Adaptive fixed‐time tracking control for stochastic pure‐feedback nonlinear systems

Abstract

The article discusses the adaptive fixed-time control problems for the stochastic pure-feedback nonlinear systems. Different from the existing results, the priori information of unknown virtual control coefficients (UVCC) is no longer needed in this article, which is realized by emplying the bound estimation method and well-defined smooth functions. A novel semi-global practical fixed-time stability criterion for the stochastic nonlinear systems is presented. Correspondingly, a new construction of Lyapunov function is proposed for the nonlinear stochastic system by adding the lower bounds of the UVCC. Based on the fuzzy logical system and fixed time stability theorem, a novel adaptive fuzzy fixed-time tracking control algorithm for stochastic nonlinear system is raised firstly. By theoretical analysis, we can conclude that the whole variables of the controlled system are bounded almost surely and the output can track the desired reference signal to a very small compact set within a predefined fixed-time interval. Finally, the raised method is illustrated by two simulation examples.

Adaptive predefined‐time tracking control for high‐order strict‐feedback nonlinear systems with unknown mismatched disturbances

“…Remark Compared with recent adaptive tracking control and finite‐time (fixed‐time) control schemes, like References 18, 19, 28, 29, and 31, our method can achieve trajectory tracking with a predefined convergence bound of tracking error in a predefined time, and the given time can be chosen arbitrarily in advance and independent of the initial states. Compared with recent predefined‐time control like References 36, 39, and 41, unknown mismatched disturbances can be tackled, and it is no longer a hold‐up in the predefined tracking control problem.…”

“…In Reference 30, fixed‐time stabilization was presented, where the convergence time is independent of initial conditions. A fixed‐time controller of stochastic nonlinear systems was designed by introducing a fixed‐time stability theorem in Reference 31. However, the regulation time in finite‐time and fixed‐time control may not be chosen arbitrarily, and it is difficult to select maximum convergence time or regulation time by adjusting the parameters of control systems 32 …”

Adaptive practical fixed‐time tracking control for uncertain non‐strict‐feedback systems with input delay and prescribed boundary constraints

“…Since θj θ3 j = θj (𝜃 3 j − 3𝜃 2 j θj + 3𝜃 j θ2 j − θ3 j ), combining with (47), then (46) can be obtained…”

Incipient fault prediction for nonlinear stochastic distribution systems

“…In References 17 and 18, asynchronous control methods were proposed for Markovian jump systems. In References 19‐25 some other methods are proposed for the control problem of stochastic systems. Observers are designed for fault detection in stochastic systems in References 26‐28.…”