Optimization of multiagent systems with increasing state dimensions: Hybrid LQ approach

In this paper, we study a specific optimal control problem associated with a multiagent dynamic system. The interest is placed on minimization of the tracking error in the multiagent leader-follower model. We replace this problem by a specific hybrid optimal control problem. In particular, we consider control systems with monotonically increasing dimensions of the state vector. The change of the state dimension has the character of a jump and is modeled by an impulsive hybrid system. The paper proposes an effective computational procedure for the above optimal tracking control problem in a multiagent setting. The theoretical and numerical approaches obtained in this contribution are tested on a practically motivated example.