SIMULTANEOUS COMPUTATION OF OPTIMAL CONTROLS AND THEIR SENSITIVITIES

This paper presents a method for solving a class of fixed-time optimal control problems for non-linear dynamical systems. The method focuses on obtaining an approximate solution to the Hamilton-Jacobi-Bellman (HJB) partial differential equation, valid at the initial time and for the initial state. It uses finite-order approximations of the partial derivatives of the cost function and, successive higher-order differentiations of the HJB equation. The proposed method converts the HJB partial differential equation into a set of ordinary differential equations via the method of lines. Natural byproducts of the proposed method are the sensitivities of the cost function, which can be used to obtain approximations to the optimal controls at the initial time, in the event of initial state perturbations. Two numerical examples are considered to demonstrate the applications of this methodology. Results are compared to the respective open-loop solutions to determine the accuracy of the approximations.

SIMULTANEOUS COMPUTATION OF OPTIMAL CONTROLS AND THEIR SENSITIVITIES Conference Paper