The fixed-time formation control problem for uncertain nonlinear multiagent systems (MASs) with time-varying actuator failures is investigated. Actuator failures would have a huge impact on the system performance, especially when the actuator failures are time-varying, which may even cause system insecurity. In order to cope with time-varying actuator failures, a fixed-time convergence approach is proposed based on adaptive fuzzy control technology. Simultaneously, solving the above problems would aggravate the occupation of communication resources of the system. Therefore, a periodic adaptive event-triggered control scheme is developed, in which the triggering period can be adjusted adaptively. Furthermore, the convergence time of formation errors can be preset by applying the fixed-time control method. The convergence velocity can be accelerated immensely. Eventually, theoretical analysis and simulation illustrate that the proposed method can effectively compensate the time-varying actuator failures, and the MASs can achieve formation within a fixed time by using less communication resources.

This paper studies the leader-following consensus problem for a class of strict-feedback multiagent systems with unknown nonlinearities and state time-delays under directed topology. By using the backstepping technique, an adaptive consensus control protocol is proposed, where neural networks are employed to neutralize uncertain nonlinearities. To eliminate the effects of time-delays, Lyapunov-Krasovskii functionals, and Young's inequalities are used in the design process. It is notable that the computation burden is dramatically alleviated by proposing a novel adaptive mechanism. For communication topology containing a spanning tree, the proposed controller guarantees that the consensus tracking error will converge to an adjustable neighborhood of the origin. Finally, a numerical example is provided to validate the effectiveness of our result.

As the control tasks become complex, fulfilling such tasks cooperatively is the first choice in practice. In this article, the output consensus problem of heterogeneous multiagent systems is studied by deploying distributed observers in follower agents. Each observer in the follower only measures part of the leader’s output, which relieves the burden of a simple agent when the leader’s output is of large-scale dimensions. Then, all followers in the system work cooperatively to estimate the full state of the leader. By using parameterized Riccati equation and output regulation theory, sufficient conditions are given to design the distributed observers and the output consensus protocol. Finally, a numerical example is conducted to verify the obtained result.

In our recent work, we propose an indirect adaptive fuzzy control scheme for uncertain unparametrizable nonlinear systems, which ensures that the number of adaptive laws does not increase with the number of fuzzy rules, and the time derivative of the chosen Lyapunov function is negative semidefinite. However, the scheme involves a class of high-order smooth functions and their time derivatives, which can make the controller structure become sophisticated especially when the relative degree of system is quite large. To overcome this problem, in the article, we propose a new direct adaptive fuzzy control scheme based on a class of reduced-order smooth functions. With the scheme, no partial-derivative term is involved in controller and virtual controllers, only one adaptive law is used regardless of the increase of fuzzy rules, and also the time derivative of Lyapunov function can be ensured negative semidefinite. It is proved that all closed-loop signals are bounded, and the output tracking error converges to a prescribed interval asymptotically. The transient tracking performance and robustness of the proposed control scheme are also considered. The effectiveness of the obtained results is illustrated by two practical control systems.