On the synthesis of control laws for a network of autonomous agents

We study the synthesis problem of a LQR controller when the matrix describing the control law is additionally constrained to lie in a particular vector space. Our motivation is the use of such control laws to stabilize networks of autonomous agents in a decentralized fashion; with the information flow being dictated by the constraints of a pre-specified topology. We formulate the problem as an optimization problem and provide numerical procedures to solve it. Then, we apply the technique to the decentralized vehicle formation control problem and show that the topology can have a significant effect on the optimal cost.