6 papers
On the Strong Duality in Continuous-time and Discrete-time Linear Quadratic Regulators
Yuto Watanabe, Yang Zheng
This paper revisits the strong duality in the linear quadratic regulator (LQR) for continuous-time and discrete-time systems, and explores its interconnection with typical assumpti…
Policy Optimization of Mixed H2/H-infinity Control: Benign Nonconvexity and Global Optimality
Chih-Fan Pai, Yuto Watanabe, Yujie Tang +1
Mixed H2/H-infinity control balances performance and robustness by minimizing an H2 cost bound subject to an H-infinity constraint. However, classical Riccati/LMI solutions offer l…
Gradient Dominance in the Linear Quadratic Regulator: A Unified Analysis for Continuous-Time and Discrete-Time Systems
Yuto Watanabe, Yang Zheng
Despite its nonconvexity, policy optimization for the Linear Quadratic Regulator (LQR) admits a favorable structural property known as gradient dominance, which facilitates linear…
Policy Optimization in Robust Control: Weak Convexity and Subgradient Methods
Yuto Watanabe, Feng-Yi Liao, Yang Zheng
Robust control seeks stabilizing policies that perform reliably under adversarial disturbances, with control as a classical formulation. It is known that polic…
Semidefinite Programming Duality in Infinite-Horizon Linear Quadratic Differential Games
Yuto Watanabe, Chih-Fan Pai, Yang Zheng
Semidefinite programs (SDPs) play a crucial role in control theory, traditionally as a computational tool. Beyond computation, the duality theory in convex optimization also provid…
Revisiting Strong Duality, Hidden Convexity, and Gradient Dominance in the Linear Quadratic Regulator
Yuto Watanabe, Yang Zheng
The Linear Quadratic Regulator (LQR) is a cornerstone of optimal control theory, widely studied in both model-based and model-free approaches. Despite its well-established nature,…