Pinning dynamic systems of networks with Markovian switching couplings and controller-node set

In this paper, we study pinning control problem of coupled dynamical systems with stochastically switching couplings and stochastically selected controller-node set. Here, the coupling matrices and the controller-node sets change with time, induced by a continuous-time Markovian chain. By constructing Lyapunov functions, we establish tractable sufficient conditions for exponentially stability of the coupled system. Two scenarios are considered here. First, we prove that if each subsystem in the switching system, i.e. with the fixed coupling, can be stabilized by the fixed pinning controller-node set, and in addition, the Markovian switching is sufficiently slow, then the time-varying dynamical system is stabilized. Second, in particular, for the problem of spatial pinning control of network with mobile agents, we conclude that if the system with the average coupling and pinning gains can be stabilized and the switching is sufficiently fast, the time-varying system is stabilized. Two numerical examples are provided to demonstrate the validity of these theoretical results, including a switching dynamical system between several stable sub-systems, and a dynamical system with mobile nodes and spatial pinning control towards the nodes when these nodes are being in a pre-designed region.Comment: 9 pages; 3 figure

Output Feedback Control for Couple-Group Consensus of Multiagent Systems

This paper deals with the couple-group consensus problem for multiagent systems via output feedback control. Both continuous- and discrete-time cases are considered. The consensus problems are converted into the stability problem of the error systems by the system transformation. We obtain two necessary and sufficient conditions of couple-group consensus in different forms for each case. Two different algorithms are used to design the control gains for continuous- and discrete-time case, respectively. Finally, simulation examples are given to show the effectiveness of the proposed results

Semiglobal observer-based leader- following consensus with input saturation

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Containment Control of Multi-Agent Systems with Dynamic Leaders Based on a PInPI^n-Type Approach

This paper studies the containment control problem of multi-agent systems with multiple dynamic leaders in both the discrete-time domain and the continuous-time domain. The leaders' motions are described by $(n-1)$-order polynomial trajectories. This setting makes practical sense because given some critical points, the leaders' trajectories are usually planned by the polynomial interpolations. In order to drive all followers into the convex hull spanned by the leaders, a $PI^n$-type ($P$ and $I$ are short for {\it Proportion} and {\it Integration}, respectively; $I^n$ implies that the algorithm includes high-order integral terms) containment algorithm is proposed. It is theoretically proved that the $PI^n$-type containment algorithm is able to solve the containment problem of multi-agent systems where the followers are described by any order integral dynamics. Compared with the previous results on the multi-agent systems with dynamic leaders, the distinguished features of this paper are that: (1) the containment problem is studied not only in the continuous-time domain but also in the discrete-time domain while most existing results only work in the continuous-time domain; (2) to deal with the leaders with the $(n-1)$-order polynomial trajectories, existing results require the follower's dynamics to be $n$-order integral while the followers considered in this paper can be described by any-order integral; and (3) the "sign" function is not employed in the proposed algorithm, which avoids the chattering phenomenon. Furthermore, in order to illustrate the practical value of the proposed approach, an application, the containment control of multiple mobile robots is studied. Finally, two simulation examples are given to demonstrate the effectiveness of the proposed algorithm

Distributed Cooperative Regulation for Multiagent Systems and Its Applications to Power Systems: A Survey

Cooperative regulation of multiagent systems has become an active research area in the past decade. This paper reviews some recent progress in distributed coordination control for leader-following multiagent systems and its applications in power system and mainly focuses on the cooperative tracking control in terms of consensus tracking control and containment tracking control. Next, methods on how to rank the network nodes are summarized for undirected/directed network, based on which one can determine which follower should be connected to leaders such that partial followers can perceive leaders’ information. Furthermore, we present a survey of the most relevant scientific studies investigating the regulation and optimization problems in power systems based on distributed strategies. Finally, some potential applications in the frequency tracking regulation of smart grids are discussed at the end of the paper