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.     

Solution of linear optimal control problems with time delay using a composite Chebyshev finite difference method

In this paper, a composite Chebyshev finite difference method is introduced and applied for finding the solution of optimal control of time‐delay systems with a quadratic performance index. This method is an extension of the Chebyshev finite difference scheme. The proposed method can be regarded as a nonuniform finite difference scheme and is based on a hybrid of block‐pulse functions and Chebyshev polynomials using the well‐known Chebyshev–Gauss–Lobatto points. Various types of time‐delay systems are included to demonstrate the validity and the applicability of the technique. The method is easy to implement and provides very accurate results. Copyright © 2012 John Wiley & Sons, Ltd.