scholarly journals Averaged No-Regret Control for an Electromagnetic Wave Equation Depending upon a Parameter with Incomplete Initial Conditions

2021 ◽  
Author(s):  
Abdelhak Hafdallah ◽  
Mouna Abdelli
Keyword(s):  
Optimal Control ◽  
Wave Equation ◽  
Electromagnetic Wave ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Initial Conditions ◽  
Control Sequence ◽  
Potential Term ◽  
Average Control ◽  
Optimality Systems

This chapter concerns the optimal control problem for an electromagnetic wave equation with a potential term depending on a real parameter and with missing initial conditions. By using both the average control notion introduced recently by E. Zuazua to control parameter depending systems and the no-regret method introduced for the optimal control of systems with missing data. The relaxation of averaged no-regret control by the averaged low-regret control sequence transforms the problem into a standard optimal control problem. We prove that the problem of average optimal control admits a unique averaged no-regret control that we characterize by means of optimality systems.

scholarly journals Seeking Best-Balanced Patch-Injecting Strategies through Optimal Control Approach

2019 ◽  
Vol 2019 ◽  
pp. 1-12
Author(s):  
Kaifan Huang ◽  
Pengdeng Li ◽  
Lu-Xing Yang ◽  
Xiaofan Yang ◽  
Yuan Yan Tang
Keyword(s):  
Optimal Control ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Negative Impact ◽  
Cost Effective ◽  
Control Approach ◽  
Novel Virus ◽  
Optimality Systems ◽  
Objective Functional ◽  
Optimal Control Approach

To restrain escalating computer viruses, new virus patches must be constantly injected into networks. In this scenario, the patch-developing cost should be balanced against the negative impact of virus. This article focuses on seeking best-balanced patch-injecting strategies. First, based on a novel virus-patch interactive model, the original problem is reduced to an optimal control problem, in which (a) each admissible control stands for a feasible patch-injecting strategy and (b) the objective functional measures the balance of a feasible patch-injecting strategy. Second, the solvability of the optimal control problem is proved, and the optimality system for solving the problem is derived. Next, a few best-balanced patch-injecting strategies are presented by solving the corresponding optimality systems. Finally, the effects of some factors on the best balance of a patch-injecting strategy are examined. Our results will be helpful in defending against virus attacks in a cost-effective way.

scholarly journals SOLUTION TO THE OPTIMAL CONTROL PROBLEM BY SOURCES IN THE BOUNDARY CONDITIONS OF A HYPERBOLIC SYSTEM OF A NETWORK STRUCTURE

2021 ◽  
Vol 8 (1) ◽  
pp. 004-012
Author(s):  
Y. R. Ashrafova ◽  
◽  
S. R. Rasulova ◽  
◽  
Keyword(s):  
Optimal Control ◽  
Optimal Control Problem ◽  
Boundary Conditions ◽  
Control Problem ◽  
Initial Conditions ◽  
Nonlocal Boundary ◽  
Nonlocal Boundary Conditions ◽  
Distributed Parameters ◽  
Long Duration ◽  
Internal Sources

The solution to the optimal control problem by power of external and internal sources acting on the multilink system in nonlocal boundary conditions is investigated. Each arc of the system is an object with distributed parameters, described by a differential equation of hyperbolic type and related only by boundary values, and in an arbitrary way. Due to the long duration of the object's functioning, the exact values of the initial conditions are not known, but a set of their possible values is given. Based on the results of additional measurements of the state of the process at the input or output ends of the arcs (which are not internal vertices), a target functional is constructed, for which minimization a formula for its gradient is obtained.

scholarly journals The Problem of the Optimal Control with a Lower Coefficient for Weakly Nonlinear Wave Equation in the Mixed Problem

2020 ◽  
Vol 13 (2) ◽  
pp. 314-322
Author(s):  
Gunay Ismayilova
Keyword(s):  
Optimal Control ◽  
Wave Equation ◽  
Variational Inequality ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Nonlinear Wave ◽  
Nonlinear Wave Equation ◽  
Necessary Condition ◽  
Weakly Nonlinear ◽  
Necessary Condition Of Optimality

In this paper, we consider the problem of determining the lowest coefficient of weakly nonlinear wave equation. The problem is reduced to the optimal control problem, in the new problem. In the this existence theorem of the optimal control and, the Fre ́echet differentiability of the functional is proved. Also the necessary condition of optimality is derived in view of variational inequality.

Stochastic optimal control problem of constrained switching system with delay

Filomat ◽  
2016 ◽  
Vol 30 (3) ◽  
pp. 711-720
Author(s):  
Charkaz Aghayeva
Keyword(s):  
Optimal Control ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Stochastic Optimal Control ◽  
Initial Conditions ◽  
Necessary Condition ◽  
Switching System ◽  
Stochastic Delay Differential Equations ◽  
Stochastic Optimal Control Problem ◽  
Necessary Condition Of Optimality

This paper concerns the stochastic optimal control problem of switching systems with delay. The evolution of the system is governed by the collection of stochastic delay differential equations with initial conditions that depend on its previous state. The restriction on the system is defined by the functional constraint that contains state and time parameters. First, maximum principle for stochastic control problem of delay switching system without constraint is established. Finally, using Ekeland?s variational principle, the necessary condition of optimality for control system with constraint is obtained.

scholarly journals Optimal Control Problem Solution with Phase Constraints for Group of Robots by Pontryagin Maximum Principle and Evolutionary Algorithm

Mathematics ◽  
2020 ◽  
Vol 8 (12) ◽  
pp. 2105
Author(s):  
Askhat Diveev ◽  
Elena Sofronova ◽  
Ivan Zelinka
Keyword(s):  
Optimal Control ◽  
Maximum Principle ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Evolutionary Algorithm ◽  
Pontryagin Maximum Principle ◽  
Initial Conditions ◽  
Problem Solution ◽  
Dynamic Phase ◽  
Phase Constraints

A numerical method based on the Pontryagin maximum principle for solving an optimal control problem with static and dynamic phase constraints for a group of objects is considered. Dynamic phase constraints are introduced to avoid collisions between objects. Phase constraints are included in the functional in the form of smooth penalty functions. Additional parameters for special control modes and the terminal time of the control process were introduced. The search for additional parameters and the initial conditions for the conjugate variables was performed by the modified self-organizing migrating algorithm. An example of using this approach to solve the optimal control problem for the oncoming movement of two mobile robots is given. Simulation and comparison with direct approach showed that the problem is multimodal, and it approves application of the evolutionary algorithm for its solution.

scholarly journals Optimal control problem for systems governed by nonlinear parabolic equations without initial conditions

2016 ◽  
Vol 8 (1) ◽  
pp. 21-37
Author(s):  
M.M. Bokalo ◽  
A.M. Tsebenko
Keyword(s):  
Optimal Control ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Parabolic Equations ◽  
Initial Conditions ◽  
Nonlinear Parabolic Equations ◽  
State Equations ◽  
Control Functions ◽  
Nonlinear Parabolic ◽  
Final Observation

An optimal control problem for systems described by Fourier problem for nonlinear parabolic equations is studied. Control functions occur in the coefficients of the state equations. The existence of the optimal control in the case of final observation is proved. 

scholarly journals Optimal finite element error estimates for an optimal control problem governed by the wave equation with controls of bounded variation

2020 ◽  
Author(s):  
Sebastian Engel ◽  
Boris Vexler ◽  
Philip Trautmann
Keyword(s):  
Optimal Control ◽  
Finite Element ◽  
Wave Equation ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Bounded Variation ◽  
Convergence Rates ◽  
The State ◽  
Linear Wave ◽  
Element Discretization

Abstract This work discusses the finite element discretization of an optimal control problem for the linear wave equation with time-dependent controls of bounded variation. The main focus lies on the convergence analysis of the discretization method. The state equation is discretized by a space-time finite element method. The controls are not discretized. Under suitable assumptions optimal convergence rates for the error in the state and control variable are proven. Based on a conditional gradient method the solution of the semi-discretized optimal control problem is computed. The theoretical convergence rates are confirmed in a numerical example.

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