Navid Moshtaghi Yazdani*

Ph.d in Electrical Engineering, Department of Electrical Engineering, Mashhad Branch, Islamic Azad University, Mashhad, Iran

*Corresponding Author: Navid Moshtaghi Yazdani, Ph.d in Electrical Engineering, Department of Electrical Engineering, Mashhad Branch, Islamic Azad University, Mashhad, Iran.

Received: January 22, 2023; Published: March 02, 2023

Abstract

Safety, stability and robustness are some fundamental issues in design and analysis of safety-critical systems. As a result, designing an efficient controller that simultaneously considers design goals such as safe performance in the presence of disturbances and considering system’s limitations, is an interesting field of research. While safe control design has been investigated in the literature, design of safe robust controllers with ability of disturbance reduction is newly proposed in this article. The mentioned safe controller is defined using a two stage policy iteration algorithm which is applied to solve the Hamilton-Jacobi-Isaacs equation. During the proposed algorithm possible conflicts between safety and robustness are minimized during each iteration. The simulation results indicates the effectiveness of proposed method.

Keywords: Optimal Control; Safety System; Critical Systems; Simulation; Efficient Controller

References

1. A Isidori and W Lin. “Global L2-gain design for a class of nonlinear systems”. Systems and Control Letters5 (1998): 245-252.
2. A Isidori. "H∞ control via measurement feedback for affine nonlinear systems”. International Journal of Robust and Nonlinear Control 4 (1994): 553-574.
3. G Zames. "Feedback and optimal sensitivity: model reference transformations, multiplicative semi norms, and approximate inverses”. IEEE Transactions on Automatic Control2 (1981): 301-320.
4. A Isidori and A Astolfi. “Disturbance attenuation and H∞-control via measurement feedback in nonlinear systems”. IEEE Transactions on Automatic Control9 (1992): 1283-1293.
5. A J van der Schaft. “L2-gain analysis of nonlinear systems and nonlinear state-feedback H∞ control”. IEEE Transactions on Automatic Control6 (1992): 770-784.
6. Q Zhang., et al. "Event-triggered H∞ control for continuous-time nonlinear system via concurrent learning”. IEEE Transactions on Systems, Man, and Cybernetics: Systems 7 (202).
7. H Zhang., et al. "Online adaptive policy learning algorithm for H∞ state feedback control of unknown affine nonlinear discrete-time systems”. IEEE Transactions on Cybernetics12 (2014): 2706-2718.
8. A Bemporad., et al. "The explicit solution of model predictive control via multiparametric quadratic programming”. in Proceedings of the 2000 American Control Conference. ACC (IEEE Cat. No.00CH36334) 2 (2000): 872-876.
9. M Abu-Khalaf and F L Lewis. “Nearly optimal state feedback control of constrained nonlinear systems using a neural networks hjb approach”. Annual Reviews in Control2 (2004): 239-251.
10. Aaron D Ames., et al. "Control Barrier Functions: Theory and Applications”. in Proceedings of the 2019 18^th European Control Conference. 25-28 June (2019).
11. Shishir Kolathaya., et al. "Input-to-State Safety With Control Barrier Functions”. IEEE Control Systems Letters1 (2019).
12. L Wang., et al. "Permissive barrier certificates for safe stabilization using sum-of-squares”. in 2018 Annual American Control Conference (ACC) (2018): 585-590.
13. Navid Moshtaghi Yazdani., et al. "A Safety-Certified Policy Iteration Algorithm for Control of Constrained Nonlinear Systems”. IEEE Control Systems Letters3 (2020).
14. R Beard and T McLain. “Successive Galerkin approximation algorithms for nonlinear optimal and robust control”. International Journal of Control5 (1998): 717-743.
15. M Abu-Khalaf., et al. "Policy iterations on the Hamilton-Jacobi-Isaacs equation for state feedback control with input saturation”. IEEE Transactions on Automatic Control12 (2006): 1989-1995.
16. A D Ames., et al. "Control barrier functions: Theory and applications”. In European Control Conference (ECC) (2019): 3420-3431.
17. Q Nguyen and K Sreenath. “Exponential control barrier functions for enforcing high relative-degree safety-critical constraints”. In American Control Conference (ACC) (2016): 322-328.
18. L Wang., et al. "Safety barrier certificates for collisions-free multirobot systems”. IEEE Transactions on Robotics 3 (2017): 661-674.
19. S Kolathaya and A D Ames. “Input-to-state safety with control barrier functions”. IEEE Control Systems Letters 1 (2018): 108-113.
20. AJ Taylor., et al. "A Control Barrier Perspective on Episodic Learning via Projection-to-State Safety”. in IEEE Control Systems Letters 5.3 (2021): 1019-1024.
21. Y Zhu., et al. "Policy Iteration for H∞ Optimal Control of Polynomial Nonlinear Systems via Sum of Squares Programming”. in IEEE Transactions on Cybernetics 48.2 (2018): 500-509.

Citation

Citation: Navid Moshtaghi Yazdani. “Robust Optimal Control of Safety-Critical Systems".Acta Scientific Computer Sciences 5.4 (2023): 02-10.

Copyright

Copyright: © 2023 Navid Moshtaghi Yazdani. This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.