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.