Cooperative Control and Performance Evaluation of a Linear MIMO Parabolic Spatiotemporal Dynamic System on Directed and Switching Topologies
针对多输入多输出抛物型偏微分方程描述的时空动态系统，提出一种基于有向和切换拓扑网络的协同控制协议，实现指数稳定并提升空间域控制性能，通过数值算例和热处理过程验证有效性。
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 <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$|\cdot|_{2}$</tex-math> </inline-formula> . 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.