Cooperative Control and Performance Evaluation of a Linear MIMO Parabolic Spatiotemporal Dynamic System on Directed and Switching Topologies

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
$|\cdot |_{2}$
. 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.