College of Control Science and Engineering, Zhejiang University, Hangzhou, 310027, Zhejiang, China.
Department of Electrical and Electronics Engineering, Ajay Kumar Garg Engineering College, Ghaziabad, 201009, Uttar Pradesh, India.
ISA Trans. 2023 Jul;138:1-9. doi: 10.1016/j.isatra.2023.03.024. Epub 2023 Mar 22.
This article focuses on the design of tracking control for chaotic fractional order systems subjected to perturbations in a port-Hamiltonian framework. The fractional order systems of general form are modeled into port-controlled Hamiltonian form. Then, the extended results on the dissipativity, energy balance, and passivity of the fractional order systems are proved and presented in this paper. The port-controlled Hamiltonian form of the fractional order systems are proved to be asymptotically stable via energy balancing concept. Furthermore, a tracking controller is designed for the fractional order port-controlled Hamiltonian form by utilizing the matching conditions of the port-Hamiltonian systems. Stability of the system is established and analyzed explicitly for the closed-loop system with the help of direct Lyapunov method. Finally, an application example is solved with simulation results and discussions to prove the effectiveness of the propounded control design approach.
本文主要研究了在端口哈密顿框架下，受到摄动影响的混沌分数阶系统的跟踪控制设计。将一般形式的分数阶系统建模为端口控制哈密顿系统。然后，本文证明并提出了分数阶系统的耗散性、能量平衡和被动性的扩展结果。通过能量平衡的概念，证明了分数阶端口控制哈密顿系统的渐近稳定性。此外，通过端口哈密顿系统的匹配条件，为分数阶端口控制哈密顿系统设计了一个跟踪控制器。借助直接 Lyapunov 方法，对闭环系统的稳定性进行了明确的建立和分析。最后，通过仿真结果和讨论解决了一个应用实例，以证明所提出的控制设计方法的有效性。
