State Reconstruction And Point-wise Control Of The Parabolic Distributed Parameter System

This dissertation discusses the state reconstruction and the optimal point-wise control problem for the parabolic distributed parameter systems (DPS). The dissertation proposes a state reconstruction method to solve the state reconstruction problem. Further, according to the optimal control theory for the DPS, the dissertation applies the Galerkin's method and proposes a method for determining an optimal point-wise control. For practical implementation of the optimal point-wise control, knowing the state of the DPS is a prerequisite. Due to this need, the dissertation combines the state reconstruction method and the optimal point-wise control method to realize the optimal point-wise control for the parabolic DPS.The state space of DPS is infinite dimensional. Meanwhile, the number of sensors used for measuring the state of DPS is always finite. Thus, the only way to acquire the state of DPS is to reconstruct the state of the system through finite sensor information.On the other side, point-wise control is an important and practical control approach for the control of DPS. Since controller locations and the control law of each point-wise controller are two factors that directly influence the control performance, in order to solve point-wise control problem for DPS, both controller locations and the control law that should be exerted on each controller must be determined. The optimal point-wise control method is proposed in this dissertation to solve both the controller location and the optimal control law problem.The main work of this dissertation is described here: on the basis of the study of state reconstruction methods for DPS, a state reconstruction method is proposed for parabolic DPS, and the effectiveness of this method is verified by both theoretical deduction and a series of simulations; for the DPS point-wise control problem, on the basis of DPS optimal control theory, a method is proposed to determine both the controller locations and the control law; combining the state reconstruction method and the point-wise control method, the dissertation conducts a simulation study of a catalytic rod's temperature distribution point-wise control problem. The simulation results verifies the effectiveness of the state reconstruction and point-wise control methods.