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Linear Quadratic Control Theory for Models with Long Lags

Alfred Lorn Norman
Woo Sik Jung

Abstract

A new formulation of the linear quadratic control, LQC, problem with known coefficients, called the LAG, is presented. The LAG generally does not generate a recursive Ricatti system. For models with long lags an important issue is whatformulation leads to an efficient algorithm both with respect to storage and speed. At present the most efficient known formulation is the minimum state variable representation, MSV. The LAG requires much less storage than the MSV as the LAG does not require conversion to state space representation. For short time horizons the LAG is computationally faster than the MSV. As the time horizon increases, the efficiency of the LAG relative to the MSV declines. Numerical comparisons of the Theil, Chow, MSV, and LAG formulations are shown.