Optimal control of multiple Markov-switching stochastic systems with numerical applications

Shi, Jianmin

doi:10.1016/j.rico.2022.100113

Results in Control and Optimization

2022

DOI: 10.1016/j.rico.2022.100113

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Optimal control of multiple Markov-switching stochastic systems with numerical applications

Jianmin Shi

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2023

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“…steadily [7,8] and has become an effective mathematical tool to tackle engineering problems in diverse research fields. A stochastic control problem can be systematically solved by resolving an optimality equation either analytically or numerically [9][10][11].…”

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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

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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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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

show abstract

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Optimal control of multiple Markov-switching stochastic systems with numerical applications

Cited by 1 publication

References 42 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

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