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\begin{document}
\title{\textbf{Optimal Control of Nonlinear Time-Delay Systems by Equal Delay in State and Control Vector's}}
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\begin{abstract}
A new feedforward and feedback optimal control law for a class of nonlinear time-delay systems with equal delay in state and control vector's is presented in this paper. By using a successive approximation approach (SAA), the original nonlinear optimal control problem is transformed into a sequence of nonhomogeneous linear two-point boundary value (TPBV) problems. The optimal control law obtained consists of analytical linear feedforward and feedback terms and a nonlinear compensation term which is the limit of the solution sequence for the adjoint vector differential equations. By using the finite-step iteration of nonlinear compensation sequence, we can obtain a feedforward and feedback suboptimal control law. . Simulation examples show the effectiveness of the approach. 

\end{abstract}
\textbf{Keywords:} Nonlinear time-delay systems, successive approximation approach, optimal control, feedforward control.
\section{Introduction}
The control of systems with time delay has been of considerable concern. Delays occur frequently in biological, chemical, transportation, electronic, communication, manufacturing and power systems [5]. Time 
delay and multi-delay control systems are therefore very important classes of systems whose control and optimization have been of interest to many investigators\cite{bib1}-\cite{bib7}

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 Farahi,M. H., Dadkhah, M., Solving Nonlinear Time Delay Control Systems by Fourier series, Int. Journal of Engineering Research and Applications,Vol. 4 ,pp. 217-226, 2014. 
 \bibitem{bib7}
 ZHAO Yan-dong.GE Su-nan.,Optimal Disturbance Rejection for the Status Delay Systems with Time Delay in Control Action,Intelligent Control and Automation (WCICA), 2010 8th World Congress on,pp. 3839 - 3843,2010. 
\bibitem{bib8}
TANG,G.Y.,and ZHAO,Y. D.,Optimal Control of Nonlinear Time-Delay Systems with Persistent Disturbances,Journal of Optimization Theory and Applications, Vol. 132, pp. 307–320, 2007
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\bibitem{bib9} 
TANG,G.Y.,Suboptimal Conrol for Nonlinear Systems:A Successive Approximation Approach, Systems and Control Letters,Vol.8,pp. 429-434,2005.
\end{LTRbibitems}
\bibitem{bib10}
RAY,W. H.,and SOLIMAN,M. A.,The optimal control of processes containing pure time delays - I Necessary conditions for an optimum,Chemical Engineering Science, Vol. 25, pp. 1911-1925,1970
\end{thebibliography}
\end{document}