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  • 1
    Electronic Resource
    Electronic Resource
    Optimal control of lumped parameter systems via shifted Legendre polynomial approximation (1985)
    Springer
    Journal of optimization theory and applications 45 (1985), S. 313-324 
    Details
    ISSN: 1573-2878
    Keywords: Shifted Legendre polynomials ; operational matrix ; functional differential equations ; optimal control problems
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract Shifted Legendre polynomial functions are employed to solve the linear-quadratic optimal control problem for lumped parameter system. Using the characteristics of the shifted Legendre polynomials, the system equations and the adjoint equations of the optimal control problem are reduced to functional ordinary differential equations. The solution of the functional differential equations are obtained in a series of the shifted Legendre functions. The operational matrix for the integration of the shifted Legendre polynomial functions is also introduced in the simulation step in order to simplify the computational procedure. An illustrative example of an optimal control problem is given, and the computational results are compared with those of the exact solution. The proposed method is effective and accurate.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00939983
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    Paper (German National Licenses)
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  • 2
    Electronic Resource
    Electronic Resource
    Shifted Legendre direct method for variational problems (1983)
    Springer
    Journal of optimization theory and applications 39 (1983), S. 299-307 
    Details
    ISSN: 1573-2878
    Keywords: Shifted Legendre polynomials ; operational matrix ; variational problems ; optimization
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract The shifted Legendre polynomial series is employed to solve variational problems. The solution is carried out by using an operational matrix for integrating the shifted Legendre polynomial vector. Variational problems are reduced to solving algebraic equations. Two illustrative examples are given, and the computational results obtained by Legendre series direct method are compared with the exact solutions.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00934535
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    Paper (German National Licenses)
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