Analysis of linear‐quadratic optimal control via a hybrid control lens

Abstract

Linear‐quadratic regulator (LQR) is a landmark problem in the field of optimal control, which is investigated based on the method of hybrid dynamic system and continuous‐time optimization algorithms. We show that the above‐mentioned hybrid system converges exponentially to the optimal feedback gain with any order, and the solution trajectory is Zeno‐free. Then, the forward‐Euler method is utilized to discretize the hybrid system, and a new algorithm called hybrid dynamics‐based gradient descent (HGD) is proposed that could converge to the optimal controller exponentially.