A new approach to fast global finite-time stabilization of high-order nonlinear system
TL;DR: The novel control strategy unifies the construction of Lyapunov functions, which are used to deal with high-order and low-order nonlinear growth rates separately in the existing results.
About: This article is published in Automatica.The article was published on 2017-07-01. It has received 202 citations till now. The article focuses on the topics: Lyapunov function & Nonlinear system.
Citations
More filters
TL;DR: A high-order tan-type barrier Lyapunov function (BLF) is constructed to handle the full-state constraints of the control systems and by the BLF and combining a backstepping design technique, an adding a power integrator, and a fuzzy control, the proposed approach can control high- order uncertain nonlinear system with full- state constraints.
Abstract: This paper focuses on the practical output tracking control for a category of high-order uncertain nonlinear systems with full-state constraints. A high-order tan-type barrier Lyapunov function (BLF) is constructed to handle the full-state constraints of the control systems. By the BLF and combining a backstepping design technique, an adding a power integrator, and a fuzzy control, the proposed approach can control high-order uncertain nonlinear system with full-state constraints. A novel controller is designed to ensure that the tracking errors approach to an arbitrarily small neighborhood of zero, and the constraints on system states are not violated. The numerical example demonstrates effectiveness of the proposed control method.
200 citations
TL;DR: A novel second-order sliding mode control algorithm, which can be used to deal with the output constraint problem, has been developed and enables the output variable not to violate the boundary of the constraint region.
180 citations
TL;DR: A new finite-time stability result is established to provide a less conservative estimation of convergent time in uncertain situation, and a state feedback stabilizer with an adaptive mechanism is constructed by applying continuous domination to adaptive fashion of the systems to be considered.
153 citations
TL;DR: Finite-time adaptive fuzzy output-feedback control for a class of nontriangular nonlinear systems with full-state constraints and unmeasurable states with finite-time stability theory is focused on.
Abstract: This article focuses on finite-time adaptive fuzzy output-feedback control for a class of nontriangular nonlinear systems with full-state constraints and unmeasurable states. Fuzzy-logic systems and the fuzzy state observer are employed to approximate uncertain nonlinear functions and estimate the unmeasured states, respectively. In order to solve the algebraic loop problem generated by the nontriangular structure, a variable separation approach based on the property of the fuzzy basis function is utilized. The barrier Lyapunov function is incorporated into each step of backstepping, and the condition of the state constraint is satisfied. The dynamic surface technique with an auxiliary first-order linear filter is applied to avoid the problem of an “explosion of complexity.” Based on the finite-time stability theory, an adaptive fuzzy controller is constructed to guarantee that all signals in the closed-loop system are bounded, the tracking error converges to a small neighborhood of the origin in a finite time, and all states are ensured to remain in the predefined sets. Finally, the simulation results reveal the effectiveness of the proposed control design.
130 citations
TL;DR: This article reports the study on the issue of finite-time adaptive fuzzy tracking control for a class of uncertain nonlinear systems with the prescribed performance by incorporating the technique of prescribed performance control with the method of command filtered design.
Abstract: This article reports our study on the issue of finite-time adaptive fuzzy tracking control for a class of uncertain nonlinear systems with the prescribed performance. A novel finite-time prescribed performance control approach, in which fuzzy systems are employed to approximate completely unknown nonlinear functions, is proposed by incorporating the technique of prescribed performance control with the method of command filtered design. Based on the finite-time stability theory, all the signals of the closed-loop system can be bounded and the output tracking error can converge to a prescribed small region within a finite-time by the proposed scheme; meanwhile, the problem of complexity explosion can be avoided. The effectiveness of the presented method is verified by two examples.
120 citations
Cites background from "A new approach to fast global finit..."
...The problem of adaptive stabilization with fast finite-time convergence is discussed in [32] for high-order uncertain nonlinear systems....
[...]
References
More filters
TL;DR: It is shown that the regularity properties of the Lyapunov function and those of the settling-time function are related and converse Lyap Unov results can only assure the existence of continuous Lyap unov functions.
Abstract: Finite-time stability is defined for equilibria of continuous but non-Lipschitzian autonomous systems. Continuity, Lipschitz continuity, and Holder continuity of the settling-time function are studied and illustrated with several examples. Lyapunov and converse Lyapunov results involving scalar differential inequalities are given for finite-time stability. It is shown that the regularity properties of the Lyapunov function and those of the settling-time function are related. Consequently, converse Lyapunov results can only assure the existence of continuous Lyapunov functions. Finally, the sensitivity of finite-time-stable systems to perturbations is investigated.
3,894 citations
2,725 citations
TL;DR: Two types of nonlinear control algorithms are presented for uncertain linear plants, stabilizing polynomial feedbacks that allow to adjust a guaranteed convergence time of system trajectories into a prespecified neighborhood of the origin independently on initial conditions.
Abstract: Two types of nonlinear control algorithms are presented for uncertain linear plants. Controllers of the first type are stabilizing polynomial feedbacks that allow to adjust a guaranteed convergence time of system trajectories into a prespecified neighborhood of the origin independently on initial conditions. The control design procedure uses block control principles and finite-time attractivity properties of polynomial feedbacks. Controllers of the second type are modifications of the second order sliding mode control algorithms. They provide global finite-time stability of the closed-loop system and allow to adjust a guaranteed settling time independently on initial conditions. Control algorithms are presented for both single-input and multi-input systems. Theoretical results are supported by numerical simulations.
2,380 citations
TL;DR: Conditions under which it is possible to prove the existence of continuous state feedback control laws that achieve global strong stability (GSS) in the sense of Kurzweil (1956) are described.
Abstract: We present a continuous feedback approach to the problem of global strong stabilization, for genuinely nonlinear systems that may not be stabilized, even locally, by any smooth feedback. We describe conditions under which it is possible to prove, while no smooth controllers exist, the existence of continuous state feedback control laws that achieve global strong stability (GSS) in the sense of Kurzweil (1956). The proof is constructive and carried out by developing a machinery, which combines the theory of homogeneous systems with the idea of adding a power integrator, for the explicit construction of globally stabilizing continuous controllers. We then illustrate, by means of examples, how this machinery can be used to overcome the topological obstruction caused by smooth feedback, and hence resulting in new solutions to a variety of open control problems, including global stabilization of an underactuated unstable two degree of freedom mechanical system.
1,041 citations
TL;DR: It is proved that global finite-time stabilizability of uncertain nonlinear systems that are dominated by a lower-triangular system can be achieved by Holder continuous state feedback.
982 citations