Introduction to modeling and control of complex systems

The modeling of complex dynamic systems has always been a challenging research topic due to the fact that mathematical models cannot accurately describe nature. A real system is often nonlinear, with infinite dimensions, noise, and external disturbances, and characteristics that can vary with time. It is impossible to describe these dynamic characteristics with mathematical equations and achieve a high level of accuracy in the sense that for the same inputs the outputs of the model match those of the real system over the whole frequency spectrum. What is possible, however, and useful for all practical purposes is to achieve model/system output matching over the frequency range of interest, which is often the low-frequency range. In this case modeling is even more challenging as decisions have to be made as to which phenomena and dynamics are neglected and which ones are modeled. Modeling is therefore not only a mathematical exercise but involves a good understanding of the system and its functionality. Models can be developed using physical laws as well as experiments and processing of data. Once a model is developed it has to be validated using real data over the frequency spectrum of interest.