Optimal Control
The optimal control problems can be seen as a functional minimization, called target, subjected to ordinary differential constraints.
This part introduces the variational formulation of optimal control, the transformations that bring a problem into a standard form, a set of worked examples, numerical solution methods, and a summary of the necessary conditions.
Prerequisites: ODEs, KKT conditions, and the Euler–Lagrange framework.
Objectives: formulate optimal-control problems, derive necessary conditions, transform constraints, and compare indirect and direct numerical methods.
Expected outcomes: the reader can build a Hamiltonian formulation, transcribe an OCP into a nonlinear program, interpret costates and path constraints, and validate a computed trajectory.