Observability and Controllability of Ventricular Muscle Model

Abstract

Biological systems contain many components and these components are intricately linked. Understanding the behavior of the system in medical science facilitates the recognition and treatment of diseases. Although diseases have long been studied but the exact mechanism of many of them is not still well understood. Knowing the dynamics of a disease usually needs to understand the dynamics of the cell. By identifying and modeling the dynamics of such systems, diseases can be controlled. An efficient method for systems analysis is observability and controllability. Observability is defined to be the state variables based on the inputs, outputs and their time derivatives and these measured values for the variables are unique without having to know the exact amount of the initial conditions of the system. For observing states of the system, the system must have observability property and for arbitrary controlling states of the system, the system must have controllability property. In this paper observability and controllability of a typical ventricular muscle model are investigated. This model has nonlinear dynamics. observability of nonlinear systems obtain with Lie derivative. With the system state space and by calculation of Lie derivative, O matrix will be calculated. After these calculations, the nonlinear system is observable if the O matrix has full rank. Controllability of nonlinear systems obtains Lie bracket. With the system state space, after calculation of Lie bracket, C matrix will be calculated. According to calculations, the nonlinear system is controllable if the C matrix is full rank.