Solution of the multipoint control problem for a dynamic system in partial derivatives

2020 ◽  
Author(s):  
Svetlana P. Zubova ◽  
Elena V. Raetskaya
Keyword(s):  
Dynamic System ◽  
Control Problem ◽  
Partial Derivatives ◽  
Multipoint Control

scholarly journals Robust Guaranteed-Cost Preview Repetitive Control for Polytopic Uncertain Discrete-Time Systems

Algorithms ◽  
2019 ◽  
Vol 12 (1) ◽  
pp. 20 ◽  
Author(s):  
Yong-Hong Lan ◽  
Jun-Jun Xia ◽  
Yue-Xiang Shi
Keyword(s):  
Dynamic System ◽  
Control Problem ◽  
Discrete Time ◽  
Repetitive Control ◽  
Original System ◽  
Linear Matrix ◽  
Discrete Time Systems ◽  
Guaranteed Cost ◽  
Time Systems ◽  
Repetitive Controller

In this paper, a robust guaranteed-cost preview repetitive controller is proposed for a class of polytopic uncertain discrete-time systems. In order to improve the tracking performance, a repetitive controller, combined with preview compensator, is inserted in the forward channel. By using the L-order forward difference operator, an augmented dynamic system is constructed. Then, the guaranteed-cost preview repetitive control problem is transformed into a guaranteed-cost control problem for the augmented dynamic system. For a given performance index, the sufficient condition of asymptotic stability for the closed-loop system is derived by using a parameter-dependent Lyapunov function method and linear matrix inequality (LMI) techniques. Incorporating the controller obtained into the original system, the guaranteed-cost preview repetitive controller is derived. A numerical example is also included, to show the effectiveness of the proposed method.

scholarly journals The nonsmoth optimal control problem for ensamble of trajectories of dynamic system under conditions of indeterminaci

2020 ◽  
Vol 5 ◽  
pp. 38-42
Author(s):  
Otakulov Salim ◽  
Rahimov Boykxuroz Shermuhamedovich ◽  
Haydarov Tulkinjon Turgunbayevich
Keyword(s):  
Optimal Control ◽  
Dynamic System ◽  
Control Problem ◽  
Differential Inclusions ◽  
Sufficient Conditions ◽  
Value Analysis ◽  
Minimax Control ◽  
Informational Model ◽  
The One ◽  
Necessary And Sufficient

In the paper we consider the one model of dynamic system under conditions of indeterminacy – linear controllable differential inclusions. For the informational model of the control system the minimax control problem for ensemble trajectories is researched. This control problem is study with a methods nonsmooth and multi-value analysis. The necessary and sufficient conditions of optimality are obtained.

scholarly journals Second-Order PDE Constrained Controlled Optimization Problems with Application in Mechanics

Mathematics ◽  
2021 ◽  
Vol 9 (13) ◽  
pp. 1472
Author(s):  
Savin Treanţă
Keyword(s):  
Control Problem ◽  
Necessary Conditions ◽  
Optimization Problems ◽  
Multiple Integral ◽  
Second Order ◽  
Final Part ◽  
Control Problems ◽  
Partial Derivatives ◽  
The One ◽  
Cost Functionals

The present paper deals with a class of second-order PDE constrained controlled optimization problems with application in Lagrange–Hamilton dynamics. Concretely, we formulate and prove necessary conditions of optimality for the considered class of control problems driven by multiple integral cost functionals involving second-order partial derivatives. Moreover, an illustrative example is provided to highlight the effectiveness of the results derived in the paper. In the final part of the paper, we present an algorithm to summarize the steps for solving a control problem such as the one investigated here.

scholarly journals Robust Guaranteed-Cost Preview Repetitive Control for Polytopic Uncertain Discrete-Time Systems

2018 ◽  
Author(s):  
Yong-Hong Lan ◽  
Xia Jun-Jun
Keyword(s):  
Dynamic System ◽  
Control Problem ◽  
Discrete Time ◽  
Repetitive Control ◽  
Original System ◽  
Linear Matrix ◽  
Discrete Time Systems ◽  
Guaranteed Cost ◽  
Time Systems ◽  
Repetitive Controller

A robust guaranteed cost preview repetitive controller is proposed for a class of polytopic uncertain discrete-time systems. In order to improve the tracking performance, the repetitive controller combined with preview compensator is inserted in the forward channel. By using the L-order forward difference operator, an augmented dynamic system is constructed. Then, the guaranteed cost preview repetitive control problem is transformed into the guaranteed cost control problem for the augmented dynamic system. For given performance index, the sufficient condition of asymptotic stability for the closed-loop system is derived by combining parameter-dependent Lyapunov function method with linear matrix inequality (LMI) techniques. By incorporating the controller obtained into the original system, the guaranteed-cost preview repetitive controller is derived. A numerical example is also included to show the effectiveness of the proposed method.

Control Problem for Dynamical Systems with Partial Derivatives

2020 ◽  
Vol 249 (6) ◽  
pp. 941-953
Author(s):  
S. P. Zubova ◽  
E. V. Raetskaya ◽  
Le Hai Trung
Keyword(s):  
Dynamical Systems ◽  
Control Problem ◽  
Partial Derivatives

On the motion of comet P/d’Arrest

1974 ◽  
Vol 22 ◽  
pp. 145-148
Author(s):  
W. J. Klepczynski
Keyword(s):  
Equations Of Motion ◽  
Variational Equations ◽  
Partial Derivatives

AbstractThe differences between numerically approximated partial derivatives and partial derivatives obtained by integrating the variational equations are computed for Comet P/d’Arrest. The effect of errors in the IAU adopted system of masses, normally used in the integration of the equations of motion of comets of this type, is investigated. It is concluded that the resulting effects are negligible when compared with the observed discrepancies in the motion of this comet.

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