(Nazarbayev University School of Sciences and Humanities, 2024-04-26) Raikhankyzy, Arailym
This master’s thesis explores the intersection of optimal control theory and risk-sensitive decision-making by addressing the finite-horizon discrete-time linear quadratic regulator (LQR) problem with a focus on the average-value-at-risk (AVaR) criteria. The study aims to mathematically formalize the LQR-AVaR problem within the dynamic programming framework and develop a computational algorithm based on approximate dynamic programming techniques to solve it. The algorithm’s effectiveness is rigorously assessed through the analysis of experiment results and plot evaluations. The experiment results indicate that the approximate dynamic programming algorithm, when applied properly, performs well for the problem, with experiments suggesting high accuracy.