Numerical Methods for Optimal Trajectory Planning with Aerospace Applications

Abstract

Optimal control theory focuses on finding the inputs that optimize the performance measure of a system subject to differential constraints. Differential game theory focuses on problems involving two separate parties, one of which tries to find the inputs to minimize a performance measure, while the other party tries to find the inputs which maximize the same performance measure. Both parties involved are subject to differential constraints. Both optimal control and differential game problems have a high degree of complexity except for the simplest of problems. This leads to the need for numerical methods to find the solutions to optimal control and differential game problems. In this thesis, we present our original numerical toolbox capable of finding feedback control policies, which solve optimal control and differential game problems by computing the solutions to the Hamilton-Jacobi-Bellman and Hamilton-Jacobi-Isaacs equations.