Nonlinear model-predictive control and dynamic real-time optimization on infinite horizons
Final Report Abstract
This project focused on theoretical as well as numerical aspects of nonlinear model-predictive control and dynamic real-time optimization on infinite horizons. A stability proof has been derived for sampled-data ENMPC on finite horizons taking the model mismatch between the continuous-time process and its discrete-time counterpart used in the controller into account. To ensure recursive feasibility, closed-loop admissible sets are first defined despite the discretization error induced by the numerical solution strategy. Important assumptions introduced by M. Diehl et al. (2011) to proof stability as well as to define a suitable Lyapunov function have been transferred to the sampled-data ENMPC context and some further assumptions have been made. The stability proof is based on the fact that the inevitable discretization error induced by the integrator leads to a disturbance in the undisturbed control trajectory. Thus, input-to-state stability has been proven for the continuous-time system with the feedback control law provided by the ENMPC. A novel optimality-based control grid adaptation strategy has been suggested to address the trade-off between solution time and solution accuracy rigorously. It makes use of the switching function defined for optimal control problems based on input-affine systems and input-affine objective functions. Applying the switching function, it can be seen whether an optimal control trajectory is at its bounds or in between its bounds. If it is at its bounds, control grid points can be safely eliminated because the optimal control trajectory is accurate at the bounds also for a coarsely discretized control grid. However, if it lies between its bounds, control grid points are inserted if the optimality conditions of the continuous-time optimal control problem are not met within user-specified bounds. Finally, a corrected time transformation function has been suggested for the multi-stage case.
Publications
- Economic model-predictive control for chemical processes. PhD thesis, RWTH Aachen University, 2015. Aachen / Shaker Verlag (2016). - 978-3-8440-4248-1
I. J. Wolf
- Optimality-based grid adaptation for input-affine optimal control problems. Computers & Chemical Engineering Volume 92, 2 September 2016, Pages 189-203
F. Assassa and W. Marquardt
(See online at https://doi.org/10.1016/j.compchemeng.2016.04.041)
