Distributed fixed‐time optimization for multi‐agent systems with time‐varying objective function

Abstract

In this article, a distributed time-varying convex optimization problem for multi-agent systems is studied. The goal of this article is to use only the local information and interaction information of each agent to drive all agents to achieve consensus and minimize the time-varying global objective function within a fixed time. In order to solve this problem, a centralized fixed-time algorithm based on predictive correction method is proposed, which can optimize the time-varying global objective function based on global information within a fixed time. Then, based on the distributed average tracking method, the centralized algorithm is improved to a distributed fixed-time algorithm based on local information. The theoretical analysis ensures that the algorithms in this article can solve the time-varying optimization problem in a fixed time, and numerical examples are proposed to verify the effectiveness of algorithms. Finally, the distributed algorithm is applied to solve battery packages problem.

Fixed-Time Distributed Time-Varying Optimization for Nonlinear Fractional-Order Multiagent Systems with Unbalanced Digraphs

“…Designing fixed-time distributed optimization algorithms that are independent of any initial states is required. So far, little work about the fixed-time distributed optimization problem of MASs [16][17][18][19] has been addressed by utilizing the idea of fixed-time stability [20]. Note that, all the aforementioned finite-and fixed-time optimization algorithms have some constraints, i.e., each local cost function and its gradient are respectively required to be (strongly) convex and/or Lipschitz, and the agents' topology is considered to be undirected.…”

“…(4) Time-Varying Local Cost Functions: Furthermore, while time-varying local cost functions are frequently used in applications like monitoring a time-varying optimal solution, the studies listed above primarily focus on the distributed optimization issue using time-invariant local cost functions. The authors of [11,13,15,19,28,36,37] study the distributed optimization problem with time-varying local cost functions, also known as the distributed time-varying optimization problem, which is more challenging to solve because its optimal point (trajectory) may be time-varying. A connectivity-preserving optimization algorithm is developed in [11] to make all agents achieve consensus within a finite-time and the consensus values converge to a time-varying optimal trajectory asymptotically.…”

“…A connectivity-preserving optimization algorithm is developed in [11] to make all agents achieve consensus within a finite-time and the consensus values converge to a time-varying optimal trajectory asymptotically. Via distributed average tracking, some optimization algorithms are designed to cooperatively minimize the sum of time-varying local cost functions within a finite time in [15] and within a fixed time in [19]. At present, there are several limitations in the aforementioned distributed time-varying optimization problems.…”

“…At present, there are several limitations in the aforementioned distributed time-varying optimization problems. For example, the considered network topologies in [11,13,15,19,28,37] are undirected and the designed algorithms in [11,13,28,37] can only achieve asymptotic convergence. Moreover, the authors in [11,15,19,28,37] only consider the integrator-type agent dynamics, each time-varying local cost function and its Hessian are forced to be convex and invertible in [11,13,37], respectively.…”

“…(1) A fixed-time optimal convergence protocol independent of any initial states is designed; this is different from the designed asymptotic optimal convergence protocols in [5,30,37], and the finite-time optimal convergence protocols in [3,14,15] depen-dent of initial states. However, the fixed-time optimal convergence protocols are designed in [16][17][18][19], where the considered topologies among agents are undirected. (2) A weight-unbalanced directed topology without employing certain additional information is considered, which includes the undirected topologies considered in [8,16,18], weightbalanced directed topologies in [19,21,30], and weight-unbalanced directed topologies, and employs certain additional information in [23][24][25][26] as its special cases.…”