This article devotes to solve the fault-tolerant control problem based on interval type-2 (IT2) Takagi-Sugeno (T-S) fuzzy stochastic switched uncertain time-delayed systems with signal quantization. Stochastic switched systems can model a dynamic structure susceptible to abrupt faults, making it more practically significant in power systems or economic systems. The core design is an observer-based fault-tolerant control scheme that can estimate incomplete measurable variables and eliminate the influence of fault dynamically well and enhancing the robust stability of the systems subject to quantization effects. A novel method in seeking the upper bound solution of time-varying delay efficiently decreases conservativeness, especially for the proposed time-delayed system. The simulated analysis is specified to verify the availability and validity of the obtained design method.

Comparing with traditional stochastic differential equations involving white noise, random differential equations (RDEs) with colored noise are claimed to have more practical meaning. This article considers the event-triggered adaptive tracking control for RDE systems with coexisting parametric uncertainties and severe nonlinearities. Combining a tracking error-based dynamic gain with a relative threshold event triggered control mechanism, the tracking control problem for the random systems is solved without Zeno behavior. The tracking error can be rendered small enough by tuning design parameters. First, a series of adaptive control laws are designed by using backstepping technique. Then, two special cases are considered and the main results are extended to MIMO systems. Finally, a simulation example confirms the validity of the results. To the best of the authors’ knowledge, this article serves as the first attempt of event-based control for RDE systems.

This article investigates the bipartite time-varying output formation tracking problem of heterogeneous linear multiagent systems with disturbances by adaptive dynamic event-triggered control. The goal is to make the outputs of all followers complete the preset formation configuration, and track the convex combination composed of the leaders’ outputs at the same time. Distributed dynamic event-triggered compensator is first designed to estimate the convex combination of the leaders’ states, where the internal variable is introduced into the dynamic event-triggered mechanism to dynamically adjust the threshold of each follower. Compared with the traditional static threshold, the time-varying threshold ensures larger adjacent triggering time intervals. Then, the output formation control law based on distributed compensator, compensation input and time-varying formation signal is proposed, where the compensation input provides a degree of freedom for the feasible formation set. Finally, two examples are introduced to verify the main results.

For the nonlinear system with partially unknown dynamic, the problems of fault estimation and fault-tolerant control are considered. A novel adaptive observer is designed to reconstruct the system state, process fault, sensor fault, and the measurement disturbance, simultaneously. The designed observer can be treated as a dynamic proportional-integral observer, where both the output information and the derivative of the output are used, while the output derivative can be unmeasurable. Utilizing the estimation information obtained by the designed observer, a nonlinear fault-tolerant control technique is proposed to stabilize the system. At the end of this article, three examples are listed to verify the proposed method.

This article addresses an adaptive fuzzy control for the nonstrict-feedback nonlinear systems with asymmetric time-varying full state constraints. To prevent the state constraints being violated, the nonlinear state-dependent function (NSDF) is introduced instead of the tradition barrier lyapunov function (BLF). The constrained systems are transformed into a novel free-constrained systems based on the NSDF. A direct approach is given to cope with the state constraints. Fuzzy logic system is utilized to approximate the uncertain nonlinear system functions. The new affine variables are constructed for the transformed systems, and the prior knowledge of the control gains is not required necessarily. Under the designed control scheme, the boundedness of the signals in the closed-loop systems is guaranteed certainly, and the asymmetric time-varying constraints are maintained. This proposed method removes the feasibility condition on the virtual controller derived from the method of BLF. The effectiveness of the proposed control strategy is verified by two simulation examples.

In this paper, fault estimation (FE) and fault-tolerant control (FTC) are investigated for Takagi-Sugeno (T-S) fuzzy systems with multiple time-varying delays as well as actuator and sensor faults. Local nonlinear models and external disturbances are also considered. Inspired by the information from the (k-1)th induction FE, a novel observer is addressed to establish the kth error dynamics. The k-step induction FE observer can weaken the effect from input disturbances caused by the derivatives of actuator faults and can perform better FE subject to sensor and actuator faults and multiple time delays simultaneously. Compared with the existing results, the proposed observer can realistically better show the sizes and shapes of the actuator and sensor faults. In addition, according to online information from the k-step FE, an active dynamic output feedback fault-tolerant controller is proposed to make the closed-loop fuzzy system asymptotically stable. Moreover, the fuzzy Lyapunov-Krasovskii functional is developed by introducing some free-weighting matrices such that the delay dependent sufficient conditions are given in the form of a set of linear matrix inequalities (LMIs) with less conservatism for the existence of observer and fault-tolerant controller. At last, two simulation examples are given to prove the advantages and effectiveness of the approach given in this paper.