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Integration and action describes how the nervous system converts processed sensory information into effective motor commands. The optimal control framework provides the theoretical basis: the optimal action u* simultaneously minimizes the error (distance to target) and the cost of control (energy, effort).

The LQR regulator is the analytical solution for linear systems with a quadratic cost function. The gain K_LQR distributes the control effort among the components of the state according to their importance (Q matrix) and the cost of each action (R matrix). The Riccati equation determines P_LQR, which is the optimal value function. Increasing evidence suggests that the cerebellum implements a regulator analogous to the LQR.

Hill's model captures fundamental muscle properties: the force-length relationship f_L(L) (muscles are strongest at optimal length) and the force-velocity relationship f_V(V) (force falls with the speed of shortening and increases with lengthening). These properties confer passivity and intrinsic stability to the musculoskeletal system.

Fitts' law is one of the most robust empirical laws in motor psychology: the movement time MT to reach a target of width W at distance D scales logarithmically with the difficulty index ID = log(2D/W). This law holds for humans, primates, and mice, and reflects the fundamental trade-off between speed and accuracy in control systems with signal-dependent noise.

The total reaction time RT 150300 ms imposes a fundamental limit on the response to unexpected events. For predictable events, the system can use prediction (forward model) to start the action before the stimulus occurs, reducing the effective RT. Tennis players return balls at 200 km/h in a time impossible to process reactively, using prediction.

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ID:(0, 586)