Adaptive local linear modelling and control of nonlinear dynamical systems

Systems theory is a well-established and mature area of engineering research, where many strong general mathematical results are available. Especially the analysis of linear identification and control systems have been pursued by many researchers leading to a complete understanding of various mechanisms that are effective in the stability, controllability and observability of these. Due to the availability of such an extensive knowledge base about linear systems, modern industrial control applications are still typically designed utilising the results from linear control systems theory. Nevertheless, academic research has been concentrating around problems involving the stability, identification and control of nonlinear dynamical systems in the last few decades. These efforts have now also matured into a broad theory of nonlinear systems, their identification and control. Initial efforts in this area pursued parametric approaches, inspired by the established linear systems theory, where the system dynamical equations are generally assumed to be known from physical principles, possibly with some uncertainty in the values of certain parameters. In this framework, the system identification and system control problems are decoupled, therefore can be solved sequentially. More recently, adaptive system identification and control methodologies have also been investigated, once again leading to a very good understanding of the adaptation in linear systems and a satisfactorily general insight to 169