Globally Optimal Control of Nonlinear Input-Affine Systems Under Quadratic Objective Functions Based on Trajectory Database

Abstract

In this paper, an approach to optimally control nonlinear input-affine systems under quadratic objective functions based on a trajectory database is proposed. In the proposed approach, the control input is calculated by solving a two-point boundary value problem of the Euler-Lagrange equation, whose initial solution is searched from the trajectory database. By a mechanism for eliminating trajectories which found to be locally optimal from the database, the proposed approach is able to obtain globally optimal solutions for problems with multiple locally optimal trajectories that are difficult to handle appropriately with existing methods. The effectiveness of the proposed approach is demonstrated through a simulation of swing-up control of one-link inverted pendulum.