An optimal control problem for systems described by partial differential equations of hyperbolic type with delay

1987 ◽  
Vol 52 (2) ◽  
pp. 311-322 ◽  
Author(s):  
M. E. Salukvadze ◽  
M. T. Tcutcunava
Keyword(s):  
Optimal Control ◽  
Partial Differential Equations ◽  
Differential Equations ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Hyperbolic Type ◽  
Partial Differential

Solution for fractional distributed optimal control problem by hybrid meshless method

2016 ◽  
Vol 24 (11) ◽  
pp. 2149-2164 ◽  
Author(s):  
Majid Darehmiraki ◽  
Mohammad Hadi Farahi ◽  
Sohrab Effati
Keyword(s):  
Optimal Control ◽  
Partial Differential Equations ◽  
Differential Equations ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Least Squares ◽  
Meshless Method ◽  
Basis Functions ◽  
Moving Least Squares ◽  
Distributed Optimal Control

We use a hybrid local meshless method to solve the distributed optimal control problem of a system governed by parabolic partial differential equations with Caputo fractional time derivatives of order α ∈ (0, 1]. The presented meshless method is based on the linear combination of moving least squares and radial basis functions in the same compact support, this method will change between interpolation and approximation. The aim of this paper is to solve the system of coupled fractional partial differential equations, with necessary and sufficient conditions, for fractional distributed optimal control problems using a combination of moving least squares and radial basis functions. To keep matters simple, the problem has been considered in the one-dimensional case, however the techniques can be employed for both the two- and three-dimensional cases. Several test problems are employed and results of numerical experiments are presented. The obtained results confirm the acceptable accuracy of the proposed method.

Optimality of Hyperbolic Partial Differential Equations With Dynamically Constrained Periodic Boundary Control—A Flow Control Application

2006 ◽  
Vol 128 (4) ◽  
pp. 946-959 ◽  
Author(s):  
Nhan Nguyen ◽  
Mark Ardema
Keyword(s):  
Boundary Condition ◽  
Optimal Control ◽  
Partial Differential Equations ◽  
Differential Equations ◽  
Control Problem ◽  
Boundary Control ◽  
Periodic Boundary Condition ◽  
Periodic Boundary ◽  
Hyperbolic Partial Differential Equations ◽  
Partial Differential

This paper is concerned with optimal control of a class of distributed-parameter systems governed by first-order, quasilinear hyperbolic partial differential equations that arise in optimal control problems of many physical systems such as fluids dynamics and elastodynamics. The distributed system is controlled via a forced nonlinear periodic boundary condition that describes a boundary control action. Further, the periodic boundary control is subject to a dynamic constraint imposed by a lumped-parameter system governed by ordinary differential equations that model actuator dynamics. The partial differential equations are thus coupled with the ordinary differential equations via the periodic boundary condition. Optimality of this coupled system is investigated using variational principles to seek an adjoint formulation of the optimal control problem. The results are then applied to solve a feedback control problem of the Mach number in a wind tunnel.

An Efficient Computational Procedure for the Optimization of a Class of Distributed Parameter Systems

1969 ◽  
Vol 91 (2) ◽  
pp. 190-194 ◽  
Author(s):  
D. A. Wismer
Keyword(s):  
Optimal Control ◽  
Differential Equations ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Broad Class ◽  
Distributed Parameter Systems ◽  
Parabolic Partial Differential Equation ◽  
Distributed Parameter ◽  
Total System ◽  
Partial Differential

The optimal control problem for a broad class of distributed parameter systems defined by vector parabolic partial differential equations is considered. The problem is solved by discretizing the spatial domain and then treating the (large) resultant set of ordinary differential equations as a set of independent subsystems. The subsystems are determined by decomposition of the total system into lower-dimensional problems and the necessary conditions for optimality of the overall system are then satisfied by an iterative procedure. With this treatment, the optimal control problem can be solved for larger systems (or finer spatial discretizations) than would otherwise be feasible. An example is given for a system described by a nonlinear parabolic partial differential equation in one space dimension.

scholarly journals Stability of Nonlinear Dirichlet BVPs Governed by Fractional Laplacian

2014 ◽  
Vol 2014 ◽  
pp. 1-10 ◽  
Author(s):  
Dorota Bors
Keyword(s):  
Optimal Control ◽  
Partial Differential Equations ◽  
Differential Equations ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Boundary Data ◽  
Fractional Laplacian ◽  
Dirichlet Boundary ◽  
Sufficient Condition ◽  
Variational Structure

We consider a class of partial differential equations with the fractional Laplacian and the homogeneous Dirichlet boundary data. Some sufficient condition under which the solutions of the equations considered depend continuously on parameters is stated. The application of the results to some optimal control problem is presented. The methods applied in the paper make use of the variational structure of the problem.

scholarly journals An Optimal Control Problem by a Hybrid System of Hyperbolic and Ordinary Differential Equations

Games ◽  
2021 ◽  
Vol 12 (1) ◽  
pp. 23
Author(s):  
Alexander Arguchintsev ◽  
Vasilisa Poplevko
Keyword(s):  
Optimal Control ◽  
Differential Equations ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Ordinary Differential Equations ◽  
Hyperbolic Equations ◽  
Control Methods ◽  
The Right ◽  
The Cost ◽  
Optimal Control Methods

This paper deals with an optimal control problem for a linear system of first-order hyperbolic equations with a function on the right-hand side determined from controlled bilinear ordinary differential equations. These ordinary differential equations are linear with respect to state functions with controlled coefficients. Such problems arise in the simulation of some processes of chemical technology and population dynamics. Normally, general optimal control methods are used for these problems because of bilinear ordinary differential equations. In this paper, the problem is reduced to an optimal control problem for a system of ordinary differential equations. The reduction is based on non-classic exact increment formulas for the cost-functional. This treatment allows to use a number of efficient optimal control methods for the problem. An example illustrates the approach.

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