Wang JW, He W. Cooperative Control and Performance Evaluation of a Linear MIMO Parabolic Spatiotemporal Dynamic System on Directed and Switching Topologies.
IEEE TRANSACTIONS ON CYBERNETICS 2024;
54:3626-3637. [PMID:
38153829 DOI:
10.1109/tcyb.2023.3339730]
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Abstract
The current work concerns on cooperative control of exponential stabilization and control performance improvement in the spatial domain for a linear spatiotemporal dynamic system associated with multiple control actuators and multiple collaborative measurement sensors. By assuming that the system dynamics is modeled by a MIMO parabolic partial differential equation (PPDE) and each sensor can share measurement information with its topological neighbors in directed and switching topological networks, a cooperative control protocol is proposed to achieve the control aim of this article. With the help of a combination of multiagent consensus theory, Lyapunov's method, and integral inequality technique, sufficient conditions are presented for the closed-loop exponential stability of the PPDE in the norm |·|2 . Moreover, some performance indexes are defined to evaluate the closed-loop control performance improvement in the spatial domain. Extensive simulation results are finally presented for a simple numerical example and a practical heat treatment process to verify the effectiveness and performance improvement capability of the proposed cooperative control protocol.
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