Practical Methods for Optimal Control Using Nonlinear Programming, Third Edition [Bookshelf] - Rao, Anil V. (IEEE control systems, 2023)
Optimal control is a subject that dates back nearly 100 years. The roots of optimal control lie in the subject of variational calculus, which was originally invented by Leonhard Euler (1707-1783). Fundamentally, an optimal control problem is one where it is desired to determine the state and control of a controlled dynamical system while optimizing (minimizing or maximizing) a performance index (generally referred to as an objective functional ) that is subject to additional constraints such as boundary conditions, interior-point constraints, and path constraints. Such a problem, stated so succinctly, can also be formulated mathematically in a deceivingly simple manner. Because of the seeming simplicity of both the problem statement and the problem formulation, one might conclude that solving an optimal control problem is an easy task. To the contrary, obtaining the solution to a (generally nonlinear) optimal control problem is by no means a simple process. The author states this last point quite elegantly in the very first sentence of the preface of the book: "Solving an optimal control problem is not easy."