A linear quadratic control problem is considered, where several different controllers act as a team, but with access to different measurement variables. Under appropriate assumptions on communication between the controllers, a quadratic control objective can be optimized using finite-dimensional convex optimization.
Versions of this problem has been discussed in economic literature, as well as in statistical decision theory. Some instances were solved in the 1960-70's, but significant progress on the role of controller communication has recently been made. In this tutorial presentation we focus on the connection between distributed control and stochastic optimization with correlation constraints. The method gives a non-conservative extension of linear quadratic control theory to distributed control with bounds on the rate of information propagation.
The theory is illustrated by application to control of vehicle formations and control of a flexible mirror in a telescope. It is possible to study how the achievable control performance depends on the local availability of measurements. For vehicle formations, the control performance when each vehicle measures the distance to its nearest neighbors is compared with the performance achievable when observing also vehicles further away.
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