Abstract
Since existing results about fixed-time stabilization are only applied to strict feedback systems, this paper investigates the nonsingular fixed-time stabilization of more general high-order nonlinear systems. Based on a novel concept named coordinate mapping of time domain, a control method is first proposed to transform the nonsingular fixed-time convergence problem into the finite-time convergence problem of a transformed time-varying system. By extending the existing, adding a power integrator technique into the considered time-varying system, a periodic controller is constructed to stabilize the original system in fixed time. The results of simulations verify the effectiveness of the proposed method.
Highlights
In recent years, more and more attention has been paid to the controller design of high-order nonlinear systems due to its wide application in modeling aerospace craft, rigid robotic systems, and machine systems with underactuation, weak coupling, and instability [1,2,3,4]
The convergence time is decided by the initial state of the system in recent achievements. at is to say, the convergence time cannot be prespecified, since the state can be initialed at any point
When the initial state of the system tends to infinity, the time tends to infinity as well
Summary
More and more attention has been paid to the controller design of high-order nonlinear systems due to its wide application in modeling aerospace craft, rigid robotic systems, and machine systems with underactuation, weak coupling, and instability [1,2,3,4]. A nonsmoothed controller is constructed by using the recursive design method to solve the fixed-time stabilization problem of high-order nonlinear interconnected systems [14]. E fixed-time stabilization of strict feedback nonlinear systems with only matching uncertainties is achieved by ingenious state transformation [15]. The nonsingular global fixed-time stabilization of high-order nonlinear systems is proposed. (1) A control method based on time-domain mapping is proposed, which transforms the nonsingular fixedtime stabilization problem of the original system into the finite-time stabilization problem of the corresponding time-varying system and provides a new idea for the design of the fixed-time convergence control law. (3) e existing method can only solve the problem of fixed-time stabilization for strict feedback systems with only matching uncertainties, while the proposed method can solve the fixed-time stabilization problem of high-order nonlinear systems with unmatched uncertainties. It is noted that the strict feedback systems are special cases of high-order nonlinear systems; the results of this paper greatly extend the research scope of fixed-time stabilization
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