NDLI: Dynamic method of multipliers in terminal control

Content Provider	Springer Nature Link
Author	Antipin, A. S. Vasilieva, O. O.
Copyright Year	2015
Abstract	A method for solving the terminal control problem with a fixed time interval and fixed initial conditions is proposed. The solution to the boundary value problem posed at the right end of the time interval determines the terminal conditions. This boundary value problem is a finite-dimensional convex programming problem. The dynamics of the terminal control problem is described by a linear controllable system of differential equations. This system is interpreted as a conventional system of linear equality constraints. Then the terminal control problem can be regarded as a dynamic convex programming problem posed in an infinite-dimensional functional Hilbert space. In this paper, the functional problem is treated as a saddle-point problem rather than optimization problem. Accordingly, a saddle-point approach to solving the problem is proposed. This approach is based on maximizing the dual function generated by the modified Lagrangian function of the convex programming problem posed in the functional space. The convergence of the proposed methods is also proved in the functional space. This convergence has the additional property of being monotone in norm with respect to controls, phase trajectories, adjoint functions, as well as finite-dimensional terminal variables.
Starting Page	766
Ending Page	787
Page Count	22
File Format	PDF
ISSN	09655425
Journal	Computational Mathematics and Mathematical Physics
Volume Number	55
Issue Number	5
e-ISSN	15556662
Language	English
Publisher	Pleiades Publishing
Publisher Date	2015-05-27
Publisher Place	Moscow
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	linear problem terminal control Lagrangian function modified Lagrangian function saddle-point method convergence Computational Mathematics and Numerical Analysis
Content Type	Text
Resource Type	Article
Subject	Computational Mathematics

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