Tutorial workshop II: Dynamics and control of biological oscillations

Oscillations are often observed in nature at multiple levels, and form a basis for sustained operation of various functionalities. The objective of this workshop is to introduce biological principles for coordinated oscillations to the control engineering community, and to provide a tutorial overview of recent developments on the analysis and design of dynamical mechanisms for oscillations, inspired by biological control systems. A particular focus will be placed on rhythmic body movements observed in animal locomotion, controlled by neuronal circuits called central pattern generators (CPGs). An introduction to biological oscillations will be given frst through an example of undulatory swimming. Biological mechanisms for locomotion will be mathematically formalized by viewing rhythmic movements as a limit cycle resulting from dynamic interactions of a CPG, body, and environment. We then discuss a neuronal pattern formation problem, where it is examined how the interconnection structure within a CPG relates to the oscillation profle. A biomechanical pattern formation problem is also discussed, where an optimal periodic body motion (or gait) is sought to minimize a quadratic cost function while maintaining a prescribed locomotion velocity.