Fixed-time cooperative control is currently a hot research topic in multi-agent systems since it can provide a guaranteed settling time, which does not depend on initial conditions. Compared with asymptotic cooperative control algorithms, fixed-time cooperative control algorithms can achieve better closed-loop performance and disturbance rejection properties. Different from finite-time control, fixed-time cooperative control produces the faster rate of convergence and provides an explicit estimation of the settling time independent of initial conditions, which is desirable for multi-agent systems. This paper aims at presenting an overview of recent advances in fixed-time cooperative control of multi-agent systems. Some fundamental concepts about finite- and fixed-time stability and stabilization are first recalled with insight understanding. Then recent results in finite- and fixed-time cooperative control are reviewed in detail and categorized according to different agent dynamics. Finally, this paper raises several challenging issues that need to be addressed in the near future.

Fixed-time and prescribed-time consensus control can bring an explicit estimate of the settling time without dependence on initial conditions, which is important in providing control engineers a priori system information. This article aims at presenting a survey of recent trends and methodologies of fixed-time and prescribed-time consensus control in multiagent systems. First, some typical fixed-time consensus results are reviewed. Despite the advantage in deriving a fixed settling time bound, fixed-time consensus controllers usually result in a conservative estimate of the bound and a large magnitude of initial control input, which in turn show the necessity of designing prescribed-time consensus controllers. Second, characteristics and controller design of (practical, respectively) prescribed-time consensus are provided in detail. Particularly, representative time-varying function-based controllers are presented, by which (practical, respectively) consensus can be achieved in prescribed time. Third, applications of fixed-time and prescribed-time consensus control in mobile robots and smart grids are illustrated in case studies. Finally, several challenging issues in prescribed-time consensus control are discussed for future research.

This paper deals with the problem of distributed optimization for multiagent systems by using an edge-based fixed-time consensus approach. In the case of time-invariant cost functions, a new distributed protocol is proposed to achieve the state agreement in a fixed time while the sum of local convex functions known to individual agents is minimized. In the case of time-varying cost functions, based on the new distributed protocol in the case of time-invariant cost functions, a distributed protocol is provided by taking the Hessian matrix into account. In both cases, stability conditions are derived to ensure that the distributed optimization problem is solved under both fixed and switching communication topologies. A distinctive feature of the results in this paper is that an upper bound of settling time for consensus can be estimated without dependence on initial states of agents, and thus can be made arbitrarily small through adjusting system parameters. Therefore, the results in this paper can be applicable in an unknown environment such as drone rendezvous within a required time for military purpose while optimizing local objectives. Case studies of a power output agreement for battery packages are provided to demonstrate the effectiveness of the theoretical results.

This paper addresses the problem of distributed resilient finite-time control of multiple heterogeneous battery energy storage systems (BESSs) in an islanded microgrid subject to denial-of-service (DoS) attacks. Note that DoS attacks may block information transmission among BESSs by jamming a communication network. A distributed secure control framework is presented by introducing a communication recovery mechanism which can repair the paralyzed topology graphs caused by DoS attacks back into the initial connected graph. Under this framework, a distributed resilient finite-time secondary control scheme is proposed such that frequency regulation, active power sharing and energy level balancing of BESSs can be achieved simultaneously in a finite time, meanwhile, operational constraints can be satisfied at any control transient time. Moreover, based on theoretical analysis, the impact of the duration time of DoS attacks on the convergence time of the control algorithm can be explicitly revealed. Finally, validity and effectiveness of the proposed control scheme are demonstrated by case studies on a modified IEEE 57-bus testing system.

This paper is concerned with bipartite consensus tracking for second-order multi-agent systems with signed directed graphs. A time-varying function based preset-time approach is proposed to realize the convergence in predetermined time. First, a class of time-varying functions with generalized properties are presented. Second, two time-varying function based auxiliaries and a corresponding manifold are constructed. Under a structurally balanced and strongly connected graph, a time-varying function based controller considering the neighboring state is proposed to guarantee that the system trajectory is constrained on the manifold such that bipartite consensus tracking is achieved in preset-time. Third, for first-order multi-agent systems, a preset-time controller is further developed with simplified design. Finally, numerical examples are provided to demonstrate the effectiveness of the proposed controllers.