5. CONVERGENCE AND STABILITY OF ADAPTIVE DUAL CONTROL

Abstract

The investigations in the field of dual controllers concentrated for many years on the design of various adaptive dual controllers using approximative approaches. However, problems of convergence and stability were not considered. The main reasons for this are the complexity and nonlinearity of many adaptive controllers as well as insufficient experience in the application of stochastic methods to convergence and stability analysis of adaptive systems. This experience was accumulated during the 1970s and 1980s and the first convergence analysis of an explicit dual controller that uses the martingale convergence theory was presented by Radenkovic (1988). This approach was extended for convergence analysis and stability of dual controllers with direct adaptation (Filatov and Unbehauen, 1994) and will be applied below with some modifications to analyse convergence and stability of the adaptive dual controllers discussed in Chapter 4.