1. INTRODUCTION

Abstract

Most adaptive controllers are based on the separation of parameter estimation and controller design. In such cases, the certainty-equivalence (CE) approach is applied, that is, the uncertainty of estimation is not taken into consideration for the controller design, and the parameter estimates are used in the control law as if they were the real values of the unknown parameters. This approach is simple to implement. It has been used in many adaptive control schemes from the beginning of the development of adaptive control theory (the mid-’50 s) and is still being used today. In his early works, A. Feldbaum (1960-61, 1965) considered the problem of optimal adaptive control and indicated that systems based on the CE approach are not always optimal but can indeed be far from so. He postulated two main properties that the control signal of an optimal adaptive systems should have: it should ensure that (i) the system output cautiously tracks the desired reference value and that (ii) it excites the plant sufficiently for accelerating the parameter estimation process so that the control quality becomes better in future time intervals. These properties are known as dual properties (or dual features). Adaptive control systems showing these two properties are named adaptive dual control systems.