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This article studies the adaptive prescribed-time control problem for a class of nonlinear systems with unknown time-varying control coefficients. Existing methods for unknown control direction problems can only achieve asymptotic stability based on Barbalat's lemma. Different from these results, we present a new theorem in conjunction with Nussbaum functions to achieve the prescribed-time stability. Meanwhile, the conservative condition of Nussbaum parameters is relaxed under time-varying control coefficients, which increases the applicability of the control algorithm. Based on this theorem, an adaptive prescribed-time control method for high-order nonlinear systems is proposed, which guarantees that the state variables of the system converge to zero in a prescribed time rather than infinity. Finally, theoretical analysis and numerical simulations are provided to validate the effectiveness of the proposed method.

This article is concerned with the distributed leader-following fault-tolerant consensus control problem of uncertain nonlinear delayed multiagent systems with hybrid faults including actuator faults and sensor faults. The faults are described as unknown time-varying functions, which can cause uncertain changes in the fault coefficients of sensors and actuators. In this case, we put forward a novel distributed consensus algorithm. First, we transform the consensus problem into the stability one of a single system by utilizing the sensor fault model and directed topology. Then, the dynamic gain is devised to compensate for uncertain parameters. Based on the backstepping control method, a distributed dynamic controller is designed via measurement data of nonideal sensors. By means of a new Lyapunov function, it is strictly proved that the designed controller can render all agents realizing the full-state consensus in the global sense. Moreover, the proposed algorithm allows that nonlinear dynamics include the state delays, and can be expanded to a fully distributed result. Finally, an example of application in chemical reactor systems is presented to confirm the effectiveness of our theoretical results.

The event-triggered control problem is investigated for nonlinear uncertain systems via a prescribed-time approach. Different from the existing event-triggered control methods that can only achieve bounded or finite-time stability, this article focuses on the prescribed-time stability under the event-based design method. First, a novel prescribed-time stability criterion is presented, which provides explicit theoretical supports and systematic guidelines for addressing the studied problem. Then, we put forward a new method for co-designing the controller and event-triggering mechanism by utilizing the idea of backstepping design. Based on the proposed stability criterion, it is proved that the controller constructed with the new method can regulate the system states to zero in the prescribed-time interval while avoiding the Zeno phenomenon, thus improving the previous prescribed-time stabilization results that are all based on the real-time control signals. Finally, a simulation example is given to show the effectiveness of proposed control strategy.

This article investigates the problem of the fixed directed topology-based leader–following consensus control for nonlinear multiagent systems with output delays. Diverging from existing results, this study focuses on large time-varying output delay. Taking this condition into account, a novel delay classification-based distributed output feedback consensus algorithm is developed. First, we divide the output delay into two types through a designed constant and introduce a switching signal to distinguish these two types. Then, we build a distributed compensator for each follower using relevant outputs to reconstitute the leader–following tracking errors. This compensator relies on the output delay and is irrelevant to the nonlinear dynamics of the system. Then, we design a distributed linear controller for each follower with the compensator's assistance. Subsequently, a new unified Lyapunov–Krasovskii functional is developed to prove that all agents can realize leader–following full-state consensus with the action of the controller. We also provide sufficient conditions to demonstrate the controller's validity. Finally, a simulation example is supplied to validate the efficiency of our algorithm.