Doğrusal olmayan bazı sistem sınıflarının Euler-Lagrange geri integrasyon yöntemi ile optimal denetimi
Abstract
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.
Keywords
Doğrusal olmayan optimal denetim HJB denklemi doğrusal girişli doğrusal olmayan sistemler genişlik öncelikli arama Euler-Lagrange geri integrasyon yöntemi üçgenleme
References
- 1. Kirk D. E., Optimal control theory: an introduction, Courier Corporation, 2004.
- 2. Lewis F. L., Optimal control, John Wiley & Sons, 2012.
- 3. Dupree K., Patre P. M., Wilcox Z. D., Dixon W. E., Asymptotic optimal control of uncertain nonlinear Euler–Lagrange systems, Automatica, 47 (1), 99-107, 2011.
- 4. Murad A. K., Lewis F. L., Nearly optimal control laws for nonlinear systems with saturating actuators using a neural network HJB approach, Automatica, 41 (5), 779-791, 2005.
- 5. Vamvoudakis K. G., Frank L. L., Online actor–critic algorithm to solve the continuous-time infinite horizon optimal control problem, Automatica, 46 (5), 878-888, 2010.
- 6. Bhasin S., Kamalapurkar R., Johnson M., Vamvoudakis K. G., Lewis F. L., Dixon W. E., A novel actor–critic–identifier architecture for approximate optimal control of uncertain nonlinear systems, Automatica, 49 (1), 82-92, 2013.
- 7. Kiumarsi B., Vamvoudakis K. G., Modares H., Lewis F. L., Optimal and autonomous control using reinforcement learning: A survey, IEEE transactions on neural networks and learning systems, 29(6), 2042-2062, 2017.
- 8. Liu D., Wei Q., Wang D., Yang X., Li H., Adaptive dynamic programming with applications in optimal control, Springer International Publishing, 2017.
- 9. Holzhüter T., Optimal regulator for the inverted pendulum via Euler–Lagrange backward integration., Automatica, 40 (9), 1613-1620, 2004.
- 10. Holzhüter T., Klinker T., Method to solve the nonlinear infinite horizon optimal control problem with application to the track control of a mobile robot, International Journal of Bifurcation and Chaos, 17 (10), 3607-3611, 2007.
- 11. Nekoo S. R. and Rahaghi M. I., Recursive approximate solution to time-varying matrix differential Riccati equation: linear and nonlinear systems, International Journal of Systems Science, 49 (13), 2797-2807, 2018.
- 12. Aksoy O., Doğrusal olmayan ve belirsiz Euler-Lagrange sistemlerinin optimal çıkış geri beslemeli denetimi üzerine, Doktora Tezi, Gebze Teknik Üniversitesi, Fen Bilimleri Enstitüsü, Kocaeli, 2016.
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.
Keywords
Nonlinear optimal control HJB equation breadth first search Euler-Lagrange back integration method tessellation
References
- 1. Kirk D. E., Optimal control theory: an introduction, Courier Corporation, 2004.
- 2. Lewis F. L., Optimal control, John Wiley & Sons, 2012.
- 3. Dupree K., Patre P. M., Wilcox Z. D., Dixon W. E., Asymptotic optimal control of uncertain nonlinear Euler–Lagrange systems, Automatica, 47 (1), 99-107, 2011.
- 4. Murad A. K., Lewis F. L., Nearly optimal control laws for nonlinear systems with saturating actuators using a neural network HJB approach, Automatica, 41 (5), 779-791, 2005.
- 5. Vamvoudakis K. G., Frank L. L., Online actor–critic algorithm to solve the continuous-time infinite horizon optimal control problem, Automatica, 46 (5), 878-888, 2010.
- 6. Bhasin S., Kamalapurkar R., Johnson M., Vamvoudakis K. G., Lewis F. L., Dixon W. E., A novel actor–critic–identifier architecture for approximate optimal control of uncertain nonlinear systems, Automatica, 49 (1), 82-92, 2013.
- 7. Kiumarsi B., Vamvoudakis K. G., Modares H., Lewis F. L., Optimal and autonomous control using reinforcement learning: A survey, IEEE transactions on neural networks and learning systems, 29(6), 2042-2062, 2017.
- 8. Liu D., Wei Q., Wang D., Yang X., Li H., Adaptive dynamic programming with applications in optimal control, Springer International Publishing, 2017.
- 9. Holzhüter T., Optimal regulator for the inverted pendulum via Euler–Lagrange backward integration., Automatica, 40 (9), 1613-1620, 2004.
- 10. Holzhüter T., Klinker T., Method to solve the nonlinear infinite horizon optimal control problem with application to the track control of a mobile robot, International Journal of Bifurcation and Chaos, 17 (10), 3607-3611, 2007.
- 11. Nekoo S. R. and Rahaghi M. I., Recursive approximate solution to time-varying matrix differential Riccati equation: linear and nonlinear systems, International Journal of Systems Science, 49 (13), 2797-2807, 2018.
- 12. Aksoy O., Doğrusal olmayan ve belirsiz Euler-Lagrange sistemlerinin optimal çıkış geri beslemeli denetimi üzerine, Doktora Tezi, Gebze Teknik Üniversitesi, Fen Bilimleri Enstitüsü, Kocaeli, 2016.
Details
| Primary Language | Turkish |
|---|---|
| Subjects | Engineering |
| Journal Section | Makaleler |
| Authors | |
| Publication Date | April 12, 2023 |
| Submission Date | February 6, 2021 |
| Acceptance Date | December 24, 2022 |
| Published in Issue | Year 2023 Volume: 38 Issue: 4 |