Optimal control of a class of nonlinear systems using Euler-Lagrange back integration method

Abstract

In this study, an algorithm is presented that aims to extend the use of Euler-Lagrange back integration method to optimal control of linearizable, affine-in-the-input nonlinear systems having more than two states. The algorithm generates optimal paths by selecting a starting point iteratively on the ellipsoid close to the equilibrium point, representing the optimal borderline of the linearized system, and backward integrating the optimal nonlinear dynamics. The generated paths are then utilized in the optimal control loop.