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  • 1
    Electronic Resource
    Electronic Resource
    Pseudospectral Chebyshev Optimal Control of Constrained Nonlinear Dynamical Systems (1998)
    Springer
    Computational optimization and applications 11 (1998), S. 195-217 
    Details
    ISSN: 1573-2894
    Keywords: optimal control ; spectral numerical methods ; Chebyshev polynomials ; smoothing filters
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science
    Notes: Abstract 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 to its dynamic nature, the proposed method avoids many of the numerical difficulties typically encountered in solving standard optimal control problems. Furthermore, for discontinuous optimal control problems, we develop and implement a Chebyshev smoothing procedure which extracts the piecewise smooth solution from the oscillatory solution near the points of discontinuities. Numerical examples are provided, which confirm the convergence of the proposed method. Moreover, a comparison is made with optimal solutions obtained by closed-form analysis and/or other numerical methods in the literature.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1018694111831
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    Paper (German National Licenses)
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  • 2
    Electronic Resource
    Electronic Resource
    Optimal control computation for integro-differential aerodynamic equations (1998)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 21 (1998), S. 653-664 
    Details
    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: In order to maintain spectrally accurate solutions, the grids on which a non-linear physical problem is to be solved must also be obtained by spectrally accurate techniques. The purpose of this paper is to describe a pseudospectral computational method of solving integro-differential systems with quadratic performance index. The proposed method is based on the idea of relating grid points to the structure of orthogonal interpolating polynomials. The optimal control and the trajectory are approximated by the m th degree interpolating polynomial. This interpolating polynomial is spectrally constructed using Legendre-Gauss-Lobatto grid points as the collocation points, and Lagrange polynomials as trial functions. The integrals involved in the formulation of the problem are calculated by Gauss-Lobatto integration rule, thereby reducing the problem to a mathematical programming one to which existing well-developed algorithms may be applied. The method is easy to implement and yields very accurate results. An illustrative example is included to confirm the convergence of the pseudospectral Legendre method, and a comparison is made with an existing result in the literature. © 1998 B. G. Teubner Stuttgart-John Wiley & Sons Ltd.
    Additional Material: 2 Tab.
    Type of Medium: Electronic Resource
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    Paper (German National Licenses)
  • 3
    Electronic Resource
    Electronic Resource
    An Alternative Method for a Classical Problem in the Calculus of Variations (1996)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 19 (1996), S. 1091-1097 
    Details
    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: A numerical technique for determining the solution of the brachistochrone problem is presented. The brachistochrone problem is first formulated as a non-linear optimal control problem. Using Chebyshev nodes, we construct the Mth degree polynomial interpolation to approximate the state and the control variables. Application of this method results in the transformation of differential and integral expressions into some non-linear algebraic equations to which Newton-type methods can be applied. Simulation studies demonstrate computational advantages relative to existing methods in the literature.
    Additional Material: 3 Tab.
    Type of Medium: Electronic Resource
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    Paper (German National Licenses)
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