A sub-optimal algorithm to synthesize control laws for a network of dynamic agents

We study the synthesis problem of a linear quadratic regulator (LQR) controller when the matrix describing the control law is constrained to lie in a particular vector space. Our motivation is the use of such control laws to stabilize networks of autonomous agents in decentralized fashion, with the information flow being dictated by the constraints of a pre-specified topology. In this paper, we consider the finite-horizon version of the problem and provide both a computationally intensive optimal solution and a sub-optimal solution that is computationally more tractable. Then we apply the technique to the decentralized vehicle formation control problem. It is numerically illustrated that while the loss in performance due to the use of the sub-optimal solution is not huge, the topology can have a large effect on performance.

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