Research On Dual Control In LQG With Uncertainty Parameters Problem

This thesis discusses the dual adaptive control in Linear Quadratic Gaussian(LQG) with uncertainty parameters problem.Stochastic control is one of the most important branches in modern control theory. Both the measurements and the control in stochastic problem are stochastic processes. The theory on the system with certain parameters and output fully measured is well formed. Nevertheless, a great deal of uncertainty exists in many practical stochastic control problems, which makes the problem one of the most difficult challenges. The world is full of uncertainty. Even when the simplest uncertainty emerges in the LQG problem, the optimal solution of the problem cannot be obtained directly. When control a stochastic system with uncertainty, on the one hand, the control should change smoothly to achieve the control objective; on the other hand, it must perturb the system so that the uncertainty can be probed. These two requirements are always conflicting.The conflict can be well solved by dual adaptive control. Focusing on the control in the LQG with uncertainty problem, this thesis first investigated the natural characteristics of active dual control. Then, according to the outcome, a dual adaptive control strategy based on rolling optimization has been proposed. The control law used the information embedded in the posterior probability, introduced the innovations of system. The estimations of system parameters are obtained by Kalman filtering. The explicit concise control law is eventually obtained and the simulation results show the desired dual property of the control strategy. Then follows the study on LQG system with uncertain noise. A practical dual adaptive control is achieved by modified filtering and active dual control methodology. At the end of the thesis, some related aspects of dual adaptive control are discussed.