Formulation of dynamic optimization problems using Modelica and their efficient solution

Dynamic optimization problems often arise in advanced model based control. For example in model based predictive control and in the estimation of process parameters or not measured process signals, the underlying problems can be treated with optimization. A process model formulated in Modelica [10] can be used as a core part in the formulation of dynamic optimization problems. This allows an efficient engineering of advanced control applications as simulation models are reused for optimization. The paper discusses, how different types of dynamic optimization problems can be formulated based on a nonlinear dynamic system model. Furthermore, the efficient numerical solution of dynamic optimization problems as large-scale nonlinear programming problems is outlined. The treatment of state constraints is emphasized in this context. Possibilities for obtaining model sensitivities as required by an optimization solver are discussed. However, the class of models that can be used for optimization in this way is limited, compared to all models that can be formulated in Modelica and used for initial-value simulation. Specific requirements by optimization solvers are discussed together with features of the Modelica language supporting their consideration in model formulations. The optimal startup of a power plant serves as a practical example.