Stanford AA203 Optimal and Learning-Based Control | Spring 2026 | Lecture 4: Optimal Control

Indirect methods for optimal control utilize the calculus of variations to define necessary optimality conditions. By formulating these conditions as a system of differential equations and boundary constraints, one can derive analytical solutions that are subsequently processed by numerical solvers to determine optimal trajectories and control sequences.

• Fundamental optimality — A function represents a local minimum when the variation of the cost functional vanishes at that point [02:31].
• Euler equations — These second-order nonlinear differential equations provide an actionable method to compute optimal paths, analogous to setting a gradient to zero in