A New Entropy-Based Performance Index for Stochastic Control System Design

A new entropy-based performance index is proposed and developed for use in the design of stochastic control systems. Starting from a postulate of desired process performance, an entropy measure is shown to naturally quantify the discrepancy between predicted and desired system behavior. The entropy measure utilizes probability density functions to represent parameter uncertainty. By using metric and convexity properties of the entropy measure, a new performance index is proposed for control system design. The new performance index is employed to develop an optimal open-loop control policy to track a reference trajectory. In a second application, a one-step ahead adaptive control policy is developed and its properties are analyzed through a comparison with dual control strategies. It is shown that the optimal control policy yields a controller which is always more aggressive than a cautious controller.