Biological dynamical systems are typically multidimensional, nonlinear, hierarchical, and noisy. Problems of control are ubiquitous; examples include fixed-point control (maintenance of posture, homeostatic control), control of rhythmic movements (locomotion, respiratory control), control of rhythmic processes (circadian activation, oscillatory neural activity). Nearly all areas of control theory have potential application to biological neural and motor systems, including feedback control; estimation and control of nonlinear systems; geometric control; optimization-based control; stability analysis; model identification and parameter estimation; model predictive control; observability and controllability in coupled networks; and stochastic control. At the same time, biological control problems can stretch control theory in new directions. For example, control theory has focused on negative feedback control (i.e. homeostasis) while neuromodulation may involve the interaction of multiple positive and negative feedback components. Moreover, neural and motor systems may prioritize robustness over optimality. Nonlinear control theory for limit cycle or other rhythmic dynamics is also much less developed than for linear systems and other forms of dynamics. The workshop will bring together experimental biologists, control theorists, mathematical biologists, and clinicians to forge new interdisciplinary connections to understand control of biological neuronal and motor systems.
One area of focus will be the rhythmic activity patterns that some brain areas produce through intrinsic dynamics, perhaps activated by tonic (sustained or transient) input signals. In some cases, these activity patterns drive repetitive behaviors such as various forms of locomotion, respiration, and mastication; similar dynamics may arise in circadian and sleep rhythms. An organism interacts with some aspect of its environment through these behaviors, and these interactions result in feedback signals that can alter the ongoing intrinsic dynamics to maintain homeostasis, meet metabolic demands, or optimize reward. Problems in this area include modeling the closed loop circuits involved, determining the control principles that modulate neural activity and behavior, and applying external (i.e., man-made) controls to remedy related disorders or otherwise improve performance.
A second major theme will be non-oscillatory motor behaviors that include stationary control problems (maintenance of posture, balancing a vertical rod) as well as nonstationary problems (maintaining one's gaze on a moving target) and single movement control problems (reaching and grasping; hitting a golf ball). Some aspects of these problems are classical, such as the mathematics of stabilizing an inverted pendulum. There is a rich body of relevant theory: state estimation and feedforward control, stabilization and negative feedback control, and internal and inverse models. But the relationship between such idealized systems and the noisy, overcomplete space of near-optimal solutions used by biological motor systems for such tasks is still poorly understood.
The workshop topics will also include the use of control to modulate pathological brain states, such as synchronization arising in epilepsy and oscillations arising in parkinsonism. Closed loop control of a distributed neuronal circuit based on sparse data represents an important frontier that arises in these clinical applications.
