Some Insights on Synthesizing Optimal Linear Quadratic Controller Using Krotov's Sufficiency Conditions
For researchers in optimal control, this work offers a new perspective on solving linear quadratic problems without iteration, but it is incremental as it applies an existing framework to a well-known problem.
This paper proposes suitable Krotov's functions for linear quadratic optimal control problems, showing that imposing convexity eliminates the need for iterative solutions, and provides insights contrasting with Calculus of Variations and Hamilton-Jacobi-Bellman approaches.
This paper revisits the problem of optimal control law design for linear systems using the global optimal control framework introduced by Vadim Krotov. Krotov's approach is based on the idea of total decomposition of the original optimal control problem (OCP) with respect to time, by an $ad$ $hoc$ choice of the so-called Krotov's function or solving function, thereby providing sufficient conditions for the existence of global solution based on another optimization problem, which is completely equivalent to the original OCP. It is well known that the solution of this equivalent optimization problem is obtained using an iterative method. In this paper, we propose suitable Krotov's functions for linear quadratic OCP and subsequently, show that by imposing convexity condition on this equivalent optimization problem, there is no need to compute an iterative solution. We also give some key insights into the solution procedure of the linear quadratic OCP using the proposed methodology in contrast to the celebrated Calculus of Variations (CoV) and Hamilton-Jacobi-Bellman (HJB) equation based approach.