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TY  - THES
AU  - Subbiah Pillai, Shyam Mohan
TI  - Numerical methods for stochastic optimal control: applications in rare event estimation and wireless networks
PB  - RWTH Aachen University
VL  - Dissertation
CY  - Aachen
M1  - RWTH-2025-05282
SP  - 1 Online-Ressource : Illustrationen
PY  - 2025
N1  - Veröffentlicht auf dem Publikationsserver der RWTH Aachen University
N1  - Dissertation, RWTH Aachen University, 2025
AB  - This thesis develops numerical methods for non-standard stochastic optimal control (SOC) problems, driven by real-world applications in rare event estimation and energy-efficient wireless networks. The underlying process models are controlled stochastic differential equations. In the first part, we introduce an efficient Monte Carlo (MC) estimator of rare event probabilities associated with the McKean-Vlasov stochastic differential equation, crucial for analysing mean-field systems in statistical physics, mathematical finance and many more applications. Using SOC, we derive an optimal importance sampling (IS) measure change that minimises the estimator's relative statistical error. We then combine IS with hierarchical sampling techniques, like multilevel and multi-index MC, to enhance its computational complexity. The resulting multi-index double loop MC estimator achieves a significantly improved computational complexity of O(TOL^-2 log(TOL^-1)^2) for estimating rare event probabilities with a prescribed relative accuracy TOL. In the second part, we develop a modelling and numerical framework to solve a chance-constrained SOC problem in cellular wireless networks, where the objective is to compute an optimal short-term power procurement strategy that minimises both operating expenditure and carbon footprint. The model accounts for uncertain renewable energy sources, stochastic wireless channels, and a probabilistic quality-of-service (QoS) constraint, making it a challenging SOC problem. The solution procedure involves a continuous-time Lagrangian relaxation of the QoS constraint, a computationally efficient numerical scheme to solve the Hamilton-Jacobi-Bellman partial differential equation associated with the relaxed problem, and an optimisation framework for the non-smooth dual problem, enabling effective handling of the probabilistic constraint. The proposed numerical procedure provides near-optimal policies for a model cellular base station powered by a hybrid energy system, using German grid and cellular user data. Results demonstrate that our approach delivers solutions in a practical time-frame, emphasising its computational efficiency and real-world applicability.
LB  - PUB:(DE-HGF)11
DO  - DOI:10.18154/RWTH-2025-05282
UR  - https://publications.rwth-aachen.de/record/1013009
ER  -