An LMI-based approach to distributed model predictive control design for spatially-interconnected systems
An LMI-based approach to distributed model predictive control design for spatially-interconnected systems
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DOI：
10.1016/j.automatica.2018.06.024
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发表时间：
2018-09
期刊：
影响因子：
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通讯作者：
Qin Liu;H. S. Abbas;J. Mohammadpour
中科院分区：
文献类型：
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作者：
Qin Liu;H. S. Abbas;J. Mohammadpour
针对具有约束条件的线性时空不变（LTSI）分布式系统，提出了一种新的分布式模型预测控制（MPC）设计框架。给出了描述子系统间分布式动力学的二维输入输出模型，证明了非极小状态空间的实现导致基于线性矩阵不等式（LMI）的终端状态反馈控制器设计在数值上易于处理。局部在线优化问题定义在子系统级别，子系统通过耦合状态交换预测，可以在所有子系统上并行非迭代地求解。通过施加一致性约束和终端约束，保证了子系统间信息交换存在一步延迟时的稳定性和递归可行性。由于非最小状态空间实现，MPC公式中保留了输入输出属性，因此在线实现不需要状态估计器。利用热方程的仿真结果表明，与集中式MPC方案相比，分布式MPC设计具有令人满意的性能。
This paper proposes a new framework to distributed model predictive control (MPC) design for linear time- and space-invariant (LTSI) distributed systems subject to constraints. Given a two-dimensional, input–output model that describes the distributed dynamics among the subsystems, it is shown that a non-minimal state space realization leads to numerically tractable linear matrix inequality (LMI) based terminal state feedback controller design. The local online optimization problem is defined at the subsystem level with subsystems exchanging predictions through coupled states and can be solved in parallel at all subsystems non-iteratively. Stability and recursive feasibility are guaranteed in the presence of one-step delayed exchanging information among subsystems by imposing consistency constraints and terminal constraints. Attributed to the non-minimal state space realization, input–output properties are preserved in the MPC formulation, and hence no state estimator is needed for the online implementation. Simulation results using a heat equation demonstrate a satisfactory performance of the proposed distributed MPC design compared to centralized MPC schemes.