The Main Results of Optimal Control Theory Made Simple

Abstract

Publisher Summary This chapter presents the main results of optimal control theory. A very special case of the optimal control problem requires the determination of the continuous and piece-wise continuously differentiable function x(t), which yields the minimum value of J. A solution x(t) satisfies the Euler–Lagrange second-order ordinary nonlinear differential equation except at points of discontinuous x. A minimizing function must satisfy the Jacobi condition, which is subtle and does not concern the discrete-time problem. The chapter discusses the simplest variational problem, the general optimal control problem, the simplest discrete-time variational problem, and an optimal control problem with scalar state and control.