Optimal Control Theory

Longuski, James M.; Guzmán, José J.; Prussing, John E.

doi:10.1007/978-1-4614-8945-0_2

Cited by 13 publications

(4 citation statements)

References 2 publications

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“…In [41], Pontryagin describes how to deal with problems with the cost function dependent not only on the state, but also on some constant parameters. In this case, a conversion from the Problem of Mayer to the Problem of Lagrange is needed [42]. That is…”

Section: B Statement Of the Problemmentioning

confidence: 99%

Aeroballistic Capture at Mars: Modeling, Optimization, and Assessment

Giordano

Topputo

2022

Journal of Spacecraft and Rockets

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this paper a novel paradigm for Mars missions is modeled, optimized, and assessed. This concept consists of a maneuver that combines aerocapture and ballistic capture upon Mars arrival, labelled aero-ballistic capture. The idea is reducing the overall cost and mass by exploiting the interaction with the planet atmosphere as well as the complex Sun-Mars gravitational field. The aero-ballistic capture paradigm is first formulated. This is then split into a number of phases, each of them is modelled with mathematical means. The problem is then stated by using optimal control theory, and optimal solutions are sought. These are specialized to four application cases. An assessment of aero-ballistic capture shows their superiority compared to classical injection maneuvers when medium-to-high final orbits about Mars are targeted.

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Section: B Statement Of the Problemmentioning

confidence: 99%

Aeroballistic Capture at Mars: Modeling, Optimization, and Assessment

Giordano

Topputo

2022

Journal of Spacecraft and Rockets

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“…The first being the more common parameter optimization, which minimizes a function of a finite number of discrete variables and has its basis in calculus [10]. The other branch, optimal control theory (OCT), seeks to find solutions to problems of infinite dimension that minimize functionals and is based more specifically in calculus of variations [10]. This distinction is related to the distinction between direct and indirect methods in trajectory optimization.…”

Section: Optimal Control Theorymentioning

confidence: 99%

Navigation Based Path Planning by Optimal Control Theory

Nolan

Grant

Rutkowski

2020

AIAA Scitech 2020 Forum

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Firstly, I thank my parents Jim and Suzana and my brother Jim who have always been there with ample love and support. Also, I want to thank my wonderful fiancée Mary who makes my work worth any difficulty. I am extraordinary grateful to my advisor Dr. Michael Grant who has gone above and beyond as an advisor. His guidance, motivation, and patience were indispensable to me not only for this work but also for my graduate school career. I am also thankful to Dr. Adam Rutkowski for his assistance to formulate and solve these problems. Without him, this thesis would not exist. I am also thankful for the Mathematical Modeling and Optimization Institute for allowing me to spend a summer dedicated to this research. I also thank Dr. Inseok Hwang for being on my committee and his instruction through his class.Dr. Daniel DeLaurentis deserves special acknowledgment for assisting me finish this work. Lastly, I greatly appreciate my fellow lab members for their previous work and assistance to me, especially

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“…The goal of optimal control is to find the “controls” for a dynamical system which allow us to reach a desired outcome by minimizing (or maximizing) an objective functional. Optimal control theory has been used to optimize policies and practices for a wide variety of industries including economics (Sheng et al (2014); Wu et al (2015); Li et al (2019); Kaszkurewicz and Bhaya (2022)), aerospace technologies (Benson (2005); Longuski et al (2014); Villegas Díaz et al (2019); García-Heras et al (2019); Sun et al (2019); Zhao et al (2019)), and the medical field (Martin and Teo (1994); Jung et al (2002); Ledzewicz et al (2013); Wang and Schättler (2016); Ledzewicz and Moore (2017); Ratajczyk et al (2018); Moore et al (2018); Fernández and Pola (2019); Ledzewicz et al (2019); Gutiérrez-Diez and Russo (2020); Jarrett et al (2020); Sharp et al (2020); Rautela et al (2023); Luo et al (2023); Valega-Mackenzie et al (2024)). Control theory was even used in the development of the “artificial pancreas,” which became FDA approved in 2016 for patients with type 1 diabetes (FDA (2016)).…”

Section: Introductionmentioning

confidence: 99%

Optimal control of combination immunotherapy for a virtual murine cohort in a glioblastoma-immune dynamics model

Anderson,

Takacs,

Harrison

et al. 2024

Preprint

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The immune checkpoint inhibitor anti-PD-1, commonly used in cancer immunotherapy, has not been successful as a monotherapy for the highly aggressive brain cancer glioblastoma. However, when used in conjunction with a CC-chemokine receptor-2 (CCR2) antagonist, anti-PD-1 has shown efficacy in preclinical studies. In this paper, we aim to optimize treatment regimens for this combination immunotherapy using optimal control theory. We extend a treatment-free glioblastoma-immune dynamics ODE model to include interventions with anti-PD-1 and the CCR2 antagonist. An optimized regimen increases the survival of an average mouse from 32 days post-tumor implantation without treatment to 111 days with treatment. We scale this approach to a virtual murine cohort to evaluate mortality and quality of life concerns during treatment, and predict survival, tumor recurrence, or death after treatment. A parameter identifiability analysis identifies five parameters suitable for personalizing treatment within the virtual cohort. Sampling from these five practically identifiable parameters for the virtual murine cohort reveals that personalized, optimized regimens enhance survival: 84% of the virtual mice survive to day 100, compared to 60% survival in a previously-studied experimental regimen. Subjects with high tumor growth rates and low T cell kill rates are identified as more likely to die during and after treatment due to their compromised immune systems and more aggressive tumors. Notably, the MDSC death rate emerges as a long-term predictor of either disease-free survival or death.

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Optimal Control Theory

Cited by 13 publications

References 2 publications

Aeroballistic Capture at Mars: Modeling, Optimization, and Assessment

Aeroballistic Capture at Mars: Modeling, Optimization, and Assessment

Navigation Based Path Planning by Optimal Control Theory

Optimal control of combination immunotherapy for a virtual murine cohort in a glioblastoma-immune dynamics model

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