Adjoint sensitivity method for parameter estimation: applications to inverted pendulum and human standing balance.

The inverted pendulum, a classical mechanical system, often serves as a platform for studying stability and control algorithms. Modelling human standing balance as an inverted pendulum controlled by the time-delayed proportional-derivative (PD) feedback controller can be used effectively to study the related biomechanical mechanisms. In this study, to investigate the human balance control strategy, an adjoint sensitivity analysis method and a corresponding optimizer are implemented to directly determine system parameters, control gains and the time delay in the human balancing model. This study validates the accuracy of the optimizer through numerical simulations and experimental verification based on the physical model of the inverted pendulum on a cart. The experimental results confirm the performance of the identification algorithm for systems involving non-smooth dynamics and inherent time delays. Moreover, the identification based on human balance data indicates that the time-delayed PD feedback controller effectively represents the human balance control strategy. Additionally, the identification reveals a tendency in the control strategy: the control gains are located in the lower-left region of the stability diagram, indicating that the human body tends to adopt an optimal control strategy that minimizes energy consumption.