Abstract
For the state consensus tracking of the singular multi-agent system, under the condition of the communication topology randomly switching only along time axis but unchanging along iteration axis, a distributed iterative learning control protocol is proposed. By singular value decomposition method, the singular multi-agent system is transformed into differential algebra system, and thus the state of the system is accordingly divided into two parts. Then applying the derivative of the tracking error for the first part of the state and the tracking error of the second part of the state and combining the switching topology graph, the distributed iterative learning control protocol is constructed. Furthermore, the convergence of the proposed algorithm is proved by the compression mapping method, and the convergence conditions of the algorithm are obtained. The proposed algorithm can make the state gradually approach the desired state with the increase of iterations. When the number of iterations is sufficient large, the state of each agent can completely track the desired state over a finite time interval. Finally, the simulation examples are given to further validate the effectiveness of the proposed algorithm.
Highlights
Coordination control for multi-agent systems has received considerable attention in recent years, and its research results have a wide range of application in such many engineering fields as micro-grid system [1], UAV formation control [2], multi-robot cooperation [3], sensor network [4], and so on
In order to solve the problem of state consensus tracking of singular multi-agent systems with random switching topology, under the assumption that the topology is randomly switched along the time axis and unchanged along the iteration axis, a distributed iterative learning control protocol is proposed
SIMULATION ANALYSIS In order to validate the effectiveness of the proposed algorithm, we consider a singular multi-agent system consisting of one virtual leader and four agents which have the same structure, where the communication topology of the system can switch randomly within the time domain but can’t change within the iteration domain
Summary
Coordination control for multi-agent systems has received considerable attention in recent years, and its research results have a wide range of application in such many engineering fields as micro-grid system [1], UAV formation control [2], multi-robot cooperation [3], sensor network [4], and so on. [23] proposed a distributed adaptive iterative learning control method, which solved the problem of consensus tracking of high-order nonlinear multi-agent systems. In [24], in order to solve the consensus tracking problem of continuous-time linear multi-agent systems, an input-sharing iterative learning control protocol was designed to improve the convergence speed of the learning controller. In order to solve the problem of state consensus tracking of singular multi-agent systems with random switching topology, under the assumption that the topology is randomly switched along the time axis and unchanged along the iteration axis, a distributed iterative learning control protocol is proposed. Compared with traditional control methods, the algorithm in this paper does not require accurate mathematical model information of the system, requires less prior knowledge, and can achieve complete tracking of the desired state over a finite time interval, rather than progressive tracking over time.
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