This article investigates the topic of adaptive tracking consensus for a family of nonlinear multi-agent systems modeled by random differential equations, which are different from well-known stochastic differential equations. This paper provides some primitive results on random nonlinear multi-agent systems. An improved backstepping method named command filtered control is adopted to derive the adaptive control law, where the convergence of the filtering error is guaranteed. To tackle the serious nonlinearities and uncertainties, a series of dynamic gains are introduced in the design process. The tracking errors for each follower concerning the output of the leader can be regulated arbitrarily to a small enough value by choosing appropriate tuning parameters. All signals of the closed-loop system are analyzed to have bounds almost surely. Moreover, the feasibility of the theory developed in this paper is validated by an example of numerical simulation. Note to Practitioners—Inspired by all kinds of biological clustering or grouping behaviors in our natural world, the research on multi-agent systems has long been popular in both theoretical and engineering scenarios. In addition, colored noises are ubiquitous and negligible when dealing with control problems of different engineering plants. Based on the above observation, this paper was motivated to realize the tracking consensus control of a class of nonlinear multi-agent systems disturbed by colored noise, which is also called random nonlinear systems, with the help of an enhanced adaptive backstepping approach called command filtered control. Although there exist nonlinearities and random noises in each follower agent, the objective of output consensus still could be achieved with the combination of the methods of dynamic gains and command filtering. The application potential of this research is considerable, such as drone formation performance and drone cruise. Our future research will further investigate control problems of random nonlinear multi-agent systems under some practical obstacles such as actuator failures.

Random differential equations (RDEs) involving colored noise hold more practical significance than stochastic differential equations (SDEs) driven by white noise. The research on random nonlinear systems is becoming more and more popular. This paper considers the problem of finite-time control for high-order random nonlinear systems with general growth conditions and unknown control coefficients. Based on the backstepping and domination idea, the technique of adding a power integrator is adopted to recursively design an adaptive controller that renders the closed-loop system finite-time stable in probability. This paper serves as a pioneering attempt at finite-time control design of random nonlinear systems. The theoretical results are corroborated by a numerical example.Note to Practitioners—This article was motivated to realize the finite-time stability of high-order random nonlinear systems, even though there are unknown control coefficients in the system. The practical significance of this paper is mainly twofold. Firstly, since random noise is ubiquitous in all kinds of engineering environments, the research on random nonlinear systems driven by colored noise is of great importance. Secondly, the asymptotic stability is infeasible in the practical implementation, so the achievement of finite-time control makes the method proposed in this paper applicable.

This research article considers the subject of finite-time control for a set of uncertain high-order stochastic nonlinear systems (HOSNSs) with unknown time-varying control coefficients. The growth conditions for the uncertain nonlinearities are more inclusive compared to those found in most previous studies. The exponents of high-order systems can take arbitrary rational numbers, which can be represented by two positive odd integers, and they are not all exactly larger than 1. Based on the conventional backstepping idea, the method ofadding a power integratoris adopted to design an adaptive controller that renders the closed-loop system stochastically finite-time stable (SFTS). Due to the general nonlinearities, high-order exponents, and stochastic characteristics, the design process requires more effort, so domination instead of cancellation techniques is used. A simulation example demonstrates the correctness of the theoretical results.

Random nonlinear systems (RNSs) are a class of nondeterministic systems that are distinguished from the intensively studied stochastic nonlinear systems (SNSs). The research on RNSs is becoming more and more popular thanks to its practical significance. To economize communication resources and alleviate network burden, a model-based event-triggered control (MBETC) scheme is applied to a family of RNSs in a strict-feedback fashion. With the help of the adaptive command filtering design technique, all signals of the closed-loop system are rendered ultimately bounded in the mean sense, and the notorious Zeno behavior is circumvented to appear. A simulation example is taken to manifest the validity of the main results.

In this work, we study simultaneous reconstructions of sensor fault and actuator fault, as well as fault-tolerant control (FTC) for nonlinear systems approximated by the T–S fuzzy model. By making the sensor fault as part of the state, a rectangular singular system is firstly given, based on which, a proportional-integral observer (PIO) is synthesized to realize the reconstructions of sensor and actuator faults simultaneously. With the support of these estimation information, an FTC scheme is well provided to maintain the stability of the closed-loop system even in the occurrence of faults. Furthermore, by resorting to linear matrix inequalities (LMIs), the stability criteria are formulated via the fuzzy Lyapunov function method. Finally, the performance of the theoretical result is verified through two real dynamics.

Compared with stochastic differential equations (SDEs) driven by white noise, random differential equations (RDEs) generated by colored noise are claimed to be more practical. This article considers reduced-order high-gain observer (ROHGO)-based neural tracking control on random nonlinear systems having output delay. In order to foster the design and analysis, the estimated states and the estimation errors are scaled by the high gain of the observer. Based on neural network (NN) approximation and state observation, an adaptive controller is designed for the overall system using the backstepping method. It is proved that all the closed-loop signals are bounded almost surely, letting alone the tracking error. By tuning the related design parameters, the asymptotic tracking error could be regulated arbitrarily small. Within the best of our knowledge, this article serves as the first attempt for NN-based control on RDE systems. Finally, the validity of main results is confirmed by a simulation example.

This article deals with delay-dependent H∞guaranteed cost control for uncertain switched Takagi-Sugeno (T-S) fuzzy systems with multiple interval time-varying delays. It is the first time that the fault tolerant control (FTC) of nonlinear systems subject to measurement noise, external disturbances, nonlinear functions, and intermittent faults (IFs) in sensors and actuators is investigated. A passive dynamic full-order output feedback controller is first addressed for the system to guarantee the exponential stability. Compared with the existing results, the restrictions on the multiple time-varying delays are relaxed in the derivation of this work. The suggested controller has a wider application. Moreover, as the piecewise fuzzy Lyapunov function is introduced with some slack matrices, the delay-dependent sufficient conditions are provided in the way of a cluster of linear matrix inequalities (LMIs) and then less conservatism is attained by our design contrast to the existing fault tolerant controllers. At last, two simulation examples and some comparisons are achieved to illustrate the novelty and feasibility of the method gathered in the article.