TY - JOUR
T1 - POINTWISE FEEDBACK STABILIZATION OF AN UNSTABLE CASCADED HEAT-HEAT SYSTEM WITH DIFFERENT REACTION COEFFICIENTS
AU - Tang, Jia Qi
AU - Wang, Jun Min
AU - Kang, Wen
N1 - Publisher Copyright:
© 2025, American Institute of Mathematical Sciences. All rights reserved.
PY - 2025/2
Y1 - 2025/2
N2 - The present paper considers a cascade of heat-heat system with different reaction coefficients, where the actuator is presented at the arbitrary position ξ in the domain (0, 1) with pointwise feedback heat flux. A sufficient and necessary condition regarding two reaction coefficients of the cascaded heat-heat model is derived to guarantee the controllability of the cascaded system. Based on the modal decomposition approach, a pointwise feedback controller is introduced to stabilize the unstable coupled system if ξ ∈ (0, 1) and satisfies (Formula Presented) for any integers n2 ∈ N+, k ∈ {0, 1, 2, · · ·, n2 − 1}. 2 Via the Lyapunov method, sufficient conditions are derived for guaranteing exponential stability and well-posedness of the closed-loop systems. Numerical simulation demonstrates that the proposed control scheme effectively stabilizes the performance of the cascaded system.
AB - The present paper considers a cascade of heat-heat system with different reaction coefficients, where the actuator is presented at the arbitrary position ξ in the domain (0, 1) with pointwise feedback heat flux. A sufficient and necessary condition regarding two reaction coefficients of the cascaded heat-heat model is derived to guarantee the controllability of the cascaded system. Based on the modal decomposition approach, a pointwise feedback controller is introduced to stabilize the unstable coupled system if ξ ∈ (0, 1) and satisfies (Formula Presented) for any integers n2 ∈ N+, k ∈ {0, 1, 2, · · ·, n2 − 1}. 2 Via the Lyapunov method, sufficient conditions are derived for guaranteing exponential stability and well-posedness of the closed-loop systems. Numerical simulation demonstrates that the proposed control scheme effectively stabilizes the performance of the cascaded system.
KW - Cascaded heat-heat system
KW - distributed parameter system
KW - exponential stability
KW - modal decomposition approach
KW - pointwise stabilization
UR - http://www.scopus.com/inward/record.url?scp=85209632495&partnerID=8YFLogxK
U2 - 10.3934/eect.2024046
DO - 10.3934/eect.2024046
M3 - Article
AN - SCOPUS:85209632495
SN - 2163-2472
VL - 14
SP - 73
EP - 95
JO - Evolution Equations and Control Theory
JF - Evolution Equations and Control Theory
IS - 1
ER -