Nodes selection strategy in cooperative tracking problem

In this paper, a new optimization problem is addressed for node selection that has application potentials in input/output switches for sensors in control system design and leader determination in social networks. The purpose of the addressed problem is to develop a strategy for selecting a subset of nodes as controlled nodes in order to minimize certain objective function consisting of the convergence speed and the energy of control action, over a finite time-horizon. For networks with fixed controlled nodes, an upper bound of the objective function is obtained which is shown to be convex and independent of the time-horizon. For networks with switched controlled nodes, a greedy algorithm is proposed to reduce the computation complexity resulting from the length of the time-horizon, where the nodes selection is carried out over divided small time-intervals. The cost gap is also analyzed between the strategy of optimizing over the whole time-horizon and the strategy of optimizing over the small intervals. Finally, the proposed nodes selection strategy is validated through simulations and two regions are found in which the number of optimal controlled nodes is determined.