Nonlinear model-predictive control and dynamic real-time optimization on infinite horizons

• Applicant: Professor Dr.-Ing. Wolfgang Marquardt
• Subject Area: Automation, Mechatronics, Control Systems, Intelligent Technical Systems, Robotics
• Term: from 2009 to 2015
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 152353704

The overall objective of this project is to develop efficient algorithms for a wide range of model-predictive control problems, in particular economic nonlinear model-predictive control problems (NMPC), with guaranteed closed-loop stability based on an infinite horizon strategy. Economic NMPC is based on a nonlinear objective function consisting of revenues and costs for process operation, which is thus not necessarily a positive-definite function. Consequently, standard stability proofs for regulatory NMPC cannot be applied as the objective function cannot serve as a Lyapunov function. Furthermore, finite moving horizon concepts are still computationally involved and not completely satisfactory.In the first three years of this project, we explored an alternative formulation relying on an infinite horizon approach. By applying Bellman's principle of optimality, this method naturally implies stability for regulatory as well as economic NMPC - provided a sufficiently accurate numerical solution can be computed. First, a transformation of the time axis was investigated leading to a finite horizon problem with bounded costs. In order to apply solution techniques from nonlinear programming, the transformed finite horizon problem was discretized. Subsequently, several possibilities to reduce computational load while maintaining sufficient solution accuracy were investigated such as a novel control grid adaptation strategy and neighboring-extremal updates. Finally, the closed-loop performance of the infinite horizon formulation was compared to a finite horizon formulation. It could be shown that the infinite-horizon formulation is a promising alternative for continuously operated processes for which no prespecified final time exists. Nonetheless, there remain open issues regarding algorithmic as well as methodological details which shall be investigated in the fourth year. First, closed-loop stability will be derived for continuous-time processes with discrete-time control moves. Second, the novel control grid adaptation strategy will be extended for path-constrained multi-stage problems in order to guarantee a sufficiently good resolution also in the transient parts of the horizon. Third, we will investigate the numerical solution of the infinite-horizon formulation with finite rewards. Finally, computational time will be further reduced with the help of a neighboring-extremal controller.

• DFG Programme: Research Grants