Reduced-order methods for nonlinear model predictive control

在与同事Lars gr<s:1> ne （Bayreuth）和Thomas Meurer的联合项目模型中，对节能建筑运行的预测PDE控制策略进行了开发。为此，采用了模型预测控制（MPC）策略。在“非线性MPC的降阶方法”这个项目中，我们推导了在MPC算法中用于快速和足够精确地解决MPC每次迭代中出现的优化问题的方法。准确度将由特定于问题的后验误差分析来控制。此外，为了估计降阶模型的质量，并在必要时对降阶模型进行修正，采用了非线性优化中的信任域框架。由于建筑作业中产生的偏微分方程组是参数相关的、非线性的和时变的，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逼近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，将研究线性化，使有效的降阶方法应用于线性二次控制问题。平坦系统给出了一个重要的特例。在这种情况下，只有解决静态（而不是动态）非线性优化问题是必要的。因此，我们对保持平面性的降阶方法的发展很感兴趣。所有策略都将在楼宇运作中测试一个基准问题。

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.