Minimum entropy control of non-Gaussian dynamic stochastic systems

This paper 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 ([11, 10, 9, 8]) 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 reduces the uncertainty of the closed loop system. A set of sufficient conditions have been established to guarantee the local minimum property of the obtained control input and the stability of the closed loop system. Discussions on the design of minimum entropy tracking error have also been made. An illustrative example is utilized to demonstrate the use of the control algorithm, and satisfactory results have been obtained.