In chapter 2 some of the facts, methods and assumptions forming the background of the presentation are described. The model structure is formulated and the connected assumptions are discussed. A review of the recursive least squares estimation method and its properties is given. The methods which are studied in the later chapters are obtained by modifying the least squares scheme, but the basic principles and variable interpretations remain the same. The chapter also contains a description of the well known adaptive controller obtained by combining least squares estimation with minimum variance control. Modified versions of this algorithm are applied and discussed throughout the thesis.
Chapter 3 gives a survey of the so-called forgetting methods designed for tracking slowly drifting system parameters. The main result of the chapter is the formulation of a general forgetting algorithm containing the existing methods as special cases.
The analytical properties of the general forgetting algorithm are studied in chapter 4. The attention is focused on an ideal environment without disturbances and with a time-invariant plant description. It is of fundamental importance that the estimator has good performance in this simple case. The analysis leads to guite general results which can readily be applied to any forgetting method belonging to the general family.
In chapter 5 a method based on a principle of selective forgetting is formulated. The theoretical properties of the method are studied and its practical performance is examined via simulation experiments.
The last chapter, chapter 6, contains development and examination of an adaptive controller for the nitrification process. The controller has to be based on a strongly simplified model, since the true process dynamics is complicated and only partly understood. However, the model captures the basic features of the variation, and the ability of the adaptive controller to adjust itself to the current conditions compensates for the simplification. This is verified via simulation studies by application of an extended model for representation of the true system. The non-linear structure of the model and the restrictions on the control signal make it impossible directly to apply the results known from the theory of linear systems. However, closely related results are established by using slightly modified proving techniques.