Adaptive finite-time tracking control of switched nonlinear systems

Wang, Fang; Zhang, Xueyi; Chen, Bing; Lin, Chong; Li, Xuehua; Zhang, Jing

doi:10.1016/j.ins.2017.08.095

Cited by 76 publications

(43 citation statements)

References 37 publications

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“…Accordingly, inequality is restated as

{\dot{V}}_{i}^{a} ((), t) \leq - λ \sqrt{2} \sqrt{V_{i}^{b} ((), t)} \leq - η λ \sqrt{2} \sqrt{V_{i}^{a} ((), t)} + normalε = - λ η ξ \sqrt{2} \sqrt{V_{i}^{a} ((), t)} - ((), 1 - ξ) λ η \sqrt{2} \sqrt{V_{i}^{a} ((), t)} + normalε

, where 0 < ξ < 1 is a constant. Defining

Ω_{X} = ({}|, X, \sqrt{V_{i}^{a} ((), t)} \leq normalε false/ ((), ((), 1 - ξ) λ η \sqrt{2}))

and referring to the work of Wang et al, it can be proved that the states X ( t ) of each subsystem will converge to the set Ω X in the finite time

T_{i} \leq \frac{\sqrt{2}}{λ η ξ} ((), \sqrt{V_{i}^{a} ((), t_{r})} - \frac{ϵ \sqrt{0.5}}{((), 1 - ξ) λ η}) + t_{r}

and they will not go over this set. This implies that the state trajectories X ( t ) of each subsystem will be finite‐time stable in the sense of Definition and based on , they will converge to zero after they reach the set Ω X .…”

Section: Design Of the Proposed Control Schemementioning

confidence: 99%

“…Thus, we will have

- K \sqrt{2} \sqrt{V^{d} ((), t)} \leq - ν K \sqrt{2} \sqrt{V^{c} ((), t)} + normalϵ .

Accordingly, inequality is restated as

{\dot{V}}_{i}^{a} ((), t) \leq - K \sqrt{2} \sqrt{V^{c} ((), t)} \leq - ν K \sqrt{2} \sqrt{V^{c} ((), t)} + normalϵ = - K ν ξ \sqrt{2} \sqrt{V^{c} ((), t)} - ((), 1 - ξ) λ ν \sqrt{2} \sqrt{V^{c} ((), t)} + normalϵ,

where 0 < ξ < 1 is a constant. Defining

ζ = ({} S, \overset{ω}{true} - ω)

and

Ω_{ζ} = ({}|, ζ, \sqrt{V_{i}^{a} ((), t)} \leq normalϵ false/ ((), ((), 1 - ξ) K ν \sqrt{2}))

, on the basis of the work of Wang et al, it can be proved that the variables ζ ( t ) will approach to the set Ω ζ in the finite time

T_{r} \leq \frac{\sqrt{2}}{italicK ν ξ} ((), \sqrt{V^{c} ((), t_{0})} - \frac{normalϵ \sqrt{0.5}}{((), 1 - ξ) K ν}) + t_{0}

and they will not exceed this set. This implies that the state trajectories X ( t ) of the system will reach the sliding manifold in practical finite‐time sense of Definition , and based on , they will converge to S ( t ) = 0 once they...…”

Section: Design Of the Proposed Control Schemementioning

confidence: 99%

“…)} and referring to the work of Wang et al, 21 it can be proved that the states X(t) of each subsystem will converge to the set Ω X in the finite time…”

Section: Smooth Sliding Manifoldmentioning

confidence: 99%

“…In the work of Thanh et al, a geometric‐based state‐dependent switching law has been provided for finite‐time stabilization of a class of disturbed nonlinear switched systems with time delay. The work of Wang et al has introduced an adaptive neural network controller for tracking control of switched systems with practical finite‐time stability. Although the work of the aforementioned authors have developed a control scheme with arbitrary switching rules, they have not considered the effects of unknown parameters and uncertainties.…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Stabilization of a class of cascade nonlinear switched systems with application to chaotic systems

Aghababa

2018

Intl J Robust & Nonlinear

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Summary In this study, the problem of finite‐time practical control of a class of nonlinear switched systems in the presence of input nonlinearities is investigated. The subsystems of the switched system are considered as complex nonlinear systems with a cascade structure. Each subsystem is fluctuated by lumped uncertainties. Moreover, some parts of the system's dynamics are considered to be unknown in advance. This paper sets no restrictive assumption on the switching logic of the system. Therefore, the aim is to propose a controller to work under any arbitrary switching signals. After providing a smooth sliding manifold, a simple adaptive control input is developed such that the system trajectories approach the prescribed sliding mode dynamics in finite‐time sense. The adopted control signal does not use the upper bounds of the lumped uncertainties, and it is robust against unknown nonlinear parts of the subsystems. It is proved that the origin is the (practical) finite‐time stable equilibrium point of the overall closed‐loop system. Subsequently, the proposed control rule is modified to handle the same switched system with no input nonlinearities. Computer simulations via 2 chaotic electric direct current machines demonstrate the robust performance of the derived variable structure control algorithm against system fluctuations and nonlinear inputs.

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“…Accordingly, inequality is restated as

{\dot{V}}_{i}^{a} ((), t) \leq - λ \sqrt{2} \sqrt{V_{i}^{b} ((), t)} \leq - η λ \sqrt{2} \sqrt{V_{i}^{a} ((), t)} + normalε = - λ η ξ \sqrt{2} \sqrt{V_{i}^{a} ((), t)} - ((), 1 - ξ) λ η \sqrt{2} \sqrt{V_{i}^{a} ((), t)} + normalε

, where 0 < ξ < 1 is a constant. Defining

Ω_{X} = ({}|, X, \sqrt{V_{i}^{a} ((), t)} \leq normalε false/ ((), ((), 1 - ξ) λ η \sqrt{2}))

and referring to the work of Wang et al, it can be proved that the states X ( t ) of each subsystem will converge to the set Ω X in the finite time

T_{i} \leq \frac{\sqrt{2}}{λ η ξ} ((), \sqrt{V_{i}^{a} ((), t_{r})} - \frac{ϵ \sqrt{0.5}}{((), 1 - ξ) λ η}) + t_{r}

Section: Design Of the Proposed Control Schemementioning

confidence: 99%

“…Thus, we will have

- K \sqrt{2} \sqrt{V^{d} ((), t)} \leq - ν K \sqrt{2} \sqrt{V^{c} ((), t)} + normalϵ .

Accordingly, inequality is restated as

{\dot{V}}_{i}^{a} ((), t) \leq - K \sqrt{2} \sqrt{V^{c} ((), t)} \leq - ν K \sqrt{2} \sqrt{V^{c} ((), t)} + normalϵ = - K ν ξ \sqrt{2} \sqrt{V^{c} ((), t)} - ((), 1 - ξ) λ ν \sqrt{2} \sqrt{V^{c} ((), t)} + normalϵ,

where 0 < ξ < 1 is a constant. Defining

ζ = ({} S, \overset{ω}{true} - ω)

and

Ω_{ζ} = ({}|, ζ, \sqrt{V_{i}^{a} ((), t)} \leq normalϵ false/ ((), ((), 1 - ξ) K ν \sqrt{2}))

, on the basis of the work of Wang et al, it can be proved that the variables ζ ( t ) will approach to the set Ω ζ in the finite time

T_{r} \leq \frac{\sqrt{2}}{italicK ν ξ} ((), \sqrt{V^{c} ((), t_{0})} - \frac{normalϵ \sqrt{0.5}}{((), 1 - ξ) K ν}) + t_{0}

Section: Design Of the Proposed Control Schemementioning

confidence: 99%

“…)} and referring to the work of Wang et al, 21 it can be proved that the states X(t) of each subsystem will converge to the set Ω X in the finite time…”

Section: Smooth Sliding Manifoldmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Stabilization of a class of cascade nonlinear switched systems with application to chaotic systems

Aghababa

2018

Intl J Robust & Nonlinear

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show abstract

“…Finite-time control has received much attention because it can provide many benefits such as strong robustness and better disturbance resistance capability [3,4,61]. The Lyapunov theory of finite-time stability for nonlinear systems has been clearly established by several authors [62,63].…”

Section: Introductionmentioning

confidence: 99%

Adaptive finite-time tracking control for nonlinear systems with unmodeled dynamics using neural networks

Wang

2018

Adv Differ Equ

Self Cite

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This paper presents a novel adaptive finite-time tracking control scheme for nonlinear systems. During the design process of control scheme, the unmodeled dynamics in nonlinear systems are taken into account. The radial basis function neural networks (RBFNNs) are adopted to approximate the unknown nonlinear functions. Meanwhile, based on RBFNNs, the assumptions with respect to unmodeled dynamics are also relaxed. This paper provides a new finite-time stability criterion, making the adaptive tracking control scheme more suitable in the practice than traditional methods. Combining RBFNNs and the backstepping technique, a novel adaptive controller is designed. Under the presented controller, the desired system performance is realized in finite time. Finally, a numerical example is presented to demonstrate the effectiveness of the proposed control method.

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Fixed‐time adaptive neural tracking control for a class of uncertain multi‐input and multi‐output nonlinear pure‐feedback systems

Dai

et al. 2020

Adaptive Control & Signal

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This study examines the fixed-time adaptive neural network tracking control problem for a class of unknown multi-input and multi-output (MIMO) nonlinear pure-feedback systems. The introduction of the radial basis function resolves uncertain problems of unknown MIMO systems. The mean value theorem is introduced to overcome the controller design problem attributed to the nonaffine structure in pure-feedback systems. Moreover, a novel fixed-time virtual controller and an actual controller are designed to solve the issue of previous single-input and single-output and MIMO systems that have no solution in the negative domain and at the origin in finite-and fixed-time controls. Furthermore, a design method is proposed. The final designed controller ensures that all signals in the system are bounded. Simulation experiments show that the designed fixed-time controller facilitates smaller tracking error of the system compared with other finite-or fixed-time controllers. Furthermore, the selection of appropriate design parameters allows the tracking error to converge on a small neighborhood of the origin in a fixed time. K E Y W O R D S fixed-time control, multi-input and multi-output nonlinear systems, nonlinear pure-feedback systems, RBF neural network 262

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Adaptive finite-time tracking control of switched nonlinear systems

Cited by 76 publications

References 37 publications

Stabilization of a class of cascade nonlinear switched systems with application to chaotic systems

Stabilization of a class of cascade nonlinear switched systems with application to chaotic systems

Adaptive finite-time tracking control for nonlinear systems with unmodeled dynamics using neural networks

Fixed‐time adaptive neural tracking control for a class of uncertain multi‐input and multi‐output nonlinear pure‐feedback systems

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