Optim. Control·Course
Optimal Control
Optimal control: Pontryagin maximum principle, LQR, MPC, stochastic control, and reinforcement learning
Part of the Mathematics track — finish it for a verifiable diploma →
§ 01 — Orientation
New here?
What you'll be able to do, who this is for, how long it takes, and where to begin.
By the end, you will be able to
- 01Apply Pontryagin's maximum principle.
- 02Design LQR and MPC controllers.
- 03Handle stochastic control.
- 04Connect control to reinforcement learning.
- 05Model a real dynamic-control problem.
Who this is for
How long it takes
- Quick orientationSkim the opening module and the cheatsheet to get the shape of it.~2 h
- Full read-throughRead every article once, in order.~2 h
- Mastery pathRead, take the quizzes, and space out your reviews.~2 weeks
- APA
Stoa. (2026). Optimal Control [Online course]. Stoa. https://stoa.school/course/optimal-control
- MLA
Stoa. “Optimal Control.” Stoa, 2026, https://stoa.school/course/optimal-control.
- Chicago
Stoa. “Optimal Control.” Stoa. Accessed September 1, 2026. https://stoa.school/course/optimal-control.
§ 02 — Curriculum
5 modules.
Each module is a small unit. Most read in sequence — but a determined reader can begin anywhere.
- M ICalculus of VariationsThe Lagrange problem, the Euler–Lagrange equation, and classical problems3 articles
18 minBegin → - M IIPontryagin’s Maximum PrincipleOptimal control in continuous time, the Hamiltonian, and adjoint variables3 articles
18 minBegin → - M IIIBellman’s Dynamic ProgrammingThe principle of optimality, the Bellman equation, and the value function3 articles
18 minBegin → - M IVLinear Control and StabilityLinear systems, controllability, observability, and PID controllers3 articles
18 minBegin → - M VStochastic Optimal ControlStochastic systems, the Kalman filter, and stochastic dynamic programming3 articles
18 minBegin →
§ 03 — Learning outcomes
4 outcomes.
Apply Pontryagin’s maximum principle to optimal control problems.
Design linear–quadratic regulators and model predictive controllers.
Solve stochastic control problems using the Hamilton–Jacobi–Bellman equation.
Relate optimal control to reinforcement learning methods.
§ 04 — Practices