A Control Barrier Function Approach to Constrained Resource Allocation Problems in a Maximum Entropy Principle Framework
We develop a control-theoretic framework for solving constrained resource allocation problems, formulated as generalized facility location with optimal placement and assignment decisions. Leveraging Control Barrier Functions (CBFs), Control Lyapunov Functions (CLFs), and the Maximum Entropy Principle (MEP), our approach ensures feasibility while improving convergence and constraint handling. This work was submitted to CDC 2025, with a related poster presented at the 2025 Midwest Workshop on Control and Game Theory.
Reproduced and analyzed the core results of “Regret Bounds for the Adaptive Control of Linear Quadratic Systems” by Abbasi-Yadkori and Szepesvári. This work presents key theorems, lemmas, and an algorithm designed for solving Linear Quadratic (LQ) control problems with unknown model parameters—commonly referred to as adaptive control—aiming to minimize regret. The proposed algorithm estimates parameters using high-probability confidence sets and achieves a regret bound of $\tilde{O}(\sqrt{T})$.
Developed and compared deep learning architectures (CNN, VGGNet, LeNet) for facial keypoint detection on noisy and tilted images using a Kaggle dataset. Implemented data augmentation and evaluated robustness across models using training/validation losses and visual prediction outputs.
Presented and discussed “Deep Sets” by Zaheer et al., a foundational work proposing permutation-invariant neural architectures for set-structured data. The presentation covered theoretical guarantees for invariant and equivariant functions and demonstrated applications in set-based learning.
Poster Presentation – Midwest Workshop on Control and Game Theory 2023
Presented a poster based on our ACC 2023 paper, “Towards Efficient Modularity in Industrial Drying: A Combinatorial Optimization Viewpoint”. This work addresses the optimal sequencing and operating conditions of multiple drying technologies with distinct mechanisms and constraints, using combinatorial scheduling to improve energy efficiency and modular process design.
