Distributed optimal tracking control for second-order multi-agent systems

In this paper, we study the optimal tracking problem for the multi-agent systems in which both the cost function and the tracking time are considered. The tracking problem is considered in two patterns: the first one has a virtual leader which is the root of the information graph; the second one has a time-varying leader whose dynamics is given in advance. Both of the patterns are on the condition that only a portion of the agents can get the state information of the leader. For the required tracking time, an open-loop optimal controller is obtained using Pontryagins minimum principle and only depends on the relative information with respect to the neighboring agents. Considering the disturbance in the initial conditions or in the control input, it is necessary to convert the open loop control into the feedback optimal control by regarding the initial state as the current state and setting the initial time equal to the current time. Finally, the validity of the result is illustrated through some numerical examples.