Passivity and Optimal Control of Descriptor Biological Complex Systems

Accurate mathematical models, to describe and analyze complex systems, cannot be established. This is especially true for biological complex systems because of the complexity of interaction among constituent units inside the whole system. Descriptor biological complex systems are a new research field in descriptor systems; there has been little research about passivity and optimal control of descriptor biological complex systems. Passivity analysis and feedback controller design of the system offers an important basis for the research of descriptor system theory applied to biological complex systems. In this paper, a poly-chamber model of the endocrine disruptor - Diethylstibestrol - moving in a human body is developed based on physiological rules. Passivity of this model is described and proved systematically. A feedback controller for this descriptor biological complex system is designed under the station of strict passivity, and an example of the controller is given for a particular instantiation of the model.