Affine Quadratic Optimal Control and Aerospace Applications

This article proposes a class of mathematical models of aerospace control systems. The article has three main contributions. The first contribution is to present analytical solutions of optimal control problems with affine dynamics and quadratc cost with both cross terms and a tradeoff coefficient that weights time. A second contribution is to solve analytically a class of nonlinear optimal control problems with a single input and a conserved quantity. The analytical solution is obtained through a transformation of variables that leads to an equivalent affine quadratic problem. On a practical level, this article contributes by showing how the proposed class of problems can unify a class of applications in aeronautics and astronautics. The relevance of the proposed methodology is illustrated in examples of trajectory planning with linear drag and wind, as well as orbit intercept.