DYNAMIC SIMULATION AND OPTIMIZATION WITH INEQUALITY PATH CONSTRAINTS

A novel and general method for numerical integration of ODEs or DAEs w ith inequality path constraints involving state variables is proposed. In general, active inequality path constraints involving state variab les produce high-index DAEs, which complicate the solution of dynamic simulation and optimization problems. Current DAE integrators can hand le only certain limited classes of high-index problems. However, the r ecently developed method of dummy derivatives can be used to derive an index-1 problem with the same solution set as the high-index problem. This permits the use of standard DAE codes for integrating high-index DAEs, although the equivalent index-1 DAE has a larger number of equa tions than the original DAE system. Our method detects the activation and deactivation of inequality path constraints during integration, an d solves the resulting high-index DAE system as necessary. In addition to allowing the solution of dynamic simulation problems with inequali ty path constraints, we show that this method simplifies the solution of dynamic optimization problems using the control parameterization me thod. The method allows us to handle the inequality path constraints i nvolving state variables within the DAE integrator, resulting in fewer objective function and gradient evaluations for the NLP solver, and r educing the time necessary to solve the dynamic optimization problem.