Reduced-order methods for nonlinear model predictive control

• Applicant: Professor Dr. Stefan Volkwein
• Subject Area: Automation, Mechatronics, Control Systems, Intelligent Technical Systems, Robotics
• Term: from 2015 to 2021
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 274852524

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.

• DFG Programme: Research Grants