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Mathematical Problems in Engineering
Volume 2018, Article ID 5217427, 10 pages
Research Article

Time Optimal Control Laws for Bilinear Systems

Advanced System Laboratory (LSA), Tunisia Polytechnic School (EPT), University of Carthage, BP 743, 2078 La Marsa, Tunisia

Correspondence should be addressed to Salim Bichiou; moc.liamg@uoihcib.milas

Received 27 July 2017; Revised 8 February 2018; Accepted 5 March 2018; Published 8 April 2018

Academic Editor: J.-C. Cortés

Copyright © 2018 Salim Bichiou 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.


The aim of this paper is to determine the feedforward and state feedback suboptimal time control for a subset of bilinear systems, namely, the control sequence and reaching time. This paper proposes a method that uses Block pulse functions as an orthogonal base. The bilinear system is projected along that base. The mathematical integration is transformed into a product of matrices. An algebraic system of equations is obtained. This system together with specified constraints is treated as an optimization problem. The parameters to determine are the final time, the control sequence, and the states trajectories. The obtained results via the newly proposed method are compared to known analytical solutions.