Fast computation of the Hessian of the Lagrangian in shooting algorithms for dynamic optimization
- R. Hannemann, W. Marquardt
- In Proceedings of the DYCOPS 8 conference,
The optimal operation of chemical processes is challenged by frequent transitions and by the influence of process or model uncertainties. Under uncertainties, it is necessary to quickly update the optimal trajectories in order to avoid the violation of constraints and the deterioration of the economic performance of the process. Although an economically optimal operation can be ensured by online dynamic optimization, the high computational load of dynamic optimization associated with nonlinear and complex models is often prohibitive in real-time applications. To reduce the computational time required for online computation of the 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, efficient techniques for updating the nominal trajectories based on parametric sensitivities are applied, which do not require the solution of the rigorous optimization problem. However for larger perturbations, the linear 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. In this work, the sensitivity-based approach of Kadam and Marquardt (2004) is extended with a fast computational method for second-order derivatives based on composite adjoints. The application of the method to a simulated semi-batch reactor demonstrates that fast and optimal trajectory updates can be obtained.