Boundary Mittag-Leffler stabilization of a class of time fractional-order nonlinear reaction-diffusion systems

Boundary control design of a class of time fractional-order nonlinear reaction-diffusion systems (FNRDSs) is considered in three cases: domain-averaged measurement, collocated boundary point measurement, and anti-collocated boundary point measurement. For domain-averaged measurement and collocated boundary point measurement, boundary controllers are designed directly based on the measurements, respectively. For the anti-collocated boundary point measurement, to overcome the difficulty that the measurement cannot be used for the controller design directly, an observer is constructed firstly, and then, an observer-based boundary controller is designed. Sufficient conditions for Mittag-Leffler (M-L) stability of the closed-loop system are all provided in terms of linear matrix inequalities (LMIs). Numerical simulation results are provided to illustrate the feasibility and effectiveness of the proposed methods.

Automated summary

This paper considers the boundary control design of time fractional-order nonlinear reaction-diffusion systems (FNRDSs) in three cases: domain-averaged measurement, collocated boundary point measurement, and anti-collocated boundary point measurement. Boundary controllers are directly designed based on the measurements for domain-averaged measurement and collocated boundary point measurement. For anti-collocated boundary point measurement, an observer is constructed first to overcome the difficulty of using the measurement directly, and then an observer-based boundary controller is designed. Sufficient conditions for the Mittag-Leffler (M-L) stability of the closed-loop system are provided in terms of linear matrix inequalities (LMIs). Numerical simulation results are provided to demonstrate the feasibility and effectiveness of the proposed methods.