On solving optimal control problems by means of splines

V.V. Gusar (Dnipropetrovsk State University)
A.A. Ligun (Dnipropetrovsk State University)

Abstract


We consider spline-methods of solving problems, in which piecewise-smooth functions can be the sought solution. We provide and ground the algorithm of approximation of piecewise-smooth functions by splines with automatic search for points of discontinuity of the function and its derivatives. On the base of this algorithm, we describe methods to determine the spline-solution for some optimal control problems.

References


Zavialov Yu.S., Kvasov B.I., Miroshnichenko V.L. Methods of spline-functions, 1980. (in Russian)

De Bor K. Practical guide on splines, 1985. (in Russian)

Andrukh G.V., Gudymenko B.A. "Selection of optimal control, approximated by spline-functions", Kibern. i vychisl. tekhn., 1984, 62. (in Russian)

Stechkin S.B. "One optimization problem", Numer. Math., 1972; 16.

Rice J.R. "Remarks on Piecewise Polynomial Approximation", Proc. Int. Conf. on theory of function approx., Kaluga, 1975.

Ligun A.A., Storchai V.F. "On the best choice of nodes at approximation by splines in $$$L_p$$$ metric", Matem. zametki, 1975; 20(4): pp. 615-622. (in Russian) doi:10.1007/BF01098911

Ligun A.A., Shumeiko A.A. "Optimal choice of nodes at approximation of functions by splines", Dokl. AN SSSR, 1984; 6. (in Russian)

Ligun A.A., Shumeiko A.A. "On optimal choice of nodes at approximation of functions by interpolative polynomials", J. Comp. Math. and Math. Phys., 1984; 24(9). (in Russian)

Grebennikov A.I. "On choice of nodes at interpolation of functions by splines", Vychisl. metody i programmirovanie, 1977; 26. (in Russian)

Ligun A.A., Storchai V.F. "On the best choice of nodes at approximation of functions by local Hermitian splines", Ukrainian Math. J., 1980; 32(6): 824-830. (in Russian) doi:10.1007/BF01087192




DOI: https://doi.org/10.15421/248703

  

Refbacks

  • There are currently no refbacks.


Copyright (c) 1987 V.V. Gusar, A.A. Ligun

Creative Commons License
This work is licensed under a Creative Commons Attribution 4.0 International License.


Registered in

More►


ISSN (Online): 2664-5009
ISSN (Print): 2664-4991
DNU