Principle of Optimal Feedback Control / Nonlinear MPC:
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Center of Excellence for
Optimization in Engineering
u0 H. J. Ferreau, G. Lorini, M. Diehl
Fast NMPC of Gasoline Engines
NMPC applications, with decreasing timescales
Polymerisation
reactor (with
BASF)
Distillation
column (with
Univ. Stuttgart)
Chromatographic
Separation (with
Univ. Dortmund)
Looping kites for power
generation, with
Politecnico di Torino
Combined Cycle
Power Plant (with
Univ. Pavia)
PET plant: Plant wide
control project with
Politecnico di Milano
Robot arms (with
Columbia Univ. &
INRIA Grenoble)
Car Engines: EU Project
with Univ. Linz, Stuttgart,
Politecnico di Milano
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
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
Center of Excellence for
Optimization in Engineering
H. J. Ferreau, G. Lorini, M. Diehl
Fast NMPC of Gasoline Engines