Optimal control of systems with state-dependent time delay†

Asher, Robert B.; Sebesta, Henry R.

doi:10.1080/00207177108932046

Cited by 10 publications

(4 citation statements)

References 19 publications

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“…One could consider more general delays that are functions of time and state. This is motivated by the fact that, in the case of delays depending on the time and the state, Maximum Principle formulations still exist (see, e.g., [8]). Therefore, extending our main result requires to consider the C 0 -topology on the delay function t → τ (t, x(t)).…”

Section: Convergence Of Optimal Controls and Trajectories For (Ocp) τmentioning

confidence: 99%

See 1 more Smart Citation

Continuity of Pontryagin Extremals with Respect to Delays in Nonlinear Optimal Control

Bonalli¹,

Hérissé²,

Trélat³

2019

SIAM J. Control Optim.

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HAL is a multi-disciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers. L'archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

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Section: Convergence Of Optimal Controls and Trajectories For (Ocp) τmentioning

confidence: 99%

“…In [5,6], necessary conditions are obtained for optimal control problems with multiple constant delays in state and control variables. Moreover, [7,8] derive Maximum Principles for control systems with either time-or state-dependent delays. Finally, [9,10] give necessary conditions for optimal control problems with delays and mixed constraints.…”

mentioning

confidence: 99%

Continuity of Pontryagin Extremals with Respect to Delays in Nonlinear Optimal Control

Bonalli¹,

Hérissé²,

Trélat³

2019

SIAM J. Control Optim.

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“…We shall denote the problem defined by (1), (2), (3a) and (4) by problem B. For some relevant literature, see Asher and Sebesta [1], Hadley and Kemp [3], Hestenes [4,Chapter 11], Long and Vousden [5], Mangasarian [6], Neustadt [7,Chapters 5 and 6], Schwartzkopf [9], Sebesta and Clark [10], and Teo and Craven [11]. However, it is fair to say that the results available for problem B are either hard to apply, or require very stringent conditions for their validity, or both.…”

Section: Introductionmentioning

confidence: 99%

Optimal control theory with general constraints

Blatt

1981

J. Aust. Math. Soc. Series B, Appl. Math

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“…Simulation results suggest that the value of time delay may depend on the system state, rather than be a constant value. In fact, the state-dependent time delay has already been used in various research areas such as optimal control and population dynamics 33 34 . Although these ideas were proposed about 40 years ago, the relationship between time delay and system state remains uncertain for discrete chemical reaction settings.…”

mentioning

confidence: 99%

Stochastic modeling of biochemical systems with multistep reactions using state-dependent time delay

Tian

2016

Sci Rep

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To deal with the growing scale of molecular systems, sophisticated modelling techniques have been designed in recent years to reduce the complexity of mathematical models. Among them, a widely used approach is delayed reaction for simplifying multistep reactions. However, recent research results suggest that a delayed reaction with constant time delay is unable to describe multistep reactions accurately. To address this issue, we propose a novel approach using state-dependent time delay to approximate multistep reactions. We first use stochastic simulations to calculate time delay arising from multistep reactions exactly. Then we design algorithms to calculate time delay based on system dynamics precisely. To demonstrate the power of proposed method, two processes of mRNA degradation are used to investigate the function of time delay in determining system dynamics. In addition, a multistep pathway of metabolic synthesis is used to explore the potential of the proposed method to simplify multistep reactions with nonlinear reaction rates. Simulation results suggest that the state-dependent time delay is a promising and accurate approach to reduce model complexity and decrease the number of unknown parameters in the models.

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Optimal control of systems with state-dependent time delay†

Cited by 10 publications

References 19 publications

Continuity of Pontryagin Extremals with Respect to Delays in Nonlinear Optimal Control

Continuity of Pontryagin Extremals with Respect to Delays in Nonlinear Optimal Control

Optimal control theory with general constraints

Stochastic modeling of biochemical systems with multistep reactions using state-dependent time delay

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