TY - GEN

T1 - Application of Quasidifferential Calculus to Solve Optimal Control Problems with a Nonsmooth Functional

AU - Fominyh, Alexander

N1 - Conference code: 4

PY - 2022

Y1 - 2022

N2 - The paper considers the problem of optimal control of an object described by a system with a continuously differentiable right-hand side and a nondifferentiable (but only quasidifferentiable) quality functional. We consider a problem in the form of Mayer with both a free and a fixed right end. Admissible controls are piecewise continuous and bounded vector functions, which belong to a certain polyhedron at each moment of time. Standard discretization of the initial system and control parameterization is performed, and theorems on the convergence of the solution of the obtained discrete system to the desired solution of the continuous problem are presented. Further, for the obtained discrete system, the necessary and, in some cases, sufficient minimum conditions are written in terms of quasidifferential. The quasidifferential descent method is applied to this problem. The developed algorithm is demonstrated by examples.

AB - The paper considers the problem of optimal control of an object described by a system with a continuously differentiable right-hand side and a nondifferentiable (but only quasidifferentiable) quality functional. We consider a problem in the form of Mayer with both a free and a fixed right end. Admissible controls are piecewise continuous and bounded vector functions, which belong to a certain polyhedron at each moment of time. Standard discretization of the initial system and control parameterization is performed, and theorems on the convergence of the solution of the obtained discrete system to the desired solution of the continuous problem are presented. Further, for the obtained discrete system, the necessary and, in some cases, sufficient minimum conditions are written in terms of quasidifferential. The quasidifferential descent method is applied to this problem. The developed algorithm is demonstrated by examples.

UR - https://www.mendeley.com/catalogue/45a6b958-207d-377e-bffc-e547bb43bd8e/

U2 - 10.1007/978-3-030-87966-2_32

DO - 10.1007/978-3-030-87966-2_32

M3 - Conference contribution

SN - 978-3-030-87965-5

T3 - Lecture Notes in Control and Information Sciences - Proceedings

SP - 293

EP - 301

BT - Stability and Control Processes

PB - Springer Nature

CY - Cham

T2 - Stability and Control Processes: International Conference Dedicated to the Memory of Professor Vladimir Zubov

Y2 - 5 October 2020 through 9 October 2020

ER -