Decentralized control based on the value of information in large vehicle arrays

An approach for determining the value of information in a dynamic network is formulated as a data rate optimization which reduces multi-criteria linear-quadratic-Gaussian (LQG) controllers with centralized information to controllers with distributed or decentralized information. The dynamic network can be an array of vehicles, but the theory is more general. Two essential notions are used to decompose a centralized controller for each vehicle. First, given a quadratic cost criterion for each vehicle, a LQG Nash equilibrium is established where each controller has access to all the information in the network. The resulting optimal deterministic cost criteria become functions of the system parameters and statistics. Secondly, by augmenting these criteria with costs associated with transmitting the measurement and control values within the network, data rate parameters, bounded between zero and one, are determined through a deterministic multi-criteria optimization. If the data rate associated with a measurement is zero, then that measurement is not transmitted and no longer used in the local state estimator. If the control used by a vehicle is not transmitted, then that control can only be constructed from the local estimates. To simplify the computations, a static optimization problem is also suggested to obtain suboptimal solutions. Examples composed of a string of vehicles are presented. For simplification only data rates of zero or one are considered. The results of the optimization show that the control values should not be transmitted when a minimal number of measurements are used. It appears that with this minimal number of measurements, a priori knowledge of the control structure produces observable and detectable systems when no control is transmitted, whereas the knowledge of the control value and the minimal measurement set leads to an unobservable system and therefore, system instability.