Abstract
This analysis formulates an approach for converting minimax LQ (linear-quadratic) tracking problems into LQ regulator designs, and develops a Matlab application program to calculate an H-infinity robust control for discrete-time systems with perfect state measurements. It uses simulations to explore examples in financial asset decisions and utility input purchasing, in order to demonstrate the method. The user is allowed to choose the parameters, and the program computes the generalized Riccati Equation conditions for the existence of a saddle-point solution. Given that it exists, the program computes a minimax solution to the linear quadratic (LQ) soft-constrained game with constant coefficients for a general scalar model, and also to a class of matrix systems. The user can set the bound to achieve disturbance attenuation.
Highlights
When addressing any economic, finance, or engineering problem where there is uncertainty, there must be some approaches for modeling the disturbances
This analysis formulates an approach for converting minimax linear quadratic (LQ) tracking problems into LQ regulator designs, and develops a Matlab application program to calculate an H-infinity robust control for discrete-time systems with perfect state measurements
The problem with these probabilistic approaches, such as the LQG, is that minimizing the expected value of a performance index leads to maximum system performance in the absence of misspecification, but it leads to poor performance and instability under small or large misspecifications [5]
Summary
Finance, or engineering problem where there is uncertainty, there must be some approaches for modeling the disturbances. One of the problems is that the system must be formulated properly with an appropriately accurate model of the system; otherwise, optimizing the wrong controller makes performance worse instead of better Another problem with applying the H∞-approach to macroeconomic problems is that many analyses model the interdependent prices and agent’s decisions separately, so that the existing H∞-methods cannot be applied [5]. The analysis in [5] performs simulations that demonstrate that when robustness is high, prices are more volatile than dividends These findings add further impetus for the use of a robust approach in many areas of finance and economics. These programs allow the analyst to make better decisions by exploring the worstcase disturbance strategy in conjunction with other approaches to dynamic systems that contain disturbances and uncertainty
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