Fractional order uncertainty estimator based hierarchical sliding mode design for a class of fractional order non-holonomic chained system. (June 2018)

• Record Type: Journal Article
• Authors: Deepika, ; Kaur, Sandeep; Narayan, Shiv
• Is Part Of: ISA transactions. Volume 77(2018)
• Page Start: 58
• Page End: 70
• Publication Date: 2018-06
• Subjects: Fractional calculus -- Fractional order lyapunov stability -- Fractional order systems -- Fractional order uncertainty estimator -- Non-holonomic systems -- Sliding mode control; Engineering instruments -- Periodicals; Engineering instruments; Periodicals; Electronic journals; 629.805
• DOI: 10.1016/j.isatra.2018.04.004
• Languages: English
• ISSNs: 0019-0578

Abstract

Abstract: This paper proposes a novel fractional order sliding mode control approach to address the issues of stabilization as well as tracking of an N-dimensional extended chained form of fractional order non-holonomic system. Firstly, the hierarchical fractional order terminal sliding manifolds are selected to procure the desired objectives in finite time. Then, a sliding mode control law is formulated which provides robustness against various system uncertainties or external disturbances. In addition, a novel fractional order uncertainty estimator is deduced mathematically to estimate and mitigate the effects of uncertainties, which also excludes the requirement of their upper bounds. Due to the omission of discontinuous control action, the proposed algorithm ensures a chatter-free control input. Moreover, the finite time stability of the closed loop system has been proved analytically through well known Mittag-Leffler and Fractional Lyapunov theorems. Finally, the proposed methodology is validated with MATLAB simulations on two examples including an application of fractional order non-holonomic wheeled mobile robot and its performances are also compared with the existing control approach. Highlights: A novel control design is proposed using fractional order hierarchical SMC for the fractional order non-holonomic systems. Tracking and stabilization objectives are achieved. No requirement of upper bounds on various system uncertainties due to novel fractional order uncertainty estimator. Chatter free control is ensured with Mittag Leffler's stability method. Two examples have also been illustrated to validate our result.