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Optimal Control Theory - University of Washington

To appear inBayesian Brain, Doya, K. (ed), MIT Press (2006) Optimal Control TheoryEmanuel TodorovUniversity of California San DiegoOptimal Control Theory is a mature mathematical discipline with numerous applicationsin both science and engineering. It is emerging as the computational framework of choicefor studying the neural Control of movement, in much the same way that probabilistic infer-ence is emerging as the computational framework of choice for studying sensory informationprocessing. Despite the growing popularity of Optimal Control models, however, the elab-orate mathematical machinery behind them is rarely exposed and the big picture is hardto grasp without reading a few technical books on the subject. While this chapter cannotreplace such books, it aims to provide a self-contained mathematical introduction to opti-mal Control Theory that is su ciently broad and yet su ciently detailed when it comes tokey concepts.

zon formulations, basics of stochastic calculus. 3. Pontryagin™s maximum principle, ODE and gradient descent methods, relationship to classical mechanics. 4. Linear-quadratic-Gaussian control, Riccati equations, iterative linear approximations to nonlinear problems. 5. Optimal recursive estimation, Kalman –lter, Zakai equation. 6.

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