The Existence Problem of Optimal Control for Nonlinear Processes

Peng Shi-ge; Chen Zu-hao

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Peng Shi-ge, Chen Zu-hao. The Existence Problem of Optimal Control for Nonlinear Processes[J]. Applied Mathematics and Mechanics, 1983, 4(6): 809-820.

Citation:

Peng Shi-ge, Chen Zu-hao. The Existence Problem of Optimal Control for Nonlinear Processes[J]. Applied Mathematics and Mechanics, 1983, 4(6): 809-820.

Citation:

Peng Shi-ge, Chen Zu-hao. The Existence Problem of Optimal Control for Nonlinear Processes[J]. Applied Mathematics and Mechanics, 1983, 4(6): 809-820.

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The Existence Problem of Optimal Control for Nonlinear Processes

Shandong University, Ji'nan

Received Date: 1982-10-22
Publish Date: 1983-12-15

Abstract

Abstract

The existence problem of optimal control systems described by x=f(t,x,u) is discussed in this paper, where f(t.x,u) is a more general function and the class of admissible control functions are general enough to contain those control functions which are frequently used in engineering. The problem for an optimal control approximated by a sequence of control functions being part of certain function classes is considered here, an example in contradiction with the conclusion of ref. [1] about this problem is given, and a correct conclusion is presented.

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References(4)

References

[1]	Lee,E.B.and L.Markus,Optimal control for nonlinear processes,Arch.Rational Mech.Anal.,Vol.8,No.1,(1961),36-38.
[2]	Berkovitz,L.D.,Optimal Control Theory,(1974).
[3]	夏道行等.《实变函数论与泛函分析》人民教育出版社.(1979).
[4]	刘斯铁尔尼克,Л.Е.等,《泛函分析概要》中译本,杨从仁译.科学出版社.