Distributed optimization enables a network of agents to solve a global objective using only local data and neighbor-to-neighbor communication. A representative case is federated learning, where each agent retains its own dataset while jointly training a global model that minimizes the aggregate loss.

My work develops robust algorithms that provably converge despite complex agent dynamics, parametric uncertainties, and exogenous disturbances. We co-design the optimizer and controller—leveraging output regulation, extremum seeking, and reinforcement learning—and certify stability and performance using the small-gain theorem and singular perturbation theory. Applications include distributed computation, sensor networks, robotic swarms, and smart grids.

Urban traffic signals are often fixed or heuristically actuated, and they struggle to handle uncertain and time-varying demand. I use a data-driven approach that learns traffic dynamics from sensor data and optimizes signal timings in real time via various data-based control strategies. I built and calibrated a 42-intersection SUMO model from field data; learned the traffic flow dynamics with linear regression, multi-layer perceptrons, and deep neural networks ; engineered an optimization pipeline to meet real-time constraints, integrating linear quadratic regulator, gain scheduling, reinforcement learning, and model predictive control (MPC) .

Deployed across 24 intersections with computer-vision sensors, the pipeline reduced average travel time by 19.4% and vehicle queue lengths by 15.6% in field experiments. The figures left illustrate the queue-length comparison between the proposed MPC controller and the standard NEMA controller.

As line conditions and operating scenarios grow more complex, classical optimal control struggles to compute energy-efficient train speed profiles. Dynamic programming can handle this numerically, but the standard approach suffers from the curse of dimensionality. To address this, I develop reinforcement learning methods that efficiently generate the approximate optimal speed profiles.

Concretely, I use three complementary approximators for value functions: a rollout estimator, an interpolation-based approximator, and a neural-network approximator. The resultant strategies can closely match solutions from the classical maximum principle. To make the comparison, I resolve an open question by proving the uniqueness of the optimal trajectory under speed limit constraints (see left figure). The proposed approach yields energy-efficient driving strategies in both single-train and multi-train operations when exploiting regenerative energy .