The codifferential descent method in the problem of finding the global minimum of a piecewise affine objective functional in linear control systems

Author:

Fominyh Alexander V., ,Karelin Vladimir V.,Polyakova Lyudmila N.,Myshkov Stanislav K.,Tregubov Vladimir P., , , ,

Abstract

The article considers the problem of optimal control of an object described by a linear nonstationary system and with a piecewise affine quality functional. The problem is examined in Mayer’s form with both free and partially fixed right endpoints. Piecewise continuous and bounded controls that lie in some parallelepiped at each moment of time are admissible. The standard discretization of the original system and the control parametrization are used, some convergence theorems of the discrete problem solution to the continuous problem solution are presented. Further, for the obtained discrete system, the necessary and sufficient minimum conditions are written out in terms of the codifferential, the method of the modified codifferential descent is applied to it, which guarantees to find the global minimum of this problem in a finite number of steps. The proposed algorithm is illustrated with examples.

Publisher

Saint Petersburg State University

Subject

Applied Mathematics,Control and Optimization,General Computer Science

Cited by 4 articles. 订阅此论文施引文献 订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献

1. Optimal control of the Navier— Stokes system with a space variable in a network-like domain;Vestnik of Saint Petersburg University. Applied Mathematics. Computer Science. Control Processes;2023

2. Method for solving an optimal control problem in the Mayer form with a quasidifferentiable functional in the presence of phase constraints;Vestnik of Saint Petersburg University. Applied Mathematics. Computer Science. Control Processes;2023

3. Stability of operator-difference schemes with weights for the hyperbolic equation in the space of summable functions with carriers in the network-like domain;Vestnik of Saint Petersburg University. Applied Mathematics. Computer Science. Control Processes;2022

4. Modified Genetic Algorithm of Global Extremum Search in Combination with Directional Methods;The Bulletin of Irkutsk State University. Series Mathematics;2022

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