Chapter 1 - The Modeling Problem for Controlled Motion of Nonlinear Dynamical Systems

Abstract

Chapter 1 is devoted to a statement of the modeling problem for controlled motion of nonlinear dynamical systems. We consider the classes of problems that arise from the processes of design and operation of dynamical systems (analysis, synthesis, and identification problems) and reveal the role of mathematical modeling and computer simulation in solving these problems. Among the issues discussed in this chapter we find dynamical systems as an object of study. Some aspects of this topic include a description of the system and its operating environment, factors of uncertainty in the modeling of systems, classes of dynamical systems, and the interaction of the system and the environment. The next set of questions relates to the problem of the adaptability of dynamical systems. In this regard, we analyze the kinds of adaptation, the basic types of adaptive control schemes, and the role of models in the problem of adaptive control. The need for adaptability of the controlled object model is revealed, as well as the need for neural network implementation of adaptive modeling and control algorithms. The processes of development and operation of controlled dynamical systems generate three classes of problems, i.e., the analysis of the behavior of such systems, the synthesis of control laws for them, and the identification of their characteristics. The role of mathematical modeling and computer simulation in solving these problems is revealed. The chapter concludes with an examination of the general approach to solving the problem of modeling dynamical systems. The scheme of the process of modeling a dynamical system is given, and the principal problems that need to be solved when forming a model of a dynamical system are listed.