Improving the state estimation for optimal control of stochastic processes subject to multiplicative noise

Computational models for the neural control of movement must take into account the properties of sensorimotor systems, including the signal-dependent intensity of the noise and the transmission delay affecting the signal conduction. For this purpose, this paper presents an algorithm for model-based control and estimation of a class of linear stochastic systems subject to multiplicative noise affecting the control and feedback signals. The state estimator based on Kalman filtering is allowed to take into account the current feedback to compute the current state estimate. The optimal feedback control process is adapted accordingly. The resulting estimation error is smaller than the estimation error obtained when the current state must be predicted based on the last feedback signal, which reduces variability of the simulated trajectories. In particular, the performance of the present algorithm is good in a range of feedback delay that is compatible with the delay induced by the neural transmission of the sensory inflow.