Boundary Control Of Reaction-diffusion System With Time Delay

The time delay system is worth studying in PDE control domain. The genearal research on time delay system depends on mathematics model mainly. At present, the relatively ideal control scheme mainly aims at the time delay system of linearity, time invariance and SISO. However, the research on time delay of PDE is very rare.The dissertation studies one kind of boundary control of time delay response diffusion system. It emphasizes on the stability and bases on the Lyapounov stability theory. It draws support from several important inequality, recursive estimation, numerical analysis of reproducing kernel space. Baekstepping design method, and Lyapounov function in the whole control procedure.Especially, compared with former research, the time delay problem whose re-sponse coefficient depends on space variable is disposed effectively, and the limiting condition is extended. So, there are more Realistic Significance. The basic method draw support from that one-order hyperbolic equations transform input time de-lav. The former time delay system is transformed to a PDE-PDE cascade system without time delay system. Then the invertible transform of voltcrra is used and the cascade system is transformed to a stable target system. The design procedure generates three kernel functions in usage of baekstepping method design controller. The three kernel functions are applied with recursive estimation and numerical anal-ysis of reproducing kernel space and the well posedness of the kernel functions is obtained.The system stability analysis is based on the Sobolev functionally. The energy estimation method is used and the three Lyapunov functions are constructed by former cascade system, target system and improved system. Besides, the functional relations among the three Lyapunov functions are determined skillfully. The con-troller can guarantee the whole situation index stability of the former closed-loop system is proved.At last, the examples are simulated, and the feasibility of boundary control is confirmed. The contents and main achievements of the dissertation are summarized, and the farther research is proposed.