Publications

@article{Ashyani2024DC,

title = {Ideal adaptive control in biological systems–an analysis of P-invariance and dynamical compensation properties},

author = {Akram Ashyani and Yu-Heng Wu and Huan-Wei Hsu and Torbjörn E. M. Nordling},

year  = {2024},

date = {2024-01-01},

urldate = {2024-01-01},

journal = {BMC Bioinformatics},

volume = {Accepted},

abstract = {Background: Dynamical compensation (DC) provides robustness to parameter fluctuations. As an example, DC enables control of the functional mass of endocrine or neuronal tissue essential for controlling blood glucose by insulin through a nonlinear feedback loop. Researchers have shown that DC is related to the structural unidentifiability and the P-invariance property. The P-invariance property is a sufficient and necessary condition for the DC property. DC has been seen in systems with at least three dimensions. In this article, we discuss DC and P-invariance from an adaptive control perspective. An adaptive controller automatically adjusts its parameters to optimise performance, maintain stability, and deal with uncertainties in a system. 

Results: We initiate our analysis by introducing a simplified two-dimensional dynamical model with DC, fostering experimentation and understanding of the system's behavior. We explore the system's behavior with time-varying input and disturbance signals, with a focus on illustrating the system's P-invariance properties in phase portraits and step-like response graphs. 

Conclusions: We show that DC can be seen as a case of ideal adaptive control since the system is invariant to the compensated parameter.},

keywords = {adaptive proportional-integral feedback, Dynamical compensation property, Ordinary differential equations, P-invariance property},

pubstate = {published},

tppubtype = {article}

}

@article{ashyani2023DCArxiv,

title = {An analysis of $mathbbP$-invariance and dynamical compensation properties from a control perspective},

author = {Akram Ashyani and Yu-Heng Wu and Huan-Wei Hsu and Torbjörn E. M. Nordling},

url = {https://arxiv.org/abs/2303.10996},

doi = {10.48550/arXiv.2303.10996},

year  = {2023},

date = {2023-03-20},

journal = {arXiv preprint},

publisher = {Cornell University},

abstract = {Dynamical compensation (DC) provides robustness to parameter fluctuations. As an example, DC enable control of the functional mass of endocrine or neuronal tissue essential for controlling blood glucose by insulin through a nonlinear feedback loop. Researchers have shown that DC is related to structural unidentifiability and $mathbbP$-invariance property, and $mathbbP$-invariance property is a sufficient and necessary condition for the DC property. In this article, we discuss DC and $mathbbP$-invariancy from an adaptive control perspective. An adaptive controller is a self-tuning controller used to compensate for changes in a dynamical system. To design an adaptive controller with the DC property, it is easier to start with a two-dimensional dynamical model. We introduce a simplified system of ordinary differential equations (ODEs) with the DC property and extend it to a general form. The value of the ideal adaptive control lies in developing methods to synthesize DC to variations in multiple parameters. Then we investigate the stability of the system with time-varying input and disturbance signals, with a focus on the system's $mathbbP$-invariance properties. This study provides phase portraits and step-like response graphs to visualize the system's behavior and stability properties.},

keywords = {$mathbb{P}$-invariance, Adaptive control, Dynamical compensation, Ordinary differential equations},

pubstate = {published},

tppubtype = {article}

}