Abstract
The problem of tracking error constrained adaptive fuzzy output feedback control is investigated for a class of single-input and single-output (SISO) stochastic nonlinear systems with actuator faults, unknown time-delay, and unmeasured states. The considered faults are modeled as both loss of effectiveness and lock-in-place. The fuzzy logic systems are used to approximate the unknown nonlinear functions, and a fuzzy adaptive observer is designed for estimating the unmeasured states. By transforming the tracking errors into new virtual error variables and based on backstepping recursive design technique, a new fuzzy adaptive output feedback control method is developed. It is shown that all the signals of the resulting closed-loop system are bounded in probability and the tracking error remains an adjustable neighborhood of the origin within the prescribed bounds. The simulation results are provided to show the effectiveness of the proposed approach.
Highlights
In recent years, the adaptive fuzzy or neural networks (NN) adaptive control design methods based on Ito’s stochastic differential equation and backstepping design technique have been developed for some unknown stochastic nonlinear systems; see, for example, [1,2,3,4,5,6,7,8,9,10,11]
To handle the actuator faults involved in the considered nonlinear systems, many fault-tolerant control (FTC) design methods have been developed
It should be mentioned that the aforementioned adaptive fuzzy output feedback control design methods have been developed for stochastic nonlinear systems, the unknown time-delay and tracking error constrained are neglected, which usually appear in many industrial control systems and often give rise to undesirable inaccuracy or even affect system stability
Summary
The adaptive fuzzy or neural networks (NN) adaptive control design methods based on Ito’s stochastic differential equation and backstepping design technique have been developed for some unknown stochastic nonlinear systems; see, for example, [1,2,3,4,5,6,7,8,9,10,11]. It should be mentioned that the aforementioned adaptive fuzzy output feedback control design methods have been developed for stochastic nonlinear systems, the unknown time-delay and tracking error constrained are neglected, which usually appear in many industrial control systems and often give rise to undesirable inaccuracy or even affect system stability. To the author’s best knowledge, by far, the prescribed performance design methodology has not been applied to unknown stochastic nonlinear strict-feedback systems with unknown functions, unknown time-delay, actuator faults, and immeasurable states, which is important and more practical, having motivated us for this study. Motivated by the aforementioned observations, in this paper, authors proposed an adaptive fuzzy FTC method for a class of stochastic nonlinear systems with the actuator faults, immeasurable states, unknown time-delay, and tracking error constrained. The proposed adaptive controller can accommodate the actuator faults, and has the robustness to the unknown time-delay. (iii) By introducing predefined performance, the proposed adaptive control method can ensure the closed-loop system to be stable, and guarantee the tracking error to converge to a predefined arbitrarily small residual set
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