inControl ep41 - A minimal history of optimal control
Feb 16, 2026
A lively tour of the brachistochrone puzzle and why the cycloid mattered for time-optimal paths. A sweep through Euler, Lagrange, Hamilton and the birth of variational thinking. Mid-century leaps to Pontryagin’s maximum principle and Bellman’s dynamic programming are highlighted. Modern threads include LQR, Kalman filtering, model predictive control, games, nonsmooth analysis and reinforcement learning.
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The Brachistochrone Challenge Sparks Rivalry
- Johann Bernoulli posed the 1696 brachistochrone challenge to provoke the best mathematicians worldwide.
- Newton secretly sent a terse anonymous solution that Bernoulli recognized as his.
Calculus Of Variations Becomes Systematic
- Euler and Lagrange transformed isolated puzzles into the calculus of variations with general Euler-Lagrange equations.
- Lagrange's analytic method made finding extrema mechanical and systematic for functions of curves.
Hamilton Foreshadows Dynamic Programming
- Hamilton recast mechanics via the principle of stationary action and introduced conjugate momenta and the Hamiltonian.
- His characteristic function anticipates the modern value function used in dynamic programming.
