### Boundary Control of Coupled Non-Constant Parameter Systems of Time Fractional PDEs with Different-Type Boundary Conditions

CHEN Juan1, ZHUANG Bo2

1. 1. Aliyun School of Big Data, Changzhou University, Changzhou 213164, China;
2. School of Information Engineering, Binzhou University, Binzhou 256600, China
• Received:2021-08-29 Revised:2022-08-13 Online:2023-01-25 Published:2023-02-09
• Supported by:
This research was supported by National Natural Science Foundation of China under Grant No. 62203070, Science and Technology Project of Changzhou University under Grant Nos. ZMF20020460, KYP2102196C, and KYP2202225C, Changzhou Science and Technology Agency under Grant No. CE20205048, the PhD Scientific Research Foundation of Binzhou University under Grant No. 2020Y04.

CHEN Juan, ZHUANG Bo. Boundary Control of Coupled Non-Constant Parameter Systems of Time Fractional PDEs with Different-Type Boundary Conditions[J]. Journal of Systems Science and Complexity, 2023, 36(1): 273-293.

This paper addresses a boundary state feedback control problem for a coupled system of time fractional partial differential equations (PDEs) with non-constant (space-dependent) coefficients and different-type boundary conditions (BCs). The BCs could be heterogeneous-type or mixed-type. Specifically, this coupled system has different BCs at the uncontrolled side for heterogeneous-type and the same BCs at the uncontrolled side for mixed-type. The main contribution is to extend PDE backstepping to the boundary control problem of time fractional PDEs with space-dependent parameters and different-type BCs. With the backstepping transformation and the fractional Lyapunov method, the Mittag-Leffler stability of the closed-loop system is obtained. A numerical scheme is proposed to simulate the fractional case when kernel equations have not an explicit solution.
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