Start Date
24-4-2025 12:00 AM
Description
In this project, we consider processes guided by a conformable derivative first introduced by Khalil et al in 2014. This time-weighted derivative has many of the same properties as the classical derivative but lacks the semigroup property for the exponential. Here, we study a conformable linear system where the state and control are subject to the same fixed delay. Our process is also subject to wear and tear, represented by a cost functional. Our goal is to find an optimal control that minimizes this cost. This control is propagated by a quasi-Ricatti equation, which itself includes a time delay. Finally, we offer a physical model associated with our delayed as well as numerical simulations for different rates alpha.
Recommended Citation
Baur, Seth; Smith, Joseph E.; and Wintz, Nick, "Conformable Regulator Problems with Fixed Delay" (2025). 2025 Student Academic Showcase. 14.
https://digitalcommons.lindenwood.edu/src_2025/Posters/Posters/14
Included in
Conformable Regulator Problems with Fixed Delay
In this project, we consider processes guided by a conformable derivative first introduced by Khalil et al in 2014. This time-weighted derivative has many of the same properties as the classical derivative but lacks the semigroup property for the exponential. Here, we study a conformable linear system where the state and control are subject to the same fixed delay. Our process is also subject to wear and tear, represented by a cost functional. Our goal is to find an optimal control that minimizes this cost. This control is propagated by a quasi-Ricatti equation, which itself includes a time delay. Finally, we offer a physical model associated with our delayed as well as numerical simulations for different rates alpha.