Computations for Bang–bang Constrained Optimal Control Using a Mathematical Programming Formulation

An algorithm is proposed to solve the problem of bang–bang constrained optimal control of non‐linear systems with free terminal time. The initial and terminal states are prescribed. The problem is reduced to minimizing a Lagrangian subject to equality constraints defined by the terminal state. A solution is obtained by solving a system of non‐linear equations. Since the terminal time is free, time‐optimal control is given a special emphasis. Second‐order sufficient conditions of optimality are also stated. The algorithm is demonstrated by a detailed study of the switching structure for stabilizing the F–8 aircraft in minimum time, and other examples. Copyright © 2005 John Wiley & Sons, Ltd.