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.

# A.1 Dynamic systems and mathematical models

## A.1.1 Types of Mathematical Models

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:

- Static versus Dynamic Model A static model does not include time, that is, the behavior of the described system does not vary over time, while a dynamic model does. Dynamic models are typically described by a differential equation or difference equation. Laplace and Fouriers ...