LP based upper and lower bounds for Cesàro and Abel limits of the optimal values in problems of control of stochastic discrete time systems

Avrachenkov, Konstantin; Gaitsgory, Vladimir; Gamertsfelder, Lucas

doi:10.1016/j.jmaa.2022.126121

Cited by 2 publications

(2 citation statements)

References 36 publications

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“…From Equation (35), f ε is strictly bounded both above and below, and v ε is a Lévy kernel of a compound Poisson process. Considering the boundedness of Equations ( 35) and (36), the following proposition is obtained.…”

Section: A Regularization Methods To Well-pose the Control Problemmentioning

confidence: 99%

“…However, the ergodicity assumption sometimes fails for pathdependent control problems including those subjected to habit formation. Several researchers have reported tractable examples where the ergodicity failed and the effective Hamiltonian is not a constant but a function of the initial value [35,36]. This implies that the existing methodology of the ergodic time-average control reviewed above should be extended to include the non-ergodic cases.…”

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confidence: 99%

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Time‐average stochastic control based on a singular local Lévy model for environmental project planning under habit formation

Yoshioka

Tsujimura

Hamagami

et al. 2023

Math Methods in App Sciences

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This study applies the theory of stochastic control to an environmental project planning to counteract against the sediment starvation problem in river environments. This can be considered as a time-average inventory problem to time-discretely control a continuous-time system driven by a non-smooth jump process under habit formation disturbing project implementation. The system is modeled such that the sediment storage dynamics are physically consistent with certain experimental results. Further, the habit formation is modeled as simple linear dynamics and serves as a constraint related to the replenishment amount of the sediment. We show that the time-average control problem is not necessarily ergodic. Consequently, the effective Hamiltonian may become a non-constant. Thereafter, ratcheting cases as extreme cases of the irreversible habit formation are considered, owing to them being unique exactly solvable non-ergodic control problems. The optimality equation associated with a regularized and hence well-defined control problem is verified. Furthermore, a finite difference scheme is examined against the exactly solvable case and then applied to more complicated cases.

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Section: A Regularization Methods To Well-pose the Control Problemmentioning

confidence: 99%

mentioning

confidence: 99%

Time‐average stochastic control based on a singular local Lévy model for environmental project planning under habit formation

Yoshioka

Tsujimura

Hamagami

et al. 2023

Math Methods in App Sciences

View full text Add to dashboard Cite

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On convergence of occupational measures sets of a discrete-time stochastic control system, with applications to averaging of hybrid systems

Gamertsfelder

2024

International Journal of Control

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LP based upper and lower bounds for Cesàro and Abel limits of the optimal values in problems of control of stochastic discrete time systems

Cited by 2 publications

References 36 publications

Time‐average stochastic control based on a singular local Lévy model for environmental project planning under habit formation

Time‐average stochastic control based on a singular local Lévy model for environmental project planning under habit formation

On convergence of occupational measures sets of a discrete-time stochastic control system, with applications to averaging of hybrid systems

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