Journal
AUTOMATICA
Volume 134, Issue -, Pages -Publisher
PERGAMON-ELSEVIER SCIENCE LTD
DOI: 10.1016/j.automatica.2021.109909
Keywords
Input delay; Adaptive control; PDE backstepping; Boundary control; Lyapunov design
Funding
- National Natural Science Foundation of China [61773112]
- Fundamental Research Funds for the Central Universities and Graduate Student Innovation Fund of Donghua University, China [CUSF-DH-D-2018098]
- State Key Laboratory of Synthetical Automation for Process Industries, China
- USA National Science Foundation CAREER award [CMMI-1944051]
- Jeju Island, Republic of Korea
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An adaptive full-state feedback controller was designed to stabilize a one-dimensional reaction-diffusion equation with unknown boundary input delay. The system was transformed into a transport PDE cascading with a reaction-diffusion PDE using an infinite-dimensional representation of the actuator delay, and a suitable parameter update law was designed to establish local boundedness and asymptotic convergence stability. Consistent simulation results were provided to support the theoretical findings.
We design an adaptive full-state feedback controller to stabilize a one-dimensional reaction-diffusion equation with unknown boundary input delay. An infinite-dimensional representation of the actuator delay is utilized to transform the system into a transport PDE cascading with a reaction-diffusion PDE. A suitable parameter update law is designed to establish local boundedness of the system trajectories and asymptotic convergence stability result using the well-known PDE backstepping technique and a Lyapunov argument. Consistent simulation results are provided to support the theoretical results. (C) 2021 Elsevier Ltd. All rights reserved.
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