Dynamic Fractional-Order Sliding Mode Strategy to Control and Stabilize Fractional-Order Nonlinear Biological Systems

Abstract

In this paper, we deal with the problem of stabilizing fractional-order nonlinear systems in the presence of uncertainties and disturbances. To this end, fractional-order sliding mode control is selected owing to the advantages of fractional calculus and sliding mode control, as discussed in detail in many research studies. So, two novel fractional sliding manifolds are proposed and stabilization is achieved by the designed fractional sliding mode controls with/without uncertainties and external disturbances. The two novel methodologies are fast converging robust controllers. These methods are applied to the class of fractional nonlinear biological systems and compared together. The first method is fractional sliding mode control and the second one is dynamic fractional sliding mode controller. Sufficient conditions to achieve stabilization are derived by the use of Lyapunov theory. The effectiveness and robustness of the proposed manifolds are demonstrated by different examples to verify their efficacy. It can be seen from the simulation results that fractional dynamic sliding mode control worked better than the fractional sliding mode controller.

KEYWORDS:

• Fractional nonlinear HIV model
• Fractional nonlinear tumor model
• Fractional-order sliding surface
• Stabilization

Additional information

Notes on contributors

Arash Pourhashemi

Arash Pourhashemi received the BSc degree in electrical engineering from Islamic Azad University, Gonabad Iran 2007, the MSc degree in biomedical engineering from Islamic Azad University, Mashhad, Iran, in 2013. He is now a PhD student in Islamic Azad University of Central Tehran branch. His research interests concern the optimization, development of control strategies, variable structure controls, control of complex systems, and fractional calculus. Email: [email protected]

Amin Ramezani

Amin Ramezani (IEEE Member 2005) was born in Khuzestan, Iran, in 1979. He received the BE degree in electrical engineering from the Shahid Beheshti University of Tehran, Tehran, Iran, in 2001, and the MSc in control systems for Sharif University of Technology, Tehran, Iran, in 2004 and PhD degree in electrical engineering from the University of Tehran, Tehran, Iran, in 2011.

In 2012, he joined the Department of Electrical Engineering, Tarbiat Modares University, Tehran, Iran, as a lecturer. He is the chair of Advanced Control Lab and cooperates as the PC members of some conferences and special editor and reviewer of international journals in the field of control systems. His current research interests include fault-tolerant control systems, model-based predictive control systems, stochastic control systems, hybrid systems. Dr Ramezani has been a member of IEEE since 2005 and a member of Iranian Community Instrument and Control Engineers since 2012. He has contributed in more than 30 journal papers and 70 conference papers.

Mehdi Siahi

Mehdi Siahi received the BSc degree in electrical engineering from Yazd University, Yazd Iran in 2001 and MSc degree in control engineering from the Shahrood University of Technology, Shahrood, Iran, in 2003. He obtained the PhD degree in control engineering from Shahrood University of Technology, Shahrood Iran, in 2008. He is now an associate professor and has been with Faculty of Electrical Engineering, Islamic Azad University, Iran since 2004. His current research is on fault-tolerant control systems, robust control, and nonlinear systems. Email: [email protected]