Dual Adaptive Control

This paper discusses a typical problem of stochastic systems: dual adaptive control.The uncertainty of a stochastic system with known parameters is the result of the outside unknown disturbances acting on its process and measurement. This class of uncertainty can't be lessened. However, the optimal control can be obtained based on the optimal estimation to the system state by some estimation methods such as Kalman filter. But in practical situations, some unknown dynamic behavior may lead to the change of the system parameters. Therefore it is very common that the systems parameters are unknown. So far the most common solution to this problem is the conventional adaptive control. The technique for designing a conventional adaptive controller is to divide the derivation of the control signal into two parts: state estimation and seeking for the feedback control law with the assumption that the estimated parameters are true. Evidently, the defect of this method is that it doesn't consider the interaction between the identification and the control. So it is a great breakthrough to combine the estimation objective and the control objective to a mixed problem, which is theessence of dual control. An optimal dual controller pursues two often-conflicting objectives: to drive the system toward a desired state, and to perform active learning to reduce the systems uncertainty.For systems with unknown and invariable parameters, I proposed dual control based on two-level algorithm. Further more, for systems with unknown and variable parameters, I presented innovations two-stage dual control. Simulations show that these two dual control methods can achieve satisfactory control performance and preferable estimation results. In Addition, for systems with parameters limited to several sets, I present an improved DUL algorithm with careful analysis of the relation between control and identification, thus greatly improves the response speed and control performance of the system. .Dual adaptive control is a control method for stochastic systems that currently causes great attention of the international control society. In this thesis the dual control methods are studied carefully and several new methods are presented and the relevant theorems are also proved in detail.