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<- [[:chaosbook]]

====== Chapter: Relaxation for cyclists ======

(ChaosBook.org blog, chapter [[http://chaosbook.org/paper.shtml#relax|Relaxation for cyclists]])  --- //[[predrag.cvitanovic@physics.gatech.edu|Predrag Cvitanovic]] 2011-01-04//

===== Section 3: Least action method =====

  * **Predrag 2011-01-03** Heard Jeff Moehlis talk at Northwestern Applied Math on "neural" control. Learned this:
__Hamilton-Jacobi-Bellman PDEs__ minimize trajectory //time// under a range of time dependent external  "control" inputs //u(t)//. This is a feed-forward, open lop control. Read Bardi, Capuzzo and Dolcetta 1997.

"arg min" means that the `value function' is minimized under a range of variations of the "argument" //u(t)//.

For Hodgkin-Huxley they minimize the power of electrical control input. That is done by __Euler-Lagrange equations__, with Lagrange multipliers of form //λ_1(t)(eqs of motion)//, //λ_2(t)(power constraint)//. They solve these by the shooting method.

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