Abstract
In this paper, we consider the problem of Mittag-Leffler stabilization of fractional-order nonlinear systems with unknown control coefficients. With the help of backstepping design method, the stabilizing functions and tuning functions are constructed. The controller is designed to ensure that the pseudo-state of the fractional-order nonlinear system converges to the equilibrium. The effectiveness of the proposed method has been verified by some simulation examples.
Highlights
The concept of fractional differentiation appeared for the first time in a famous correspondence between L’Hospital and Leibniz, in 1695
The fractional calculus remained for centuries a purely theoretical topic, with little if any connections to practical problems of physics and engineering
Fractional calculus is a generalization of classical calculus to non-integer order
Summary
The concept of fractional differentiation appeared for the first time in a famous correspondence between L’Hospital and Leibniz, in 1695. An interesting question arises: when the states of system are not Leibniz rule, how to deal with the stabilization problem through design of tuning functions and adaptive feedback control law? We investigate the Mittag-Leffler stabilization problem of a class of fractional-order nonlinear systems. Compared with the existing results, the main contributions of this paper are as follows: (1) The backstepping design is extended to fractionalorder nonlinear systems with unknown control coefficients, and an adaptive control scheme with tuning functions is proposed. It is proved that the stabilization problem of fractional-order nonlinear systems can be solved by the designed control scheme.
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