Near-optimum steady state regulators for stochastic linear weakly coupled systems

This paper presents an approach to the decomposition and approximation of the linear quadratic Gaussian estimation and control problems for weakly coupled systems. The global Kalman filter is decomposed into separate reduced-order local filters via the use of a decoupling transformation. A near-optimal control law is derived by approximating the coefficients of the truly optimal control law. The order of approximation of the optimal performance is O(ε^N), where N is the order of approximation of the coefficients. A real world power system example demonstrates the failure of O(ε²) and O(ε⁴) approximations and the necessity for the existence of the O(ε^N) theory. The proposed method produces the reduction in both off-line and on-line computational requirements and leads to convergence under mild assumptions. In addition, only low-order systems are involved in algebraic calculations and no analyticity requirement (a standard assumption for the power series method) is imposed on system coefficients.