Brief paper: Minimum entropy of B-spline PDF systems with mean constraint

Authors:
Hong Yue;Jinglin Zhou;Hong Wang
Affiliations:
Control Systems Centre, The University of Manchester, Manchester M60 1QD, UK and Institute of Automation, Chinese Academy of Sciences, Beijing 100080, China;Institute of Automation, Chinese Academy of Sciences, Beijing 100080, China;Control Systems Centre, The University of Manchester, Manchester M60 1QD, UK and Institute of Automation, Chinese Academy of Sciences, Beijing 100080, China
Venue:
Automatica (Journal of IFAC)
Year:
2006

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Abstract

For the B-spline approximation of the continuous probability density function (PDF), the relationships between the B-spline weights and entropy both in general and under the mean constraint have been analyzed. It provides the conditions under which the minimum entropy can be achieved subject to the mean constraint. The difference between the entropy of continuous and discrete distributions has also been clarified. A minimum entropy controller with the mean constraint is then developed and several simulations are performed to verify the main results.