Using topological equivalence to discover stable control parameters in biodynamic systems
Computer Methods in Biomechanics and Biomedical Engineering 15(8), 875-884 (2012).

Martin L. Tanaka1, Shane D. Ross2
1Department of Engineering & Technology, Western Carolina University
2Department of Engineering Science and Mechanics, Virginia Tech


In order to better understand the mechanisms which contribute to low back pain, researchers have developed mathematical models and simulations. A mathematical model including neuromuscular feedback control is developed for a person balancing on an unstable sitting apparatus, the wobble chair. When the application of a direct method fails to discover appropriate controller gain parameters for the wobble chair, we show how topological equivalence can be used to indirectly identify appropriate parameter values. The solution is found by first transforming the wobble chair into the Acrobot, another member of the same family of topologically equivalent dynamical systems. After finding appropriate gain parameters for the Acrobot, a continuous transformation is performed to convert the Acrobot back to the wobble chair, during which the gain parameters are adjusted to maintain stability. Thus, we demonstrate how topological equivalence can be used to indirectly solve a problem that was difficult to solve directly.

Keywords: stability, spine, Hilbert envelope, solution space, Lyapunov stability, topological equivalence
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