Allowable sampling period for consensus control of multiple general linear dynamical agents in random networks

Abstract

This article studies the consensus problem for a group of sampled-data general linear dynamical agents over random communication networks. Dynamic output feedback protocols are applied to solve the consensus problem. When the sampling period is sufficiently small, it is shown that as long as the mean topology has globally reachable nodes, the mean square consensus can be achieved by selecting protocol parameters so that n À 1 specified subsystems are simultaneously stabilised. However, when the sampling period is comparatively large, it is revealed that differing from low-order integrator multi-agent systems the consensus problem may be unsolvable. By using the hybrid dynamical system theory, an allowable upper bound of sampling period is further proposed. Two approaches to designing protocols are also provided. Simulations are given to illustrate the validity of the proposed approaches. IntroductionThe insertion of the communication network among agents makes the analysis and design of multi-agent systems more complex. One of the challenging problems associated with networked multi-agent systems is the influence of the sampling period. For second-order integrator multi-agent systems, if there exist static state feedback protocols solving the consensus problem of the continuous-time systems, under any sampling period there exist sampled-data state feedback protocols solving the consensus problem of the sampled-data systems (see Hayakawa, Matsuzawa, and Hara 2006). Even if the interaction topology is varying, the sampling period can be arbitrarily selected for second-order integrator multi-agent systems (Zhang and Tian 2010). The first question to be answered in this article is whether such a property holds for systems of general linear dynamical agents. Unfortunately, we will show, the answer is negative. The second question considered in this article is how to establish consensus conditions relating to the sampling period with protocol parameters and interaction topologies. Like the research on the first question there are some results on loworder integrator agent systems. For first-order systems, Olfati-Saber and Murray (2004) consider the fixed and connected undirected topology and point out that if the sampling period is less than the reciprocal of the maximum out-degree, the consensus

Consensus tracking in sensor networks with periodic sensing and switching connected topologies

“…Unlike the first-order and secondorder integrator target tracking systems, in which for any large but bounded sensing period there always exist proper linear state feedback consensus tracking protocols driving the vehicles to successfully track the target, the allowable sensing period for the feasibility of tracking general linear dynamical target should be bounded. When the sensing period is too large, the tracking problem may be unsolvable [19].…”

“…Katayama [18] considered sampled-data consensus control for nonlinear multi-agent systems of strict-feedback form. Based on the hybrid system analysis, Zhang and Tian [19] studied general linear sampled-data multi-agent systems and gave an allowable upper bound of sampling period for system under given protocols. By converting the sampled-data system to the discrete-time system with delays, Gao and Wang [20] studied the consensus of second-order multi-agent systems where the sampling period of each agent was independent of the others' and the topology was varying.…”

Leader-Following Consensus for Linear Multiagent Systems via Asynchronous Sampled-Data Control

“…Reference [7] further studied the SDLLCP for double-integrator multi-agent systems based on the impulsive control strategy. In [29], [31], the sampleddata leaderless mean square consensus problem was studied for the general linear multi-agent systems with packet losses. Reference [30] studied the SDLLCP for general linear multiagent systems with switching topologies using the input delay method.…”

Distributed consensus problem for general linear multi-agent systems with sampled-data

“…Moreover, inherent nonlinear dynamics of sampled-data consensus problems were investigated in [15]. It is well known that, most current investigate about sampled-data consensus problems are applying discrete-time approach [7][8][9][10][11][16][17] and input delay approach [12,15]. We can find that the exponential uncertainties of linear discrete-time models, which are drawn into by time-varying sampling intervals, it is hard to analyze the dynamic systems when the time delays are larger than sampling periods.…”