Mathematical Problems in Engineering
Volume 3 (1998), Issue 6, Pages 503-515

A collocation method for optimal control of linear systems with inequality constraints

M. Razzaghi,1,3 J. Nazarzadeh,2 and K. Y. Nikravesh2

1Department of Mathematics and Statistics, Mississippi State University, Mississippi State, 39762, MS, USA
2Department of Electrical Engineering, Amirkabir University, Tehran, Iran
3Department of Mathematics, Amirkabir University, Tehran, Iran

Received 29 May 1997

Copyright © 1998 M. Razzaghi et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


A numerical method for solving linear quadratic optimal control problems with control inequality constraints is presented in this paper. The method is based upon hybrid function approximations. The properties of hybrid functions which are the combinations of block-pulse functions and Legendre polynomials are first presented. The operational matrix of integration is then utilized to reduce the optimal control problem to a set of simultaneous nonlinear equations. The inequality constraints are first converted to a system of algebraic equalities, these equalities are then collocated at Legendre–Gauss–Lobatto nodes. An illustrative example is included to demonstrate the validity and applicability of the technique.