Neighboring-extremal updates for dynamic real-time optimization

Abstract:
The interest in dynamic real-time optimization (DRTO) with economic objectives and rigorous nonlinear models has increased in the past years. A profitable and flexible operation adapted to changing market conditions is ensured by the usage of economic optimization objectives in DRTO. However, the solution of optimization problems with nonlinear, possibly stiff models carries a substantial computational load. The efficient solution of complex dynamic optimization problems with nonlinear models still remains a challenge for model-based control applications. To reduce the computational time required for online computation of optimal trajectories in the neighborhood of the optimal solution under uncertainty, different strategies have been explored recently. If the operation is affected by small perturbations in the neighborhood of the nominal optimal solution, efficient techniques for updating the nominal trajectories based on parametric sensitivities can be applied, which do not require the solution of the rigorous optimization problem. However for larger perturbations and strong nonlinearities, the fast updates obtained by the neighboring extremal solutions are not sufficiently accurate, and the solution of the nonlinear optimization problem requires further iterations with updated sensitivities to give a feasible and optimal solution. The sensitivity-based approach of [1] uses a fast computational method for second-order derivatives based on composite adjoints to update the second-order sensitivities online. This strategy is extended in this work with adaptive grid refinement, which provides a reduction of the number of degrees of freedom while maintaining the same control performance. Furthermore, the uncertainty in the states and parameters estimated online is incorporated through the parametric sensitivities. The application of the method to a simulated semi-batch reactor demonstrates that fast and optimal trajectory updates can be obtained. [1] Lynn Würth, Ralf Hannemann and Wolfgang Marquardt. An Efficient Strategy for Real-Time Dynamic Optimization Based on Parametric Sensitivities. Proceedings of the IFAC World Congress, 7-12 July 2008, Seoul.

Keywords:
Dynamic real-time optimization, nonlinear model-predictive control, neighboring-extremal, sensitivity-based updates, adjoints