Many optimal control, estimation and design problems can be formulated as so-called dynamic optimization problems, which are optimization problems with differential equations and other constraints. State-of-the-art methods based on collocation, which enforce the differential equations at only a finite set of points, can struggle to solve certain dynamic optimization problems, such as those with high-index differential algebraic equations, consistent overdetermined constraints or problems with singular arcs. We show how numerical methods based on integrating the differential equation residuals can be used to solve dynamic optimization problems where collocation methods fail. Furthermore, we show that integrated residual methods can be computationally more efficient than direct collocation.
This seminar takes place at RAL (Rutherford Appleton Lab).