Control of Nonlinear Dynamical Systems Using. . .

This paper presents a first attempt to relate the experimental studies to theoretical developments and one of our aims is to propose a general methodology by which control methods based on neural networks can be made more rigorous. From a mathematical point of view, even the control of known nonlinear dynamical systems is a formidable problem. This becomes substantially more complex when the representation of the system is not completely known. In such cases, stringent assumptions have to be made if neural networks are to be used for their identification and control. Further, while several theoretically elegant results have been reported in the control literature, many of them are not directly applicable to the practical identification and control of nonlinear systems. Hence our objective in this paper is threefold: The first is to provide the reader with some background concerning concepts in control theory on which many of the results proposed are based. The second objective is to present theoretical results along with the assumptions they entail, which can be used in the practical synthesis of identifiers and controllers. It is hoped that these assumptions can be relaxed as our experience with such problems increases. A third and final objective is to demonstrate, through simulation studies, the effectiveness of the proposed methods. . Ada t e ontrol o onl near tem ng e ral etwork - r or n ormat on Consider the discrete time dynamical system described by the equations