Semi-Explicit Solution of Some Discrete-Time Higher-Order-Cost Mean-Field-Type Control
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arXiv
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| Autori principali: | , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866913849320407040 |
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| author | Barreiro-Gomez, Julian Duncan, Tyrone E. Pasik-Duncan, Bozenna Tembine, Hamidou |
| author_facet | Barreiro-Gomez, Julian Duncan, Tyrone E. Pasik-Duncan, Bozenna Tembine, Hamidou |
| contents | Traditional solvable optimal control theory predominantly focuses on quadratic costs due to their analytical tractability, yet they often fail to capture critical non-linearities inherent in real-world systems including water, energy, agriculture, and financial networks. Here, we present a unified framework for solving discrete-time optimal control with higher-order state and control costs of power-law form. By building convex-completion techniques, we derive semi-explicit expressions for control laws, cost-to-go functions, and recursive coefficient dynamics across deterministic and stochastic system settings. Key contributions include variance-aware solutions under additive and multiplicative noise, extensions to mean-field-type-dependent dynamics, and conditions that ensure the positivity of recursive coefficients. In particular, we establish that higher-order costs induce less aggressive control policies compared to quadratic formulations, a finding that is validated through numerical analyses. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_04112 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Semi-Explicit Solution of Some Discrete-Time Higher-Order-Cost Mean-Field-Type Control Barreiro-Gomez, Julian Duncan, Tyrone E. Pasik-Duncan, Bozenna Tembine, Hamidou Optimization and Control Traditional solvable optimal control theory predominantly focuses on quadratic costs due to their analytical tractability, yet they often fail to capture critical non-linearities inherent in real-world systems including water, energy, agriculture, and financial networks. Here, we present a unified framework for solving discrete-time optimal control with higher-order state and control costs of power-law form. By building convex-completion techniques, we derive semi-explicit expressions for control laws, cost-to-go functions, and recursive coefficient dynamics across deterministic and stochastic system settings. Key contributions include variance-aware solutions under additive and multiplicative noise, extensions to mean-field-type-dependent dynamics, and conditions that ensure the positivity of recursive coefficients. In particular, we establish that higher-order costs induce less aggressive control policies compared to quadratic formulations, a finding that is validated through numerical analyses. |
| title | Semi-Explicit Solution of Some Discrete-Time Higher-Order-Cost Mean-Field-Type Control |
| topic | Optimization and Control |
| url | https://arxiv.org/abs/2505.04112 |