Suggested further readings


Bertsekas, D. P. (1995). Dynamic programming and optimal control. MA: Athena scientific.


Bellman, R. (1966). Dynamic programming. Science 153(3731): 34-37. doi: 10.1126/science.153.3731.34 Closed Access publication.

Charnov, E. L. (1976). Optimal foraging, the marginal value theorem. Theoretical population biology 9(2): 129-136.

Doyle, J. C. (1978). Guaranteed margins for LQG regulators. IEEE Transactions on automatic Control 23(4): 756-757. doi: 10.1109/TAC.1978.1101812 Closed Access publication. Note: Abstract is definitely worth reading.

Kalman, R. E. (1960). Contributions to the theory of optimal control. Boletin de la sociedad matematica mexicana 5(2): 102-119.

Control as Inference

Kappen, H. J., Gómez, V., and Opper, M. (2012). Optimal control as a graphical model inference problem. Machine learning 87(2): 159-182. doi: 10.1007/s10994-012-5278-7 Open Access publication.

Todorov, E. (2009). Efficient computation of optimal actions. Proceedings of the national academy of sciences 106(28): 11478-11483. doi: 10.1073/pnas.0710743106 Closed Access publication (postprint: Open Access publication).


Castro, L. N. G., Hadjiosif, A. M., Hemphill, M. A., and Smith, M. A. (2014). Environmental consistency determines the rate of motor adaptation. Current Biology 24(10): 1050-1061. doi: 10.1016/j.cub.2014.03.049 Open Access publication.

Smith, M. A., Brandt, J., and Shadmehr, R. (2000). Motor disorder in Huntington’s disease begins as a dysfunction in error feedback control. Nature 403(6769): 544-549. doi: 10.1038/35000576 Closed Access publication (postprint: Open Access publication).

Sing, G. C., Joiner, W. M., Nanayakkara, T., Brayanov, J. B., and Smith, M. A. (2009). Primitives for motor adaptation reflect correlated neural tuning to position and velocity. Neuron 64(4): 575-589. doi: 10.1016/j.neuron.2009.10.001 Open Access publication.

Wagner, M. J., and Smith, M. A. (2008). Shared internal models for feedforward and feedback control. Journal of Neuroscience 28(42): 10663-10673. doi: 10.1523/JNEUROSCI.5479-07.2008 Open Access publication.


Bautista, L. M., Tinbergen, J., and Kacelnik, A. (2001). To walk or to fly? How birds choose among foraging modes. Proceedings of the National Academy of Sciences, 98(3), 1089-1094. doi: 10.1073/pnas.98.3.1089 Closed Access publication (postprint: Open Access publication).

Ralston, H. J. (1958). Energy-speed relation and optimal speed during level walking. Internationale Zeitschrift für Angewandte Physiologie Einschliesslich Arbeitsphysiologie 17(4): 277-283. doi: 10.1007/BF00698754 Closed Access publication.

Shadmehr, R., and Ahmed, A. A. (2020). Vigor: Neuroeconomics of movement control. MIT Press.

Xu-Wilson, M., Zee, D. S., and Shadmehr, R. (2009). The intrinsic value of visual information affects saccade velocities. Experimental Brain Research, 196(4), 475-481. doi: 10.1007/s00221-009-1879-1 Closed Access publication (postprint: Open Access publication).

Yoon, T., Geary, R. B., Ahmed, A. A., & Shadmehr, R. (2018). Control of movement vigor and decision making during foraging. Proceedings of the National Academy of Sciences 115(44): E10476-E10485. doi: 10.1073/pnas.1812979115 Closed Access publication (postprint: Open Access publication).

Yoon, T., Jaleel, A., Ahmed, A. A., and Shadmehr, R. (2020). Saccade vigor and the subjective economic value of visual stimuli. Journal of neurophysiology 123(6): 2161-2172. doi: 10.1152/jn.00700.2019 Open Access publication.