This paper discusses adaptive control problems of high-order stochastic nonlinear time-delay systems. Compared with the existing results, the considered system involves uncertain parameters, intricate stochastic drift terms and unknown time-varying delays. Based on a modified method of adding a power integrator and Lyapunov-Krasoviskii (L-K) functional technique, new controllers are successfully constructed to achieve the objectives of adaptive stabilization and adaptive tracking, respectively. Examples are given to show the effectiveness of the proposed control strategies.

In this article, the problem of nonfragile finite-time stabilization for linear discrete mean-field stochastic systems is studied. The uncertain characteristics in control parameters are assumed to be random satisfying the Bernoulli distribution. A new approach called the “state-transition matrix method” is introduced and some necessary and sufficient conditions are derived to solve the underlying stabilization problem. The Lyapunov theorem based on the state-transition matrix also makes a contribution to the discrete finite-time control theory. One practical example is provided to validate the effectiveness of the newly proposed control strategy.

This article addresses the practically predefined-time adaptive fuzzy tracking control problem of strict-feedback nonlinear stochastic systems, where the system under consideration includes stochastic disturbances and uncertain parameters. First, in this study, practically predefined-time stochastic stabilization (PPSS) in the $p$ th moment sense is introduced, and a Lyapunov-type criterion for PPSS is proposed to assure the stabilization of the system considered. With these ideas, based on the backstepping design method, a semiglobally practically predefined-time adaptive fuzzy tracking control algorithm is proposed with a fuzzy system used to approximate the unknown part of the system. Moreover, the settling time of the system response can be arbitrarily adjusted in a mean-value sense, and such freedom can be used to improve the stochastic finite-/fixed-time control results. Finally, a practical example and a numerical example of a comparison are provided to validate the effectiveness of the proposed control strategy.

This article focuses on the practically predefinedtime adaptive fuzzy quantized control for nonlinear stochastic systems with actuator dead zone. Fuzzy-logic systems are employed to approximate uncertain nonlinear functions. A novel stochastic predefined-time control scheme is proposed, which can help reduce the control parameters and increase the robustness of the closed-loop system. Taking the quantization and dead zone in the control link into account, the adaptive parameters and a part of the control are used to estimate and compensate the nonlinear disturbance, respectively. In addition, under reasonable assumptions, the complexity of the Lyapunov function compared with conventional stochastic adaptive control is reduced. Based on the stochastic predefined-time stabilization theory, an adaptive fuzzy controller is designed to make the upper bound of the expected settling-time can be arbitrarily configured. Finally, two examples show the effectiveness of the main results.

This article focuses on the event-triggered finite-time adaptive practical tracking control for uncertain nonstrict-feedback nonlinear systems in the presence of time-varying state constraints and external disturbances. First, a disturbance observer is introduced to identify the compounded disturbances which are made up of external disturbances and fuzzy approximation errors. Second, the asymmetric time-varying barrier Lyapunov functions are constructed to guarantee that all the state constraints are not violated. Meanwhile, the finite-time command filters are embedded in the backstepping-based controller design to overcome the explosion of complexity problem. Third, the event-triggered adaptive controller is developed to reduce communication burden based on the relative threshold algorithm. The proposed control strategy can guarantee that the closed-loop system is semiglobally practically finite-time stable, and the tracking error converges to a small residual set in a finite time. Finally, simulation example is included to illustrate the effectiveness of the theoretical results.