Appendix A: System Identification: State and Parameter Estimation Techniques
Building mathematical models of subsystems and components is one of the most important tasks in the analysis and design of hybrid vehicle systems. There are two approaches to building a mathematical model: based on the principles and mechanism as well as the relative physical and chemical laws describing the characteristics of a given system or based on the observed system behaviors. In engineering practice, the architecture of the mathematical model is usually determined from the first approach, and detailed model parameters are determined from the second approach. In this chapter, we introduce basic theories and methodologies used to build a mathematical model and estimate the parameters of the model.
The models mentioned in this book are one or a set of mathematical equations that describe the relationship between inputs and outputs of a physical system. These mathematical equations may have various forms such as algebra equations, differential equations, partial differential equations, or state space equations. Mathematical models can be classified as: