An online slow manifold approach for efficient optimal control of multiple time-scale kinetics

Chemical reactions modeled by ordinary differential equations are finite-dimensional dissipative dynamical systems with multiple time-scales. They are numerically hard to tackle -- especially when they enter an optimal control problem as "infinite-dimensional" constraints. Since discretization of such problems usually results in high-dimensional nonlinear problems, model (order) reduction via slow manifold computation seems to be an attractive approach. We discuss the use of slow manifold computation methods in order to solve optimal control problems more efficiently having real-time applications in view.