Minimum entropy control of non-Gaussian dynamic stochastic systems

This note presents a new method to minimize the closed loop randomness for general dynamic stochastic systems using the entropy concept. The system is assumed to be subjected to any bounded random inputs. Using the recently developed linear B-spline model [3], [11], [10] for the shape control of the system output probability density function, a control input is formulated which minimizes the output entropy of the closed-loop system. Since the entropy is the measure of randomness for a given random variable, this controller can thus reduce the uncertainty of the closed-loop system. A sufficient condition has been established to guarantee the local stability of the closed-loop system. It has been shown that this minimum entropy control concept generates a minimum variance control when the stochastic system is represented by an ARMAX model which is subjected to Gaussian noises. An illustrative example is utilized to demonstrate the use of the control algorithm, and satisfactory results have been obtained.