Fusion of hard and soft control strategies for left ventricular ejection dynamics arising in biomedicine

A model of left ventricular pumping ejection dynamical process of the circulatory system arising in biomedicine is considered with the objective of minimizing the energy requirements of the heart as the sum of the potential energy stored in the tissues and muscles of the heart and that required for pumping the blood through the circulatory system. The resulting third-order, dynamic model is described in terms of state variables of left ventricular volume, rate of blood flow ejected out of the left ventricle, and blood pressure in the aorta and one input or control variable of left ventricular pressure. Using optimal control theory, a closed-loop optimal control technique is developed for the system with fixed boundary conditions and a performance index consisting of mixed state and control functions leading to an inverse matrix differential Riccati equation (IMDRE). Further, to improve the closed-loop performance, a soft control strategy such as an adaptive neuro-fuzzy inference system (ANFIS)-based intelligent technique is used leading to the fusion of hard control such as optimal control and soft control such as ANFIS. The application of this synergetic or hybrid (hard and soft) control strategy to the circulatory system shows a good agreement between the experimental data compared with the proposed, hybrid-control based theoretical results.