The interdisciplinary nature of how the nervous system controls balance forms a barrier for mathematically oriented researchers. Not only it is necessary for researchers to appreciate the physiology and anatomy of human balance control, but also researchers must be fluent in the analysis of time-delayed dynamical systems. The starting point is to understand how the inverted position of a pendulum can be stabilized. Two “human-in-the-loop” applications of the inverted pendulum paradigm are pole balancing at the fingertip and postural sway during quiet standing. While pole balancing is a voluntary motor skill, quiet standing is achieved through the operation of “hard wired” neural reflexes. The main question in pole balancing is how it is possible to balance short poles. In case of postural sway, the challenge is to understand how balance can be maintained by an aging nervous system, to identify the nature of its failures and to reduce the risk of falling. The question naturally arises: does the nervous system face the same challenges controlling balance that a mechanical engineer faces in stabilizing mechanical structures?

This school brings together internationally recognized experts in the experimental and mathematical analysis of human balancing tasks. From different perspectives, each of them has reached the conclusion that the controller for human balance is time delayed and acts intermittently. The lectures are self- contained and are structured in a manner to give the audience an appreciation of the interplay between mathematics and experimental observations that led to the demonstration that balance control is intermittent. Where possible theoretical concepts will be illustrated with hands-on demonstrations, e.g., measurement of time delays, stick balancing, numerical analysis of delay differential equations.

The course is organized with the premise that the audience has little or no experience with the analysis of time delayed dynamical systems and the physiology and anatomy of human balance mechanisms. The course begins by first examining the evidence for time-delayed feedback control in humans and the experimental evidence that supports the intermittent nature of neural control in stick balancing, human postural control and balance control in the elderly. These lectures are followed by mathematical considerations of the stability of delay differential equations in the presence of sensory uncertainty. The approaches are then extended to other human balancing tasks.

The school is addressed to MSc and PhD students as well as to post-docs, early career researchers, and also to engineers working at the R&D departments of companies with interest in understanding human motion control. The course is designed for participants working primarily in the field of biomechanics, collaboration of human and machines. However, the course is addressed also to those generally interested in dynamical systems involving time delays, control theory and numerical analysis and/or experimental vibration measurement techniques.