Reduced-order methods for nonlinear model predictive control

在与同事Lars Grüne（拜罗伊特）和托马斯默勒（Thomas Meurer）的联合项目中，开发了用于建筑物运行的能源管理的模型预测PDE控制。为此目的，使用模型预测控制（MPC）策略。在非线性MPC的降阶方法项目中，我们推导出了MPC算法中应使用的方法，用于快速且足够准确地解决MPC每次迭代中出现的优化问题。将通过特定问题的后验误差分析控制准确度。此外，从非线性优化的信赖域框架，以估计降阶模型的质量，并在必要时修改降阶模型。由于建筑运营中出现的偏微分方程组是参数依赖的，非线性和时变的，我们将使用降基方法来计算降阶模型。我们将分析降阶模型的近似误差与模型预测控制的总体目标之间的相互作用，以获得计算控制的最优性或稳定性。此外，线性化将进行调查，使有效的降阶方法的线性二次控制问题的应用。一个重要的特例是平坦系统。在这种情况下，只有静态（而不是动态）非线性优化问题的解决方案是必要的。因此，我们感兴趣的降阶方法，保持平坦性的发展。所有策略都将针对建筑运营中出现的基准问题进行测试。

In the joint project Model predictive PDE control for energy efficient building operation with the colleagues Lars Grüne (Bayreuth) and Thomas Meurer control strategies for the energy management of building operation are developed. For that purpose model predictive control (MPC) strategies are utilized. In the project Reduced-order methods for nonlinear MPC we derive methods which should be utilized within a MPC algorithm for a fast and sufficiently accurate solution of the optimization problems arising in each iteration of the MPC. The accuracy will be controlled by a problem-specific a-posteriori error analysis. Moreover, a trust-region framework from nonlinear optimization is applied in order to estimate the quality of the reduced-order model and to modify the reduced-order model if necessary. Since the arising system of partial differential equations in building operation is parameter-dependent, nonlinear and time-variant, we will use the reduced-basis method for the computation of the reduced-order model. We will analyze the interplay of the approximation error by the reduced-order model and the overall goal of the model predictive control to attain optimality or stability properties for the computed controls. Also linearizations will be investigated that allow the application of efficient reduced-order approaches for linear-quadratic control problems. An important special case is given by flat systems. In this case only solutions of static (instead of dynamic) nonlinear optimization problems are necessary. Therefore, we are interested in the development of reduced-order methods which preserve the flatness property. All strategies will be tested for a benchmark problem arising in building operation.