Adjoint Equation Based Framework and Application for Delayed System Parameter Identification
Jingtian Chen, Li Zhang
Abstract: Delay differential equations are widely used to describe dynamic connections between system’s current states and its past states. They are particularly suited for modelling complex systems with delays, such as dynamic systems arisen from biology, engineering and physics. Since delay effects can significantly impact system dynamic behaviour, control performance and stability, accurate identification of delay parameters has become a core challenge. To improve both accuracy and efficiency, this study proposes a delay parameter identification algorithm based on adjoint equations and the gradient descent method. By leveraging the analytical properties of adjoint equations, this method solves the adjoint system backward in time, allowing for the precise calculation of the gradient of the system response with respect to the parameters, thus facilitating efficient parameter updates. This study details the mathematical derivation of the algorithm and develops a computational framework on the Python platform, incorporating automatic updates, dynamic interpolation, and a solver for delay differential equations with time-varying parameters. By simplifying the algorithm and utilizing parallel computing, the solution process is optimized to reduce computational complexity, enhancing its practical applicability. To validate the effectiveness of the algorithm, a numerical identification experiment is conducted for a two-degree-of-freedom nonlinear spring-mass system. The results demonstrate that the method accurately identifies the system delay parameters while maintaining a low error margin.
文章链接：https://dx.doi.org/10.6052/1672-6553-2024-100
