Unidentifiability of time-varying parameters in biological systems has significant implications for model-based control and optimization. When parameters cannot be uniquely identified, it leads to several challenges:
Control Strategy Limitations: In control applications, unidentifiable parameters hinder the ability to design effective control strategies. If the model cannot accurately reflect the dynamics of the system due to unidentifiable parameters, the control inputs may not achieve the desired outcomes, leading to suboptimal performance or even destabilization of the system.
Parameter Estimation Challenges: In optimization contexts, particularly in adaptive control or feedback systems, the inability to identify parameters can result in inaccurate predictions of system behavior. This can lead to poor decision-making and ineffective resource allocation, especially in dynamic environments such as those encountered in epidemiological modeling of diseases like HIV and Covid-19.
Model Reliability: The presence of unidentifiable parameters raises concerns about the reliability of the model. Stakeholders may question the validity of the model predictions, which can undermine confidence in public health interventions or therapeutic strategies based on these models.
Need for Additional Information: To overcome unidentifiability, additional information or constraints may be required. This could involve incorporating more data, utilizing advanced estimation techniques, or integrating complementary models that provide insights into the unknown parameters.
In summary, unidentifiability of time-varying parameters complicates the effective application of model-based control and optimization in biological systems, necessitating careful consideration of data collection, model structure, and parameter estimation techniques.