Computation of Non-iterative Optimal Linear Quadratic Controllers using Krotov's Sufficient Conditions

Abstract

This paper revisits the problem of synthesizing the optimal control law for linear time-varying systems by using the global optimal control framework introduced by Vadim Krotov. This approach is based on the idea of total decomposition of the original optimal control problem (OCP) with respect to time thereby providing sufficient conditions for the existence of global solution based on another optimization problem, which turns out to be nonlinear and non-convex, and is completely equivalent to the original OCP. The solution of this equivalent optimization problem is usually computed using iterative methods which may not be desirable for deploying low-cost hardware in industry. In this paper, we propose a novel method for synthesizing the global optimal control law using these sufficient conditions. The novelty of the proposed method lies in transforming the equivalent non-convex optimization problem into a convex problem by a judicious choice of the so-called Krotov functions. As an immediate consequence, there is no need to compute an iterative solution.