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... IN SIMULATION ELSEVIER Mathematics and Computers in Simulation 36 (1994) 241246 A pseudospectral collocation method for the brachistochrone problem Mohsen Razzaghi ab ... (17) into (21) the approximated J reduces to N 1 ' 1 +... more
... IN SIMULATION ELSEVIER Mathematics and Computers in Simulation 36 (1994) 241246 A pseudospectral collocation method for the brachistochrone problem Mohsen Razzaghi ab ... (17) into (21) the approximated J reduces to N 1 ' 1 + (2EN oDjtat) J(ao, al, . . . ... Math. Phys. ...
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ABSTRACT
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We develop a pseudospectral approximation scheme for solving the class of time-delayed functional differential equation control systems. The problem is first formulated as a delay free optimal control problem governed by a system of... more
We develop a pseudospectral approximation scheme for solving the class of time-delayed functional differential equation control systems. The problem is first formulated as a delay free optimal control problem governed by a system of partial differential equations with nonlocal boundary conditions. Next, a Chebyshev spectral method together with the cell-averaging Chebyshev integration technique are used to discretize the delay free optimal control problem. The optimal control problem is thereby transformed into a nonlinear programming problem which can be solved by well-developed nonlinear programming algorithms. Due to its dynamic nature, the proposed method avoids many of the numerical difficulties typically encountered in solving standard time-delayed optimal control problems. Moreover, a comparison is made with optimal solutions obtained by closed-form analysis and/or other numerical methods in the literature.
Research Interests: Mathematics, Applied Mathematics, Nonlinear Programming, Numerical Method, Control system, and 6 moreApplied Mathematics and Computational Science, Spectral method, PARTIAL DIFFERENTIAL EQUATION, Numerical Analysis and Computational Mathematics, Applied and Computational Mechanics, and Electrical And Electronic Engineering
A method for solving the linear ordinary differential equations of the two-point boundary-value problem using polynomial series is discussed. The linear ordinary differential equation of the two-point boundary-value problems are reduced... more
A method for solving the linear ordinary differential equations of the two-point boundary-value problem using polynomial series is discussed. The linear ordinary differential equation of the two-point boundary-value problems are reduced to the linear functional differential equation of the initial value problem. It is known that any polynomial series basis vector can be transformed to Taylor polynomials by the use of a suitable transformation and Taylor series have the simplest operational properties. The solution of linear two-point boundary-value problems via Taylor series is first obtained and this solution using other polynomial series is then calculated by transforming the properties of the Taylor series to other polynomial series. The method is simple and convenient for digital computation. Illustrative examples are given.
Research Interests: Engineering, Mathematics, Applied Mathematics, Optimal Control, Systems Science, and 15 moreLinear Programming, Systems Theory, Numerical Method, Mathematical Sciences, Computer Mathematics, Linear System, Taylor Series, Polynomial Interpolation, Function approximation, Differential equation, Boundary Value Problem, Fourier Series, Electrical And Electronic Engineering, LINEAR PROGRAM, and Ordinary Differential Equation
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... In this: publication; By this: publisher; In this Subject: Computer Science , Mathematics and Statistics; By this author: Gamal Elnagar ; Vasilis Zafiris. You are signed in as: Google (Institutional account). Group of crawlers... more
... In this: publication; By this: publisher; In this Subject: Computer Science , Mathematics and Statistics; By this author: Gamal Elnagar ; Vasilis Zafiris. You are signed in as: Google (Institutional account). Group of crawlers (Institutional account ...
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Research Interests: Mechanical Engineering, Mathematics, Applied Mathematics, Optimal Control, Mathematical Programming, and 15 moreNumerical Analysis, Differential Equations, Control system, Gaussian processes, Integration, Discretization, Interpolation, Discrete Optimization, Differential equation, Electrical And Electronic Engineering, Chebyshev Approximation, Non Linear Control, Discrete Systems, optimal algorithm, and Computational Techniques
A pseudospectral method for generating optimal trajectories of linear and nonlinear constrained dynamic systems is proposed. The method consists of representing the solution of the optimal control problem by an mth degree interpolating... more
A pseudospectral method for generating optimal trajectories of linear and nonlinear constrained dynamic systems is proposed. The method consists of representing the solution of the optimal control problem by an mth degree interpolating polynomial, using Chebyshev nodes, and then discretizing the problem using a cell-averaging technique. The optimal control problem is thereby transformed into an algebraic nonlinear programming problem. Due