Determination of the value of information in large vehicle arrays

An approach for determining the value of information required in the coordination of an array of vehicles is formulated as a data rate optimization of the linear-quadratic-Gaussian (LQG) problem. Two essential notions are used to decompose a centralized controller into a distributed controller. The first is that for each vehicle a special cost criterion is formulated. Secondly, a data rate parameter is introduced into the measurement power spectral densities, which is to be determined through an optimization of a multi-criteria problem. This optimization is performed by first assuming that the data rate variables are fixed, so that the optimal controller, which is affine, is determined and substituted back into the cost criteria. After taking the expectation in each cost criterion, a deterministic multi-cost criterion problem in the system variance dynamics results that is to be minimized by the data rate functions assuming a Nash equilibrium exists. For the current formulation, this decouples into a decoupled set of optimization problems. The data rate functions enter linearly into the optimization process. Their optimal values lie either on their bounds of full data rate or zero data rate or can take on intermediate values as a singular arc in the calculus of variations. If the data rate is zero, then that transmission of that measurement is removed and no longer used in the local state estimator. If the control used by a vehicle is not transmitted, then that control has to be constructed from the local estimates. The value of a control transmission is again obtained from the construction of a deterministic multi-cost criterion problem subject to the system variances which is to be minimized by the data rate functions associated with both the measurement and control transmissions. A Nash equilibrium is assumed to exist, since there is now coupling between the vehicle system variances. To simplify the computations, a static optimization problem is also suggested to- - obtain suboptimal solutions