Optimal control of a class of nonlinear systems using Euler-Lagrange back integration method

Orhan Aksoy; Erkan Zergeroğlu

Article Details

Optimal control of a class of nonlinear systems using Euler-Lagrange back integration method

Authors:

Orhan Aksoy | Erkan Zergeroğlu

Publisher:

Gazi University

Main Topics:

Mühendislik

Journal:

Gazi Üniversitesi Mühendislik Mimarlık Fakültesi Dergisi Vol.38 Issue 4, pp.2555-2564

Document Type:

Article

Publication Date:

12/2023

Document Language:

Turkish

Document ID (Org No.):

2001287713

pISSN:

1300-1884

Keywords:

Abstract:

 In this study, an algorithm is presented that aims to extend the use of Euler-Lagrange back integration method to optimal control of linearizable, affine-in-the-input nonlinear systems having more than two states. The algorithm generates optimal paths by selecting a starting point iteratively on the ellipsoid close to the equilibrium point, representing the optimal borderline of the linearized system, and backward integrating the optimal nonlinear dynamics. The generated paths are then utilized in the optimal control loop.

 In this study, an algorithm is presented that aims to extend the use of Euler-Lagrange back integration method to optimal control of linearizable, affine-in-the-input nonlinear systems having more than two states. The algorithm generates optimal paths by selecting a starting point iteratively on the ellipsoid close to the equilibrium point, representing the optimal borderline of the linearized system, and backward integrating the optimal nonlinear dynamics. The generated paths are then utilized in the optimal control loop.

 In this study, an algorithm is presented that aims to extend the use of Euler-Lagrange back integration method to optimal control of linearizable, affine-in-the-input nonlinear systems having more than two states. The algorithm generates optimal paths by selecting a starting point iteratively on the ellipsoid close to the equilibrium point, representing the optimal borderline of the linearized system, and backward integrating the optimal nonlinear dynamics. The generated paths are then utilized in the optimal control loop.

 Bu çalışmada, üç veya daha fazla boyutlu, doğrusallaştırılabilen, doğrusal girişli doğrusal olmayan sistemlerin optimal denetimi için Euler-Lagrange geri integrasyon yönteminin kullanımını geliştiren bir algoritma sunulmuştur. Algoritma, doğrusallaştırılmış sistemin sınırını temsil eden, denge noktasının yakınındaki bir hiper elipsoit üzerinde tekrarlı şekilde başlangıç koşulu seçerek doğrusal olmayan optimal dinamik üzerinde geri integrasyon yöntemini uygulamakta ve optimal yolları oluşturmaktadır. Daha sonra, bu optimal yollar optimal geri beslemede kullanılmaktadır.

Article Details

Optimal control of a class of nonlinear systems using Euler-Lagrange back integration method

Authors:

Orhan Aksoy | Erkan Zergeroğlu

Publisher:

Gazi University

Main Topics:

Mühendislik

Journal:

Gazi Üniversitesi Mühendislik Mimarlık Fakültesi Dergisi Vol.38 Issue 4, pp.2555-2564

Document Type:

Article

Publication Date:

12/2023

Document Language:

Turkish

Document ID (Org No.):

2001287713

pISSN:

1300-1884

Nonlinear optimal control

HJB equation

breadth first search

Euler-Lagrange back integration method

tessellationDoğrusal olmayan optimal denetim

HJB denklemi

doğrusal girişli doğrusal olmayan sistemler

genişlik öncelikli arama

Euler-Lagrange geri integrasyon yöntemi

üçgenleme

Issues

Article Details

Authors: Orhan Aksoy | Erkan Zergeroğlu

Publisher: Gazi University

Main Topics: Mühendislik

Journal: Gazi Üniversitesi Mühendislik Mimarlık Fakültesi Dergisi Vol.38 Issue 4, pp.2555-2564

Document Type: Article

Publication Date: 12/2023

Document Language: Turkish

Document ID (Org No.): 2001287713

pISSN: 1300-1884

Issues

Authors:

Orhan Aksoy | Erkan Zergeroğlu

Publisher:

Gazi University

Main Topics:

Mühendislik

Journal:

Gazi Üniversitesi Mühendislik Mimarlık Fakültesi Dergisi Vol.38 Issue 4, pp.2555-2564

Document Type:

Article

Publication Date:

12/2023

Document Language:

Turkish

Document ID (Org No.):

2001287713

pISSN:

1300-1884