The objective of this report is to present a piece-by-piece LQG design for large-scale systems. The proposed design procedure is developed for a hierarchical (block-triangular) representation of the system, which is obtained via a graph-theoretic decomposition algorithm. The estimator is built as a union of low-order optimal estimators attached to each individual subsystem sequentially going from the top to the bottom of the hierarchy. As the subsystem state estimates become available, optimal controllers can be designed for each subsystem separately resulting in an overall closed-loop system which is stable and suboptimal. This design process offers a considerable reduction of both off-line and on-line computations, which is especially effective in large sparse systems.

The objective of this paper is to formulate a stochastic version of the Inclusion Principle, which can be used to identify equivalent solutions of the LQG problems having different dimensions. The new notion is applied to the decentralized LQC problem with overlapping information structure constraints.

The objective of this paper is to present a "piece-by-piece" design of hierarchtical Kalman estimator for sparse systems. The proposed procedure is applied to a block-triangular representation of the system obtained via a graph-theoretic decomposition algorithm. The estimator is built as a union of low-order optimal estimators, and offers a reduction of computational requirements for systems of large dimensions.

15 A more accurate way to calculate power output from wind turbines based on fundamental Newtonian 16 mechanics is proposed for testing. This contrasts with current methods regarded as governed by flows 17 of kinetic energy through an area swept by rotating airfoils. Action mechanics measures torques caused 18 by conservation of momentum of impulsive air streams on rotor surfaces at differing radii. We integrate 19 the windward torque using inputs of rotor dimensions, the angle of incidence and strength of wind 20 impulses on the blade surfaces. A reverse torque in the plane of rotation is estimated as radial impulses 21 from the blade’s rotation. Net torque is converted to power by the angular velocity of the turbine rotors. 22 A matter of concern is significant heat production by wind turbines, partly from leeward reactions but 23 mainly from turbulent release of vortical energy. Use of wind farms as sources of renewable energy