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In this article, the consensus, collision avoidance, and distributed convex optimization problems of a class of multi‐agent systems with a time‐varying objective function are studied. Moreover, the proposed method in this article can reduce the chattering problem of the controller input caused by the sign function. First, the sign function is used to design the controller to improve the convergence rate of the system, on this basis, the optimization item is designed for the more complex time‐varying objective function to ensure that the value of the objective function is the smallest when the system achieves the speed consensus. Second, considering the chattering problem caused by the sign function, the designed controller is improved to reduce the chattering phenomenon. Third, two novel Lyapunov functions are constructed to verify the stability of the system and the distributed optimization objective. Due to the controller is designed for the time‐varying objective function, moreover, the tasks of the formation and collision avoidance are needed to take into account, therefore, the designed Lyapunov functions in this article are more difficult. Finally, the formation function is designed to ensure that the multi‐agent system achieves the desired formation configuration. The simulation results show the correctness of the theoretical design of this article and the superiority in extending the running time of the system. [ABSTRACT FROM AUTHOR]

The distributed time‐varying constrained convex optimization problem over a connected undirected network topology is studied in this article. The proposed distributed optimization algorithm is composed of a projection map term, a consensus term, and a gradient term, and is feasible for any initial condition. We first show that the states of the optimization algorithm uniformly converge to a neighborhood of the constraint set while an approximate global consensus is achieved. Then the states are proven to uniformly converge to a neighborhood of the time‐varying optimal trajectory. The theoretical results are validated by some simulations. [ABSTRACT FROM AUTHOR]

The distributed economic dispatch problem for power generation in electricity grids is studies. A simple centralised algorithm is designed to obtain the solution of the dispatch problem without the external disturbances. Inspired by the centralised algorithm, a distributed algorithm is presented using the distributed average tracking algorithm. As far as we know, the proposed algorithm is the first one that is capable of time‐varying loads and external disturbances while the tracking errors are asymptotic convergent. Simulations on the IEEE 14‐BUS system are provided to validate the theoretical results. [ABSTRACT FROM AUTHOR]

In this study, the distributed optimisation problem for linear multi‐agent systems with disturbance rejection is considered. The topology graph is assumed to be uniformly jointly strongly connected and the disturbance is not limited to satisfy the matching condition. Each agent is assigned with a local quadratic cost function and the objective is to minimise the sum of local cost functions based on information exchange. The authors propose a distributed observer for each agent such that other agents' cost functions are obtained. Then, the state feedback and output feedback optimal algorithms are designed based on the output of the distributed observer. The theoretical results are validated by simulations. [ABSTRACT FROM AUTHOR]

Abstract: This paper considers semi‐global robust output regulation problem for a class of singular nonlinear systems whose algebraic equations are not precisely known. Since the algebraic equations are not known, the output regulation problem of singular nonlinear systems cannot be solved by directly reducing the singular nonlinear system into a normal nonlinear system. Based on internal model principle, we convert the robust output regulation problem of singular nonlinear systems into a robust stabilization problem of an augmented singular nonlinear system. The augmented singular nonlinear system is also with unknown algebraic equations. However, without transforming the singular nonlinear system into a normal nonlinear system, it is shown that the augmented singular nonlinear system can be semi‐globally stabilized by a high gain output feedback control law under some reasonable assumptions. Moreover, the semi‐global stabilization control law of the augmented singular nonlinear systems also solves the semi‐global robust output regulation problem of the original singular nonlinear system. [ABSTRACT FROM AUTHOR]

This study considers the cooperative global output regulation problem for a class of non‐linear multi‐agent systems. In particular, the authors consider the case that the exosystem is of a non‐linear form. With a distributed non‐linear observer of the exosystem and the solvability assumption of the regulator equations, the authors convert the problem into a global cooperative stabilisation problem. Sufficient conditions are derived for the global cooperative stabilisation problem under fixed directed network topologies and switching undirected network topologies, respectively. Finally, the validity of the proposed approach is illustrated by simulation results. [ABSTRACT FROM AUTHOR]