For Model Predictive Control (MPC) and Moving Horizon Estimation (MHE) in industrial applications, especially embedded, reliability and efficiency of the underlying algorithms are of paramount importance. The first part of the talk presents a novel MHE-based framework for learning and adapting physics-informed models, i.e., physics-based models extended by a data-driven component. The proposed MHE-scheme provides a meaningful approach to address model mismatches appearing in industrial systems, such as part-to-part variations and time-varying changes of the system dynamics, due to the inherent ability of the MHE to learn online directly from noisy input-output data. Further, MHE, by being an optimization-based estimation algorithm, naturally allows imposing prior physical knowledge as constraints to safely guide the learning. In combination with MPC the learning-based MHE provides a powerful concept for application of learning-based control in industrial applications.

Both MPC and MHE relies on efficient numerical optimization algorithms. More specifically, the solution of Quadratic Programs (QPs) plays an important role, e.g., as a subproblem in Sequential Quadradic Programming (SQP) often used for nonlinear MPC. The second part of the talk presents a structure-exploiting QP solver based on proximal Augmented Lagrangian Method (ALM) extending the general purpose QP solver QPALM. The proposed algorithm, QPALM-OCP, explicitly accounts for the equality constraints arising from the system dynamics and exploits the problem structure when solving the ALM sub-problems. Furthermore, the algorithm relies on low-rank factorization updates as the linear systems to be solved in the iterates only changes with the active set. QPALM-OCP compares favorably against state-of-the-art QP solvers over a wide range of problem dimensions.