dSEA Lecture series: "Numerical Methods for Optimal Control"

We are pleased to welcome Dieter Grass, Research Collaborator at Technische Universität Wien and Creator of the Matlab toolbox OCMat, as guest speaker for this lecture series as part of the Static and Dynamic Optimization course, taught by Prof.  Alessandra Buratto, included in our Master’s degree in Applied Economics (MAE).

This course introduces numerical methods for analyzing and solving optimal control problems. We begin with the mathematical and computational preliminaries of solving nonlinear equations, boundary value problems, and differential-algebraic equations, with a focus on continuation methods and their role in detecting and analyzing local bifurcations. Building on this foundation, we address optimization and the formulation of first-order necessary conditions, highlighting how continuation can be applied to the resulting systems of equations. Applications include both finite- and infinite-horizon optimal control problems, with particular emphasis on the computation of stable paths, finite-time trajectories via Pontryagin’s Maximum Principle, and the continuation of multiple optimal solutions. Practical implementation and examples are provided through the Matlab toolbox OCMat, with a brief comparison to Python-based alternatives.