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.

Center of Excellence forOptimization in Engineering H. J. Ferreau, G. Lorini, M. Diehl

Fast NMPC of Gasoline Engines

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Principle of Optimal Feedback Control / Nonlinear MPC:

Center of Excellence forOptimization 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)

Center of Excellence forOptimization 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 toMoore‘s law + Algorithm Development

Center of Excellence forOptimization 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