A New Technique for Solving Optimal Control Problems of the Time-delayed Systems
0
조회
0
다운로드
0
인용
0
참고문헌
키워드
초록
An approximation scheme utilizing Bezier curves is considered for solving time-delayed optimal control problems with terminal inequality constraints. First, the problem is transformed, using a Pade approximation, to one without a time-delayed argument. Terminal inequality constraints, if they exist, are converted to equality constraints. A computational method based on Bezier curves in the time domain is then proposed for solving the obtained non-delay optimal control problem. Numerical examples are introduced to verify the efficiency and accuracy of the proposed technique. The findings demonstrate that the proposed method is accurate and easy to implement
Abstract
An approximation scheme utilizing Bezier curves is considered for solving time-delayed optimal control problems with terminal inequality constraints. First, the problem is transformed, using a Pade approximation, to one without a time-delayed argument. Terminal inequality constraints, if they exist, are converted to equality constraints. A computational method based on Bezier curves in the time domain is then proposed for solving the obtained non-delay optimal control problem. Numerical examples are introduced to verify the efficiency and accuracy of the proposed technique. The findings demonstrate that the proposed method is accurate and easy to implement
참고문헌 (14)
- H. Allouche, "Numerical solution of singular boundary value problems with logarithmic singularities by pade approximation and collocation methods", J. Comput. Appl. Math, 311, pp.324~341 (2017)
- H. Banks, "Approximation of nonlinear functional differential equation control systems", J. Optim. Theory Appl, 29, pp.383~408 (1979)
- M. Basin, "An optimal regulator for linear systems with multiple state and input delays", Optimal Control Appl. Methods, 28, pp.45~57 (2007)
- M. Basin, "Optimal control for linear systems with multiple time delays in control input", IEEE Trans. Automat. Control, 51(1), pp.91~97 (2006)
- F. Ghomanjani, "A new approach for solving fractional differential-algebric equations", J. Taibah Univ. Sci, 11, pp.1158~1164 (2017)
- F. Ghomanjani, "Bezier control points method to solve constrained quadratic optimal control of time varying linear systems", Comput. Appl. Math, 31(3), pp.433~456 (2012)
- G. L. Kharatishdi, "The maximum principle in the theory of optimal processes with time lags", Doll. Akad, 136, pp.39~43 (1961)
- N. N. Krasovskii, "On the analytic construction of an optimal control in a system with time lags", Prickl. Mat. Mech, 26, pp.39~51 (1962)
- J. P. LaSalle, "The time optimal control problem, Contributions to the Theory of Nonlinear Oscillations V", pp.1~24 (1960), Princeton Univ. Press
- A. Nazemi, "Solving optimal control problems of the time-delayed systems by Haar wavelet", J. Vib. Control, 22, pp.2657~2670 (2016)
- M. N. Oguztoreli, "A time optimal control problem for systems described by differential difference equations", J. Soc. Indust. Appl. Math. Ser. A Control, 1, pp.290~310 (1963)
- D. W. Ross, "Optimal control of systems described by differential difference equations", Ph.D, Dept of Elec. Enery, pp.1968
- K. Wong, "Optimal control computation for nonlinear time-lag systems", J. Optim. Theory Appl, 47, pp.91~107 (1985)
- C. Wu, "Optimal control of switched systems with time delay", Appl. Math. Lett, 19, pp.1062~1067 (2006)[DOI]