A Sensitivity Analysis Method for a Class of Cyber-Physical Systems and Its Application to Parameter Optimization

Sensitivity analysis is fundamental and essential in the analysis and design of any system. Sensitivities are usually defined as derivatives of system variables or system performance with respect to its parameters. This paper discusses a sensitivity analysis method for a class of cyber-physical systems. We consider the following system as a class of cyber-physical systems at the first step of the research: a hybrid system in which a continuous-time system and a discrete-time system are connected through A/D and D/A interfaces. They are represented by block diagrams in which arbitrary elements including nonlinear elements are arbitrarily connected. It is known that the sensitivity analysis based on Tellegen’s theorem has become a standard method for electric circuits. We extend Tellegen’s theorem to the hybrid system and drive a method for computing sensitivities of any signal with respect to any parameter in the system. We also propose a method to apply the proposed method to parameter optimization of the systems. In order to evaluate the performance of the proposed method, some numerical experiments are conducted. We apply the proposed method to a cyber-physical system whose parameter sensitivities can be derived analytically in order to estimate its accuracy. It is shown through numerical experiments that the proposed method can obtain sensitivities with sufficient accuracy. Furthermore, we apply it to an optimization problem of a continuous and discrete-time hybrid system. It is shown that the proposed method makes it possible to obtain optimal parameters as the hybrid system.