Adaptive dual control systems: a survey

An adaptive dual control system can be defined as an adaptive control system that operates under conditions of uncertainty and incorporates the existing uncertainty into the control strategy with the control signal having the following properties: (i) it cautiously follows the control goal and (ii) excites the plant to improve the estimation. The adaptive part of the system tries to determine the controller parameters during operation in real-time mode, whereas the dual part of it realises this actively by means of optimal excitation added to the cautious control action. Therefore adaptive dual controllers provide a number of advantages compared to the classical adaptive control schemes: (i) the accuracy of the estimation is taken into account, (ii) an optimal excitation for speeding up the estimation is provided, and (iii) the adaptation time becomes shorter and provides a smooth transitional behaviour. The paper reviews the historical stages of the development of theory and application of dual adaptive control methods elaborated from the early 60´s till today, considering also its close interconnection with the general progress in adaptive control systems. Detailed classifications of stochastic adaptive control methods and their adaptive dual versions are presented. New developments are reported