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 article deals with the problem of leader-following consensus for multiple wheeled mobile robots. Under a directed graph, a distributed observer is proposed for each follower to estimate the leader state in a fixed time. Based on the observer and a constructed nonlinear manifold, a novel protocol is designed such that the estimated leader state is tracked in a fixed time. Moreover, a switching protocol together with a linear manifold is proposed to ensure that fixed-time leader-following consensus is realized for any initial conditions without causing singularity issues. In contrast to alternative fixed-time consensus protocols in some existing results, the protocol proposed in this article is designed by constructing the nonlinear or linear manifold, which builds a new framework for fixed-time leader-following consensus. Furthermore, the obtained upper bound of settling time is explicitly linked with a single parameter in the protocol, which facilitates the adjustment of the bound under different performance requirements. Finally, the proposed protocol is applied to formation control of wheeled mobile robots.

This paper deals with the problem of environmental monitoring by developing an event-triggered finite-time control scheme for mobile sensor networks. The proposed control scheme can be executed by each sensor node independently and consists of two parts: one part is a finite-time consensus algorithm while the other part is an event-triggered rule. The consensus algorithm is employed to enable the positions and velocities of sensor nodes to quickly track the position and velocity of a virtual leader in finite time. The event-triggered rule is used to reduce the updating frequency of controllers in order to save the computational resources of sensor nodes. Some stability conditions are derived for mobile sensor networks with the proposed control scheme under both a fixed communication topology and a switching communication topology. Finally, simulation results illustrate the effectiveness of the proposed control scheme for the problem of environmental monitoring.

This paper deals with the problem of environmental monitoring by designing and analyzing a cooperative receding horizon temporal logic (CRH-TL) control approach for mobile robot networks. First, a radial basis function network is used to model the distribution of environmental attributes in the monitored environment. On the basis of the established environment model, the problem of environmental monitoring can be formulated as a dynamical optimization problem. Second, an acceptable node set is obtained by enforcing appropriate constraints from linear temporal logic (LTL) specifications on the task of environmental monitoring. Third, by designing a cooperative energy function and using the acceptable node set, the CRH-TL control approach is proposed to generate the movement trajectory of each robot, which satisfies the given LTL specifications while guiding mobile robot networks to trace the peaks of environmental attributes. Finally, the effectiveness of the proposed CRH-TL control approach is illustrated for the problem of environmental monitoring.

This article addresses the problem of cooperative control of double-integrator type multirobot systems. Different from some conventional results with the control gain explicitly known, the control gain in this article is subject to uncertainty. Three different collective behaviors are explored, i.e., leaderless consensus, leader-following consensus, and formation control. For leaderless consensus, a sliding variable is constructed, based on which a novel continuous controller is designed such that the sliding surface is reached in finite-time and thus the state agreement of all agents is realized. For leader-following consensus, two different cases are investigated, i.e., the leader with constant velocity and with time-varying velocity. In both cases, sliding-mode based controllers are developed and corresponding stability conditions are established to ensure that the leader state is tracked by all followers. Finally, the theoretical results are applied to achieve formation control of nonholonomic mobile robots and corresponding experimental studies are conducted to demonstrate the effectiveness of the proposed controllers.

This paper deals with the problem of odor source localization by designing and analyzing a cooperative control framework (CCF) for the particle swarm optimization (PSO) algorithm. The CCF consists of three items: 1) a position coordination item; 2) a velocity coordination item; and 3) a movement direction coordination item. The position coordination item is used to coordinate relative positions between particles and to improve the exploration and exploitation capabilities of particles. The velocity coordination item enables the velocities of particles to reach consensus in order to realize orderly movement behaviors of particles. The movement direction coordination item guides particles to trace plumes and to locate odor sources. Stability of dynamic systems of particles with the proposed CCF is analyzed and the corresponding stability conditions are given such that the functions of three items in the CCF are realized. The orderly movement behaviors of particles under the CCF are also investigated based on benchmark functions. Finally, the effectiveness of the PSO algorithm with the proposed CCF is illustrated for the problem of odor source localization.