Efficient Algorithms for Convex Optimization based Control

Abstract

This dissertation studies efficient optimization algorithms designed to solve control problems. It is composed of the following three parts.• Part I: This part focuses on Markovian network equilibrium, a novel class of stochastic dynamic network equilibrium problems. After introducing the problem formulation, we discuss efficient dynamic-programming-based algorithms designed for these opti- mization problems. • Part II: This part focuses on first order convex optimization methods for distributed optimization and trajectory optimization. The key idea is combining proportional- integral feedback with projected gradient or mirror descent method. • Part III: This part focuses on Willems’ fundamental lemma, a key result in system identification and data-driven control. We generalized previous results to handle un- controllable systems and systems with special structures.