1. Center of Excellence for Optimization in Engineering H. J. Ferreau, G. Lorini, M. Diehl Fast NMPC of Gasoline Engines x0x0 x0x0 u0u0 u0u0 Principle of Optimal Feedback Control / Nonlinear MPC:

2. Center of Excellence for Optimization in Engineering H. J. Ferreau, G. Lorini, M. Diehl Fast NMPC of Gasoline Engines Distillation column (with Univ. Stuttgart) Polymeri- sation reactor (with BASF) Chromatographic Separation (with Univ. Dortmund) Combined Cycle Power Plant (with Univ. Pavia) PET plant: Plant wide control project with Politecnico di Milano Car Engines: EU Project with Univ. Linz, Stuttgart, Politecnico di Milano NMPC applications, with decreasing timescales Looping kites for power generation, with Politecnico di Torino Robot arms (with Columbia Univ. & INRIA Grenoble)

3. Center of Excellence for Optimization in Engineering H. J. Ferreau, G. Lorini, M. Diehl Fast NMPC of Gasoline Engines NMPC Computation from 1998 to 2006  1998: 5th order distillation model allows sampling times of only 5 minutes [Allgower, Findeisen, 1998]  2001: 206th order distillation model, sampling times of 20 seconds [D. et al. ‚01]  2006: 5th order engine model, sampling times of 10-20 milliseconds [Ferreau et al. ‘06] 5*60*1000 / 20 = 15 000 times faster, due to Moore‘s law + Algorithm Development

4. Center of Excellence for Optimization in Engineering H. J. Ferreau, G. Lorini, M. Diehl Fast NMPC of Gasoline Engines Crucial Algorithmic Features for Fast NMPC  Direct, simultaneous optimal control approach for fast nonlinear convergence (multiple shooting or collocation)  Efficient derivative generation for ODE/DAE solvers  Initialization by „Initial Value Embedding“ („Continuation“, „Sensitivity Update“, „1st Order Predictor“,...)  Real-Time Iterations for fast tracking of optimal solutions