Keywords
control theory, stabilizability, partial stabilizability, stochastic linear quadratic, linear quadratic regulator, stochastic control theory
Abstract
Optimal Control Theory, a branch of Control Theory, is applicable in fields such as engineering, operations research, and economics. Stochastic Optimal Control deals with noisy systems and data using Ito’s formulation. Given a noisy system and a cost functional, the goal is to find a control that will minimize the cost. This thesis focuses on linear quadratic stochastic optimal control, and we explore state equations that are not stabilizable. We first address measurability concerns arising from the semigroup property of the state trajectory. The notions of partial stability and partial stabilizability are introduced, and we formulate their corresponding Lyapunov and Riccati Equations. We then develop necessary conditions for open-loop solvability and characterize closed-loop solvability.
Thesis Completion Year
2025
Thesis Completion Semester
Spring
Thesis Chair
Yong, Jiongmin
College
College of Sciences
Department
Mathematics
Thesis Discipline
Control Theory
Language
English
Access Status
Open Access
Length of Campus Access
None
Campus Location
Orlando (Main) Campus
Subjects
Stochastic control theory; Stochastic systems; Automatic control--Mathematics; Feedback control systems--Stability; Control theory--Mathematical models
STARS Citation
Imadh, Al-sadh Rahman, "Solvability of Stochastic Linear-Quadratic Optimal Control Problems Under Partial Stabilizability Conditions" (2025). Honors Undergraduate Theses. 301.
https://stars.library.ucf.edu/hut2024/301
Included in
Control Theory Commons, Dynamical Systems Commons, Other Mathematics Commons, Probability Commons
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