TY - GEN
T1 - Control of semilinear dissipative distributed parameter systems with minimum feedback information
AU - Pourkargar, Davood B.
AU - Armaou, Antonios
N1 - Publisher Copyright:
© 2020 AACC.
PY - 2020/7
Y1 - 2020/7
N2 - We focus on Lyapunov-based output feedback control for a class of distributed parameter systems with spatiotemporal dynamics described by input-affine semilinear dissipative partial differential equations (DPDEs). The control problem is addressed via adaptive model order reduction. Galerkin projection is applied to discretize the DPDE and derive low-dimensional reduced order models (ROMs). The empirical basis functions needed for this discretization are updated using adaptive proper orthogonal decomposition (APOD) which needs measurements of the complete profile of the system state (called snapshots) at revision times. The main objective of this paper is to minimize the demand for snapshots from the spatially distributed sensors by the control structure while maintaining closed-loop stability and performance. A control Lyapunov function is defined and its value is monitored as the system evolves. Only when the value violates a closed-loop stability threshold, snapshots are requested for a brief period by APOD after which the ROM is updated and the controller is reconfigured. The proposed approach is applied to stabilize the Kuramoto-Sivashinsky equation.
AB - We focus on Lyapunov-based output feedback control for a class of distributed parameter systems with spatiotemporal dynamics described by input-affine semilinear dissipative partial differential equations (DPDEs). The control problem is addressed via adaptive model order reduction. Galerkin projection is applied to discretize the DPDE and derive low-dimensional reduced order models (ROMs). The empirical basis functions needed for this discretization are updated using adaptive proper orthogonal decomposition (APOD) which needs measurements of the complete profile of the system state (called snapshots) at revision times. The main objective of this paper is to minimize the demand for snapshots from the spatially distributed sensors by the control structure while maintaining closed-loop stability and performance. A control Lyapunov function is defined and its value is monitored as the system evolves. Only when the value violates a closed-loop stability threshold, snapshots are requested for a brief period by APOD after which the ROM is updated and the controller is reconfigured. The proposed approach is applied to stabilize the Kuramoto-Sivashinsky equation.
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U2 - 10.23919/ACC45564.2020.9147399
DO - 10.23919/ACC45564.2020.9147399
M3 - Conference contribution
AN - SCOPUS:85089567785
T3 - Proceedings of the American Control Conference
SP - 2685
EP - 2691
BT - 2020 American Control Conference, ACC 2020
PB - Institute of Electrical and Electronics Engineers Inc.
T2 - 2020 American Control Conference, ACC 2020
Y2 - 1 July 2020 through 3 July 2020
ER -