The adaptive fuzzy fixed-time fault-tolerant tracking control problem for high-order nonlinear systems (HONS) with sensor and actuator faults is considered in this paper. The fuzzy logic systems is introduced to approximate the unknown nonlinear functions of the HONS. In addition, on the basis of backstepping technology and fixed-time theory, an adaptive fuzzy fixed-time fault-tolerant controller is developed to ensure all signals of the closed-loop HONS to be bounded. Eventually, the numerical example can be shown to prove rationality of developed method.

The problem of adaptive neural fixed-time tracking control for high-order systems is addressed in this article. In order to handle the difficulties from the uncertain nonlinearities within the original systems, the radial basis function neural networks (RBF NNs) are introduced to approximate the unknown nonlinear functions, and the adding a power integrator is applied to overcome the obstacle from high-order terms. It is proven that all signals in the closed-loop system are bounded and the output signal can eventually converge to a small neighborhood of the reference signal. Simulation results further verify the approaches developed.

This paper researches the predefined-time fuzzy adaptive dynamics surface consensus control problem for nonlinear multi-agent systems with input saturation. With regard to nonlinear functions existing in the control systems, fuzzy logic system is employed to estimated them. A novel improved predefined-time dynamics surface filter is designed that can avoid the explosion of complexity problem, and the proposed filter satisfies predefined-time stable simultaneously. With the support of piecewise function, the singularity problem that may exist in virtual controller can be dodged greatly. Furthermore, a ameliorative predefined-time auxiliary dynamic system is presented to cope with input saturation. Combining adaptive backstepping control and predefined-time theory, a predefined-time adaptive fuzzy dynamics surface controller is presented that can assure the systems are predefined-time bounded, though the followers exists in the control saturation. Note to Practitioners —Numerous actual physical systems and devices can be modeled as uncertain nonlinear MAS. Furthermore, MAS also can be widely applied to disaster relief, spacecraft and multitudinous fields. On the one hand, the practical systems may exist in input saturation phenomenon due to human factors and in most of the relevant literatures, which can affect the system performance or bring about instability. On the other hand, the initial values of actual systems usually cannot be chosen freely because of the influence of environment and other factors. In addition, it is currently ordinarily supposed that realize the stabilization of controlled systems when time approaches infinity. Consequently, a predefined-time adaptive fuzzy controller is presented for MAS with control saturation, which can achieve the predefined-time stabilization of MAS.

The issue of predictor-based neural fixed-time dynamic surface control for the nonlinear systems with unknown backlash-like hysteresis is the research focus of this article. By applying the predictor-based neural control scheme, the system nonlinear functions can be smoothly estimated. In addition, an improved dynamics surface is proposed to decrease the difficulty of the controller design procedure while ensuring that the dynamic surface compensating signals can satisfy the fixed-time stability. Further, on the basis of fixed-time theorem and backstepping control technology, the designed controller can ensure all signals of the considered closed-loop systems are fixed-time bounded in the presence of unknown backlash-like hysteresis. Eventually, the simulation cases are given to imply the effectiveness of the designed method.

This article explores the challenge of triggered optimal control for random differential equations (RDEs) with Markovian switching. We initially address the inherent contradiction between whether to comply with or bypass the event-triggered mechanism. By navigating this challenge, we ensure noise-to-state stability (NSS) for RDEs through event-triggered control (ETC). Furthermore, we establish that random nonlinear systems utilizing self-triggered control (STC) can achieve NSS, by setting a minimum triggering time to prevent Zeno behavior. Lastly, by adopting the adaptive dynamic programming (ADP) strategy, we develop self-triggered optimal control for random systems with Markovian switching, ensuring the uniform ultimate boundedness (UUB) of the signals in all closed-loop systems. This article addresses three key gaps in the field of RDE optimal control, contributing substantially to both theoretical and practical advancements. To demonstrate the method’s feasibility, we include a representative example with simulation results.

This research considers the predefined-time adaptive fuzzy formation control issue for high-order nonlinear multi-agent systems. By applying fuzzy logic systems, the systems unknown nonlinear functions can be approximated. To refrain from “explosion of complexity problem”, a novel dynamics surface for high-order nonlinear multi-agent systems is presented. Further, to minimize the communication burden, an event-triggered mechanism suitable for high-order nonlinear multi-agent systems is applied in the control methods. With the help of the backstepping design scheme and the adding power integral method, an adaptive fuzzy predefined-time formation control approach is proposed so that all signals in the considered systems are bounded and realize the desired formation control within predefined time. The illustrative examples are presented to verify the validity of the suggested method.