A convex approach to robust LQR

In this paper, we propose some new convex strategies for robust optimal control. In particular, we treat the problem of designing finite-horizon linear quadratic regulator (LQR) for uncertain discrete-time systems focusing on minimax strategies. A time-invariant linear control law is obtained just solving sequentially two convex optimization problems, hence obtaining a feedback law that takes into account all the available systems samples. In the case of stabilizable systems, we also generalize our approach by including additional constraints on the closed-loop stability in the optimization scheme. Extensions to time-variant control rules are also discussed, leading to novel and intriguing connections between optimal control and multitask learning.