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Outline: 00:00 - Intro 02:55 - Brachistochrone problem 20:52 - Beginning of the calculus of variations 32:00 - Principle of least action 42:37 - Maximum principle 1:02:35 - Dynamic programming 1:11:12 - Linear quadratic control 1:16:37 - Beyond optimal control: games, nonsmooth analysis, MPC, RL 1:28:40 - Outro Links: 300 years of optimal control: https://tinyurl.com/2s3t8se4 Brachistochrone: https://tinyurl.com/mwmv38ew Acta Eroditorum, 1696: https://tinyurl.com/55yf5v49 Acta Eroditorum, 1697: https://tinyurl.com/2a7msaaj Bernoulli family: https://tinyurl.com/y2vx2xdn Leibniz–Newton calculus controversy: https://tinyurl.com/3974fdhd Calculus of variations: https://tinyurl.com/3vvz8tuf Beginning of the Calculus of Variations: https://tinyurl.com/mv6btxfn Lagrangian mechanics: https://tinyurl.com/ycx5fv46 Euler–Lagrange equation: https://tinyurl.com/53yybvyx Hamiltonian mechanics: https://tinyurl.com/yfrd8zhz Hamilton–Jacobi equation: https://tinyurl.com/46m9cuvs Pontryagin: https://tinyurl.com/35ehxnex Pontryagin’s autobiography: https://ega-math.narod.ru/LSP/book.htm Discovery of the Maximum Principle: https://tinyurl.com/3s43nv4t Maximum Principle: https://tinyurl.com/4f7352t4 Goddard problem: https://tinyurl.com/5n8swp2m Hamilton–Jacobi–Bellman equation: https://tinyurl.com/4uemn5y4 Kalman filter: https://tinyurl.com/39zx5yry Clarke: https://tinyurl.com/yj2tzcjb MPC: https://tinyurl.com/4sf5pzvy RL: https://tinyurl.com/ee5ne7sz AlphaGo: https://tinyurl.com/ydrf8jsc Podcast info: Podcast website: https://www.incontrolpodcast.com/ Apple Podcasts: https://tinyurl.com/5n84j85j Spotify: https://tinyurl.com/4rwztj3c RSS: https://tinyurl.com/yc2fcv4y Youtube: https://tinyurl.com/bdbvhsj6 Facebook: https://tinyurl.com/3z24yr43 Twitter: / incontrolp Instagram: https://tinyurl.com/35cu4kr4 Acknowledgments and sponsors: This episode was supported by the National Centre of Competence in Research on «Dependable, ubiquitous automation» and the IFAC Activity fund. The podcast benefits from the help of an incredibly talented and passionate team. Special thanks to L. Seward, E. Cahard, F. Banis, F. Dörfler, J. Lygeros, ETH studio and mirrorlake . Music was composed by A New Element.