In collaboration with Payame Noor University and the Iranian Society of Instrumentation and Control Engineers

Document Type : Research Article

Authors

1 Department of Mathematics, Yazd University, Yazd, Iran

2 Assistant Professor, Faculty of Engineering, Ardakan University, Ardakan, Iran

Abstract

In order to obtain a solution to an optimal control problem‎, ‎a numerical technique based on state-control parameterization method is presented‎. ‎This method can be facilitated by the computation of performance index and state equation via approximating the control and state variable as a function of time‎. ‎Several numerical examples are presented to confirm the analytical findings and illustrate the efficiency of the proposed method.

Keywords

Main Subjects

[1] Babolian E.‎, ‎Fattahzadeh F‎. ‎(2007)‎. ‎`` Numerical solution of differential equations by using Chebyshev wavelet operational matrix of integration"‎, ‎Applied Mathematics and Computation‎, ‎188‎, ‎417-426‎.
‎[2] Fleming W.H.‎, ‎Rishel C‎. ‎J‎. ‎(1975)‎. ‎`` Deterministic and stochastic optimal control"‎, ‎New York‎, ‎Springer-Verlag‎.
‎[3] Jaddu H‎. ‎(1998)‎. ‎`` Numerical methods for solving optimal control problems using Chebyshev polynomials"‎, ‎PHD Thesis‎, ‎JAIST‎, ‎Japan‎.
‎‎[4] Jajarmi A.‎, ‎Hajipour M‎. ‎(2015)‎. ‎`` An efficient recursive shooting method for the optimal control of time-varying systems with state time-delay"‎, ‎Applied Mathematical Modelling‎. ‎40‎, ‎1-14‎.‎
[5] Kafash B.‎, ‎Delavarkhalafi A‎. ‎(2015)‎. ‎`` Restarted state parameterization method for optimal control problems"‎, ‎Journal of Mathematics and Computer Science‎, ‎151-161‎.
[6] Kafash B.‎, ‎Delavarkhalafi A.‎, ‎Karbassi S.M‎. ‎(2012)‎. ‎`` Application of Chebyshev polynomials to derive‎ ‎efficient algorithms for the solution of optimal control problems"‎, ‎Scientia Iranica‎, ‎19‎, ‎795-805‎.
[7] Mirhosseini-Alizamini S‎. ‎M.‎, ‎Effati‎, ‎S.‎, ‎Heydari A‎. ‎(2015)‎. ‎`` An iterative method for suboptimal control of linear time delayed system"‎, ‎Systems and Control Letters‎, ‎82‎, ‎40-50‎.
[8] Razmjooy N.‎, ‎Ramezani M‎. ‎(2016)‎. ‎`` Analytical solution for optimal control by the second kind Chebyshev polynomials expansion"‎, ‎Iranian Journal of Science and Technology (Sciences) in press‎.‎‎
[9] Rudin W‎. ‎(1976)‎. ‎`` Principles of mathematical analysis"‎, ‎3rd edition‎, ‎McGraw-Hill‎, ‎New York‎.
‎[10] Saberi Nik H.‎, ‎Effati S.‎, ‎Shirazian M‎. ‎(2012)‎. ‎`` An approximate-analytical solution for the Hamilton-Jacobi-Bellman equation via homotopy perturbation method"‎, ‎Applied Mathematical Modelling‎, ‎36‎, ‎5614-5623‎.
[11] Vlassenbroeck J‎. ‎(1988)‎. ‎`` A Chebyshev polynomial method for optimal control with constraints"‎, ‎International Federation of Automatic Control‎, ‎24‎, ‎499-506‎.
[12] Vlassenbroeck J.‎, ‎Van Dooren R.A‎. ‎(1988)‎. ‎`` Chebyshev technique for solving nonlinear optimal control problems"‎, ‎IEEE Transactions on Automatic Control‎, ‎33‎, ‎333-340‎.‎