Optimal Population Codes for Control and Estimation

While the theory of Optimal Control (OC) has become widely used as a framework for studying motor control, the standard framework of OC neglects many essential attributes of biological control [1, 2, 3]. The classic formulation of closed loop OC considers a dynamical system (plant) observed through sensors which transmit their output to a controller, which in turn selects a control law that drives actuators to steer the plant. This standard view, however, ignores the fact that sensors, controllers and actuators are often distributed across multiple subsystems, and disregards the communication channels between these subsystems. While the importance of jointly considering control and communication within a unified framework was already clear to the pioneers of the field of Cybernetics (e.g., Wiener and Ashby), it is only in recent years that increasing effort is being devoted to the formulation of a rigorous systems-theoretic framework for control and communication (e.g., [4]). Since the ultimate objective of an agent is to select appropriate actions, it is clear that sensation and communication must subserve effective control, and should be gauged by their contribution to action selection. In fact, given the communication constraints that plague biological systems (and many current distributed systems, e.g., cellular networks, sensor arrays, power grids, etc.), a major concern of a control design is the optimization of sensory information gathering and communication (consistently with theories of active perception). For example, recent theoretical work demonstrated a sharp communication bandwidth threshold below which control (or even stabilization) cannot be achieved (for a summary of such results see [4]). Moreover, when informational constraints exists within a control setting, even simple (linear and Gaussian) problems become nonlinear and intractable, as exemplified in the famous Witsenhausen counterexample [5]. The interdependence between sensation, communication and control is often overlooked both in control theory and in computational neuroscience, where one assumes that the overall solution to the control problem consists of first estimating the state of the controlled system (without reference to the control task), followed by constructing a controller based on the estimated state.