ABSTRACT
Representation, approximation, and identification of physical systems, linear or nonlinear, deterministic or random, or even chaotic, are three fundamental issues in systems theory and engineering. To describe a physical system, such as a circuit or a microprocessor, we need a mathematical formula or equation that can represent the system both qualitatively and quantitatively. Such a formulation is what we call a mathematical representation of the physical system. If the physical system is so simple that the mathematical formula or equation, or the like, can describe it perfectly without error, then the representation is ideal and ready to use for analysis, computation, and synthesis of the system. An ideal representation of a real system is generally impossible, so that system approximation becomes necessary in practice. Intuitively, approximation is always possible. However, the key issues are what kind of approximation is good, where the sense of “goodness” must first be defined, of course, and how to find such a good approximation. On the other hand, when looking for either an ideal or a approximate mathematical representation for a physical system, one must know the system structure (the form of the linearity or nonlinearity) and parameters (their values). If some of these are unknown, then one must identify them, leading to the problem of system identification.
