Noise, time delay and balance control

Problems related to the stabilization of an inverted pendulum are an important concern to applied mathematicians and to neuroscientists who work on balance control in humans and two–legged robots. Although feedback delay and the effect of random perturbations (“noise”) pose common and challenging problems there has been little exchange in ideas between the mathematical, engineering and neuroscience communities. However, given our aging population it has become critically important that these groups work together to devise timely strategies to reduce the risk of falling in the elderly. Traditionally the approach of neuroscientists to the study of balance control has borrowed heavily from control systems theoretic concepts developed by engineers [9, 14, 16, 23, 24, 31, 32, 33, 34]. Obviously at the most fundamental level balance is maintained by contractions of muscles that are controlled by the nervous system. These considerations have led to two types of control: 1) closed–loop, or negative, feedback control, in which corrective movements that are dependent on current sensory feedback, and 2) open–loop control in which controlling actions are much less dependent on sensory input. The necessity of open–loop control is because movements can occur faster than neural latencies (time delays), i.e. it is currently held that for fast movements the nervous system uses a feed-forward, or predictive, type of control to compensate for the presence of time delays: by making an internal model the nervous nervous predicts in advance when corrections are being made. Recent studies, initially related to how the nervous system acquires expertise in the performance of a voluntary motor task, have led to the concepts of active and passive control (for a review see [28]). This type of control is best illustrated through the example of the thermostatic control of room temperature. Typically thermostats operate as bang–bang controllers, i.e. the furnace is either on or off. Two thresholds are chosen, one higher than the other, to reduce the number of times the furnace turns on and off. The furnace is turned on whenever room temperature falls below the lowest threshold and off when the temperature exceeds the higher threshold. Once the thresholds have been set, room temperature is self–controlled: no further in the thresholds are required to ensure that room temperature stays within the desired range. Active feedback control corresponds corresponds to the trial and error process of changing the thresholds until the appropriate operating range is determined. Since the corrective actions are only made when temperature crosses a threshold, the control mechanism is discontinuous and the corrective actions are applied intermittently [1, 2, 4, 13, 15, 25, 30]. In contrast to the control theoretic concepts imported from engineering by neuroscientists which are based on linear stability theory, the concept of discontinuous, intermittent control is an essentially nonlinear control strategy. The advantage of discontinuous types of control is that they are optimal in the presence of time delays and noisy perturbations. This unique workshop allowed investigators to 1) directly compare mathematical predictions to experimental observations; 2) devise new experimental paradigms to test mathematical findings; and 3) discuss how