Comments on the Bellman functional for linear time‐delay systems

Ortega-Martinez, J.I.; Santos-Sánchez, Omar-Jacobo; Mondié, Sabine

doi:10.1002/oca.2726

Cited by 4 publications

(3 citation statements)

References 15 publications

(28 reference statements)

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“…Problem 62 was addressed in works such as [7,10,12,11,47], and was completely solved in the case of linear DDE dynamics and a quadratic objective in [48,49].…”

Section: Subvalue Functionals and Dde Controlmentioning

confidence: 99%

Peak Estimation of Time Delay Systems using Occupation Measures

Miller¹,

Korda²,

Magron³

et al. 2023

Preprint

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This work proposes a method to compute the maximum value obtained by a state function along trajectories of a Delay Differential Equation (DDE). An example of this task is finding the maximum number of infected people in an epidemic model with a nonzero incubation period. The variables of this peak estimation problem include the stopping time and the original history (restricted to a class of admissible histories). The original nonconvex DDE peak estimation problem is approximated by an infinite-dimensional Linear Program (LP) in occupation measures, inspired by existing measure-based methods in peak estimation and optimal control. This LP is approximated from above by a sequence of Semidefinite Programs (SDPs) through the moment-Sum of Squares (SOS) hierarchy. Effectiveness of this scheme in providing peak estimates for DDEs is demonstrated with provided examples.

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“…Problem 62 was addressed in works such as [7,10,12,11,47], and was completely solved in the case of linear DDE dynamics and a quadratic objective in [48,49].…”

Section: Subvalue Functionals and Dde Controlmentioning

confidence: 99%

Peak Estimation of Time Delay Systems using Occupation Measures

Miller¹,

Korda²,

Magron³

et al. 2023

Preprint

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“…Este resultado se extendió a los sistemas de tipo neutral (Cuvas et al, 2021). La construcción explícita de la funcional de Bellman y la demostración de sus principales propiedades se presenta en Ortega-Martínez et al (2021). Diversas aplicaciones de control óptimo a procesos con retardos fueron desarrolladas en Ortega-Martinez et al 2019) se muestra que las derivadas de la matriz de Lyapunov con respecto a los parámetros del sistema pueden ser calculadas de forma semianalítica.…”

Section: Control óPtimounclassified

Contribuciones al estudio de sistemas lineales con retardos: el enfoque de funcionales de tipo completo

Mondié

Gomez

2022

Rev. iberoam. autom. inform. ind.

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Se introducen resultados recientes del enfoque de funcionales de Lyapunov-Krasovski de tipo completo para sistemas lineales con retardos. Se explican brevemente los principales conceptos y resultados para el caso de sistemas con un retardo así como las condiciones necesarias y suficientes de estabilidad expresadas en terminos del análogo de la matriz de Lyapunov. Las extensiones de este tipo de condiciones de estabilidad a otras clases de sistemas con retardos son expuestas brevemente. Tambien se presentan aplicaciones existentes del efoque de funcionales de tipo completo a problemas de analisis y de diseño de controladores. El trabajo se enfoca a contribuciones de investigadores de Mexico a este tema de estudio.

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“…Problem A.92 was addressed in works such as [159,161,163,162,195], and was completely solved in the case of linear DDE dynamics and a quadratic objective in [196,197].…”

Section: A2 Continuity Of Multipliersmentioning

confidence: 99%

Safety quantification for nonlinear and time-delay systems using occupation measures

Miller

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To my parents, Wayne and Debbie. i I would like to begin by thanking my parents, Debbie Mitzner and Wayne Miller, for all of their advice and support. Wayne Miller voluntarily acted as a copy-editor for all of my publications, including this thesis. My next thanks go to my advisor, Mario Sznaier, at the Robust Systems Laboratory in Northeastern. I met Mario in Fall of 2016 as a BS/MS student, when I asked him for an override in order to attend his Spring 2017 special topics course in Big Data, Sparsity, and Control. During the opening lecture, he gave a survey of sparse methods in robust regression, computer vision, and system identification. At the close of this first lecture, I asked him how I could learn more and join his lab, and he responded by giving me the door code. I officially joined the lab as a PhD student in Fall of 2018, and then acted as a teaching assistant for his Sparsity course in 2019, 2021, and 2022. Mario introduced me to topics such as rank-minimization, sparsity, Frank-Wolfe methods, measures, polynomial optimization, and data-driven control. Mario's wealth of experience allows him to draw connections between different disciplines and rapidly determine if ideas have promise, have been done before, and/or are marginal/intractable. His discussions with myself and other members of the laboratory help us refine our approaches and experiments, providing guidance in sometimes unexpected ways, and leading us into new directions of research. I would like to thank Octavia Camps (co-director of the Robust Systems Laboratory) for the discussions and application of my methods towards computer vision. I would like to thank all of my colleagues in the Robust Systems Lab over the course of my ∼6 years there. Specific recognition goes to my collaborators Tianyu Dai, Rajiv Singh, Jian Zheng, Armand Comas, Biel Roig-Solvas, and Zachary Walker-Liang. There are many other students and professors at Northeastern (outside the Robust Systems Laboratory) to thank. Students in research include

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Comments on the Bellman functional for linear time‐delay systems

Cited by 4 publications

References 15 publications

Peak Estimation of Time Delay Systems using Occupation Measures

Peak Estimation of Time Delay Systems using Occupation Measures

Contribuciones al estudio de sistemas lineales con retardos: el enfoque de funcionales de tipo completo

Safety quantification for nonlinear and time-delay systems using occupation measures

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