Pattern formation using an intrinsic optimal control approach

This paper investigates a pattern formation control problem for a multi-agent system modeled with given interaction topology, in which $m$ of the $n$ agents are chosen as leaders and consequently a control signal is added to each of the leaders. These agents interact with each other by Laplacian dynamics on a graph. The pattern formation control problem is formulated as an intrinsic infinite time-horizon linear quadratic optimal control problem, namely, no error information is incorporated in the objective function. Under mild conditions, we show the existence of the optimal control strategy and the convergence to the desired pattern formation. Based on the optimal control strategy, we propose a distributed control strategy to achieve the given pattern. Finally, numerical simulation is given to illustrate theoretical results.