On solving optimal control problems by means of splines

V.V. Gusar; A.A. Ligun

doi:10.15421/248703

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.

Full Text:

PDF (Русский)

References

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., 1975.

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

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. doi:10.1007/BF01087192

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

De Bor K. Practical guide on splines, 1985.

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

Ligun A.A., Shumeiko A.A. "Optimal choice of nodes at approximation of functions by splines", Dokl. AN sssr, 1984; 6.

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

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