Delayed Feedback Control Requires an Internal Forward Model

Biological motor control provides highly effective solutions to difficult control problems in spite of the complexity of the plant and the significant delays in sensory feedback . Such delays are expected to lead to non trivial stability issues and lack of robustness of control solutions. However, such difficulties are not observed in biological systems under normal operating conditions. Based on early suggestions in the control literature, a possible solution to this conundrum has been the suggestion that the motor system contains within itself a forward model of the plant (e.g., the arm), which allows the system to `simulate' and predict the effect of applying a control signal. In this work we formally define the notion of a forward model for deterministic control problems, and provide simple conditions that imply its existence for tasks involving delayed feedback control. As opposed to previous work which dealt mostly with linear plants and quadratic cost functions, our results apply to rather generic control systems, showing that any controller (biological or otherwise) which solves a set of tasks, \emph{must} contain within itself a forward plant model. We suggest that our results provide strong theoretical support for the necessity of forward models in many delayed control problems, implying that they are not only useful, but rather, mandatory, under general conditions.