Classical and relaxed optimization methods for optimal control problems

Chryssoverghi, I.; Coletsos, J.; Kokkinis, B.

doi:10.12988/imf.2007.07135

Cited by 4 publications

(4 citation statements)

References 13 publications

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“…(1) The vertical separation given by . This constraint results in energy consumption of the aircraft [8,24]. On the whole, the constraints come together under the relationship…”

Section: Constraintsmentioning

confidence: 99%

“…The model considered here is non-convex and non-linear optimal control problem leading to a system of non-linear ordinary differential equations (I. Chryssoverghi& J. Colestos and B. Kokkinis, 2007). The aircraft dynamic is described by a three dimensional set of non-linear ordinary differential equations subjected to state and control constraints.…”

Section: Introductionmentioning

confidence: 99%

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The Applied Mathematical Simulation Modeling Algorithm for a Multi Aircraft Landing Dynamic System at Bujumbura International Airport Mathematics and Innovative Technologies in Africa

Nahayo

Ndimubandi

Manirabona

et al. 2019

ESJ

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The aim of this paper is to set up an efficient nonlinear application algorithm simulation model for a multi aircraft landing dynamic system in one Runway when considering Bujumbura International Airport. The mathematical modelization of the solved problem is a non-convex optimal control governed by ordinary non-linear differential equations.The dynamic programming technic is applied because it is a sufficiently high order and it does-not require computation of the partial derivatives of the aircraft dynamic. This application is be coded with Linux operating system, but it can also be run on the windows system. High runing performance are obtained with results giving feasible trajectories with a robust optimizing of the objective function. The user interfaces designed in Glade are saved as XML, and by using the GtkBuilder GTK+ object these can be loaded by applications dynamically as needed. By using GtkBuilder, Glade XML files can be used in numerous programming languages including C, C++, C#, Java, Perl, Python,AMPL,etc..

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“…(1) The vertical separation given by . This constraint results in energy consumption of the aircraft [8,24]. On the whole, the constraints come together under the relationship…”

Section: Constraintsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

The Applied Mathematical Simulation Modeling Algorithm for a Multi Aircraft Landing Dynamic System at Bujumbura International Airport Mathematics and Innovative Technologies in Africa

Nahayo

Ndimubandi

Manirabona

et al. 2019

ESJ

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“…The numerical solution of the DCOCP is studied by many researches. The GPARM or GPOSM are used to find the numerical solution of the DCOCP governing either by systems of nonlinear elliptic PDEs as in [1,2], or by systems of semi linear parabolic PDEs as in [3,4], or by systems of nonlinear ordinary differential equations (ODEs) as in [5,6], or by systems of LHBVP so as our previous work [7]. Since the GFEM is one of the most an efficient and fast methods for…”

Section: Introductionmentioning

confidence: 99%

Numerical Solution for Classical Optimal Control Problem Governing by Hyperbolic Partial Differential Equation via Galerkin Finite Element-Implicit method with Gradient Projection Method

Al-Hawasy¹,

Al-Rawdanee²

2019

IHJPAS

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This paper deals with the numerical solution of the discrete classical optimal control problem (DCOCP) governing by linear hyperbolic boundary value problem (LHBVP). The method which is used here consists of: the GFEIM " the Galerkin finite element method in space variable with the implicit finite difference method in time variable" to find the solution of the discrete state equation (DSE) and the solution of its corresponding discrete adjoint equation, where a discrete classical control (DCC) is given. The gradient projection method with either the Armijo method (GPARM) or with the optimal method (GPOSM) is used to solve the minimization problem which is obtained from the necessary condition for optimality of the DCOCP to find the DCC.An algorithm is given and a computer program is coded using the above methods to find the numerical solution of the DCOCP with step length of space variable , and step length of time variable . Illustration examples are given to explain the efficiency of these methods. The results show the methods which are used here are better than those obtained when we used the Gradient method (GM) or Frank Wolfe method (FWM) with Armijo step search method to solve the minimization problem.

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“…The model considered here is non-convex and non-linear optimal control problem leading to a system of nonlinear ordinary differential equations [6]. The aircraft dynamic is described by a three dimensional set of nonlinear ordinary differential equations subjected to state and control constraints.…”

Section: Introductionmentioning

confidence: 99%

Two-Aircraft optimal control problem. The in-flight noise reduction,

Nahayo

Haddou

Khardi³

et al. 2012

ESAIM: Proc.

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The aim of this paper is to present and solve a mathematical model of a two-aircraft optimal control problem reducing the noise on the ground during the approach. The mathematical modelization of this problem is a non-convex optimal control governed by ordinary non-linear differential equations. To solve this problem, A direct method and a Runge-Kutta RK4 discretization schema are used. This discretization schema is chosed because it is a sufficiently high order and it does-not require computation of the partial derivatives of the aircraft dynamic. The Nonlinear Interior point Trust Region Optimization solver KNITRO is applied. A large set of numerical experiments is presented. The obtained results give feasible trajectories with a significant noise reduction.

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Classical and relaxed optimization methods for optimal control problems

Cited by 4 publications

References 13 publications

The Applied Mathematical Simulation Modeling Algorithm for a Multi Aircraft Landing Dynamic System at Bujumbura International Airport Mathematics and Innovative Technologies in Africa

The Applied Mathematical Simulation Modeling Algorithm for a Multi Aircraft Landing Dynamic System at Bujumbura International Airport Mathematics and Innovative Technologies in Africa

Numerical Solution for Classical Optimal Control Problem Governing by Hyperbolic Partial Differential Equation via Galerkin Finite Element-Implicit method with Gradient Projection Method

Two-Aircraft optimal control problem. The in-flight noise reduction,

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