic pure-feedback nonlinear systems with simultaneous actuator and sensor faults, the problem of adaptive fault-tolerant control is examined. The stochastic pure-feedback nonlinear system is first converted into a strict-feedback by applying the mean value theorem and radial basis function neural networks are used to approximate the unknown functions. Only one adaptive parameter needs to be calculated online rather than the actual weight vector elements by determining the greatest value of the norm of the neural network weight vector. With the help of regrouping and parameter separation methods, the unavailability of state variables caused by sensor faults is addressed. The Lyapunov function methods and the backstepping recursive design technique are used to design an adaptive fault-tolerant controller. It is shown that by choosing proper the design parameters, the tracking errors converge to a small region of the origin, and all the signals in the closed-loop system are bounded in probability. The performance of the proposed controller is illustrated using a numerical example and a real-world example of a rigid robot manipulator system.

Automated summary

In this article, the problem of adaptive fault-tolerant control for a class of stochastic pure-feedback nonlinear systems with simultaneous actuator and sensor faults is examined. The stochastic pure-feedback nonlinear system is converted into a strict-feedback system using the mean value theorem, and unknown functions are approximated using radial basis function neural networks. By determining the greatest value of the norm of the neural network weight vector, only one adaptive parameter needs to be calculated online. The unavailability of state variables caused by sensor faults is addressed using regrouping and parameter separation methods. The Lyapunov function methods and backstepping recursive design technique are used to design an adaptive fault-tolerant controller, which ensures convergence of tracking errors and boundedness of all signals in the closed-loop system.