On the controllability of diffusively coupled multi-agent networks with switching topologies
Ming Cao · University of Groningen research database (University of Groningen / Centre for Information Technology) · 2012
The past few years has witnessed much research effort in distributed and cooperative control of multi-agent systems with linear diffusive couplings [1]. Among all relevant problems, it is very interesting to know whether the overall system behavior can be affected by only a small fraction of the agents. This question can be answered by addressing the controllability of the system after this fraction of agents are assigned as leaders, which are under the forcing of the external control inputs. The controllability problem has been formulated to, for instance, control a formation of mobile robots with the aim that, by manipulating the trajectories of the leaders, all the robots can move from any initial positions to any desired final positions within finite time [1]. The controllability of diffusively coupled multi-agent systems has been studied in [2]. There we assume that the underlying graph topology of the couplings in a system is time-invariant and reveal the role that the graph topology plays in the controllability of the given multi-agent system by using two classes of graph partitions. In this paper, we consider the same problem as in [2], but we drop the time-invariant topology assumption. Thus, we are considering a more realistic scenario when the topology of the multiagent system switches with time. Beyond being more realistic, switching topologies have an advantage in rendering a controllable system, i.e. a multi-agent system with switching topologies can become controllable even if each of these topologies leads to an uncontrollable system. Here, graph partitions are still employed to study the controllability of a system with switching topologies. By referring to the controllability results of switched linear systems, we provide the lower and the upper bounds of the controllable subspace of the system in terms of graph partitions. Moreover, we show that the two bounds are tight by finding examples where the bounds can be achieved. The rest of this abstract is organized as follows. Section 2 quickly reviews the controllability/reachability results in switched linear systems. Then we introduce the system of our interest in Section 3. As the main tools in controllability problem, graph partitions are studied in Section 4. And the main result of our paper will be mentioned in Section 5.