论文标题
用于PDE受限的非线性模型预测控制的双层雅各比方法
A Double-Layer Jacobi Method for PDE-Constrained Nonlinear Model Predictive Control
论文作者
论文摘要
本文提出了一种由部分微分方程（PDES）控制的系统的非线性模型预测控制（NMPC）的实时优化方法。通过使用有限差异方法在空间和时间内离散PDE系统来制定要解决的NMPC问题。所提出的方法称为双层雅各比方法，它利用了PDE受限的NMPC问题的空间和时间稀疏性。在上层中，通过忽略状态或稳定的（Lagrange乘数对应于状态方程）方程的状态或稳定的时间耦合来解决NMPC问题，从而保留了空间稀疏性。较低的雅各比方法是一种线性求解器，该线性求解器通过利用空间稀疏性来致力于PDE受限的NMPC问题。收敛分析表明，所提出的方法的收敛性与预测范围和正则化有关。控制传热过程的数值实验的结果表明，所提出的方法比常规结构探索牛顿的方法快两个数量级。
This paper presents a real-time optimization method for nonlinear model predictive control (NMPC) of systems governed by partial differential equations (PDEs). The NMPC problem to be solved is formulated by discretizing the PDE system in space and time by using the finite difference method. The proposed method is called the double-layer Jacobi method, which exploits both the spatial and temporal sparsities of the PDE-constrained NMPC problem. In the upper layer, the NMPC problem is solved by ignoring the temporal couplings of either the state or costate (Lagrange multiplier corresponding to the state equation) equations so that the spatial sparsity is preserved. The lower-layer Jacobi method is a linear solver dedicated to PDE-constrained NMPC problems by exploiting the spatial sparsity. Convergence analysis indicates that the convergence of the proposed method is related to the prediction horizon and regularization. Results of a numerical experiment of controlling a heat transfer process show that the proposed method is two orders of magnitude faster than the conventional structure-exploiting Newton's method.
