Fig. 1

Model of the sensorimotor control with time-delay estimation and sensory states predictor. The Plant Box symbolizes a higher level of a sensorimotor system such as the eye, associated muscles, sensors, responses, goals and objectives (e.g., minimize retinal slip in VOR). The Controller Box is the neural network responsible for achieving the required task in an “optimal” way. Delay Estimator is the circuit we are proposing as the brain, or a sensorimotor systems to estimate time delay in a sensory and motor pathway. Sate Predictor is where current and “future” sensory states are estimated and predicted, respectively, based on the estimated current time delay. The “r(t)” is the desired goal, or in the language of control theory, the reference trajectory. The “e(t)” is the error difference between the desired sensory state and predicted sensory state \( \widehat{x}(t) \). The “u(t)” are the motor commands to muscles or effector organs. The x(t − τ) are the delayed sensory states. The “x(t)” is the actual sensory state. Finally, “τ” is the time delay that could either be a natural time delay or a consequence of damage or disease