Introduction to Control of Non-Linear Dynamical Systems

Abstract

We describe in this book, new methods for modelling, simulation, and control of dynamical systems using soft computing techniques and fractal theory. Soft Computing (SC) consists of several computing paradigms, including fuzzy logic, neural networks, and genetic algorithms, which can be used to produce powerful hybrid intelligent systems. Fractal theory provides us with the mathematical tools to understand the geometrical complexity of natural objects and can be used for identification and modelling purposes. Combining SC techniques with fractal theory, we can take advantage of the “intelligence” provided by the computer methods and also take advantage of the descriptive power of fractal mathematical tools. Non-linear dynamical systems can exhibit extremely complex dynamic behavior, and for this reason, it is of great importance to develop intelligent computational tools that will enable the identification of the best model for a particular dynamical system, then obtaining the best simulations for the system, and also achieving the goal of controlling the dynamical system in a desired manner.