Adaptive fuzzy asymptotic tracking control of uncertain nonaffine nonlinear systems with non-symmetric dead-zone nonlinearities

Wu, Li‐Bing; Yang, Guang‐Hong; Wang, Hong; Wang, Fuli

doi:10.1016/j.ins.2016.02.017

Cited by 34 publications

(36 citation statements)

References 62 publications

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“…The inequality constraint only depicts a general variation of

f_{i} ((),, {\overset{x}{true}}_{i}, x_{i + 1})

with x i + 1 , which has no special requirement for each specific point on the nonlinear curve. Figure B is an illustration of the common assumption utilized in other works . The conventional controllability condition of nonaffine functions is

0 < g_{i, normalm} \leq \partial f_{i} ((),, {\overset{x}{true}}_{i}, x_{i + 1}) false/ \partial x_{i + 1} \leq g_{i, normalM}

, which requires the nonaffine function to be differentiable and its partial derivative to keep positive all the time.…”

Section: Problem Statement and Preliminariesmentioning

confidence: 99%

“…Figure 1B is an illustration of the common assumption utilized in other works. [3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19] The conventional controllability condition of nonaffine…”

Section: Problem Statement and Preliminariesmentioning

confidence: 99%

“…Namely, the upper bound and lower bound of nonaffine functions i (x i , x i+1 ) for x i+1 ≥ i+1 and x i+1 ≤ i+1 are canceled, respectively. In control schemes for nonaffine systems, [3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19] the nonaffine functions are always assumed to be differentiable, which is more restrictive than Assumption 1. Moreover, mean value theorem or Taylor series expansion [3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19] cannot be utilized to construct pseudoaffine model due to the in-differentiable points of nonaffine functions in this paper, while mathematical transformation in Part 2 of Section 5 can solve this problem.…”

Section: Problem Statement and Preliminariesmentioning

confidence: 99%

“…The past decades have witnessed a great amount of studies on control for nonaffine systems where the control inputs take their actions through a nonlinear and implicit way . There are many systems falling into this category featured with nonaffine structure, such as mechanical systems, biochemical process, and aircraft flight control system .…”

Section: Introductionmentioning

confidence: 99%

“…Most notably, mean value theorem is typically used to build a transformational model for nonaffine system under the condition that ∂f ( x , u )/ ∂u is bounded, and then, control approaches such as adaptive fuzzy control, adaptive neural network control, and prescribed performance control can be constructed on the basis of the transformational model. Moreover, Taylor series expansion is also utilized to construct an equivalent system under the hypothesis that ∂f ( x , u )/ ∂u is bounded, and then, adaptive fuzzy controllers can be designed based on the pseudoaffine system …”

Section: Introductionmentioning

confidence: 99%

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Improved prescribed performance control for nonaffine pure‐feedback systems with input saturation

Wang

et al. 2019

Intl J Robust & Nonlinear

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Summary This work considers an input and output constraint control problem for pure‐feedback systems with nonaffine functions possibly being in‐differentiable. A locally semibounded and continuous condition for nonaffine functions is presented to guarantee the controllability, and the nonaffine system is transformed to an equivalent pseudoaffine one based on the mild condition. Combined with backstepping technique, a novel prescribed performance controller with new performance functions is constructed to circumvent high frequency chattering in control input. An auxiliary system with bounded compensation term is utilized in this paper, successfully avoiding the overrun of control input. The methodology achieves the desired transient and steady‐state performance and presents excellent robustness against the system uncertainty. Finally, two numerical simulations are performed to demonstrate the effectiveness of the proposed approach.

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“…The inequality constraint only depicts a general variation of

f_{i} ((),, {\overset{x}{true}}_{i}, x_{i + 1})

0 < g_{i, normalm} \leq \partial f_{i} ((),, {\overset{x}{true}}_{i}, x_{i + 1}) false/ \partial x_{i + 1} \leq g_{i, normalM}

, which requires the nonaffine function to be differentiable and its partial derivative to keep positive all the time.…”

Section: Problem Statement and Preliminariesmentioning

confidence: 99%

Section: Problem Statement and Preliminariesmentioning

confidence: 99%

Section: Problem Statement and Preliminariesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Improved prescribed performance control for nonaffine pure‐feedback systems with input saturation

Wang

et al. 2019

Intl J Robust & Nonlinear

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Stability analysis and adaptive control for nonlinear discrete‐time systems with time delays and dead zone via state‐feedback technique

Zhang

Zheng

Xie

et al. 2019

Adaptive Control & Signal

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This research addresses the stability analysis and adaptive state-feedback control for a class of nonlinear discrete-time systems with multiple interval time-varying delays and symmetry dead zone. The multiple interval time-varying delays and symmetry dead zone are considered in the nonlinear discrete-time system. The multiple interval time-varying delays are bounded by the nonlinear function with unknown coefficients, and the symmetry dead zone is considered without the knowledge of the dead zone parameters. The adaptive state-feedback controller is designed for the nonlinear discrete-time systems with multiple interval time-varying delays and dead zone. The discrete Lyapunov-Krasovskii functional is introduced, such that the solutions of the closed-loop error system converge to an adjustable bounded region and the state errors can be rendered arbitrarily small by adjusting the adaptive parameters. The designed adaptive state-feedback controller does not require the knowledge of maximum and minimum values for the characteristic slopes of the dead zone. Finally, three simulation examples are given to show the effectiveness of the proposed methods.

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Prescribed performance adaptive fuzzy control for nonstrict‐feedback nonlinear systems with dead zone outputs

SuHang

ZhaoXiaoyu

Zhang

2020

Adaptive Control & Signal

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This paper presents an adaptive fuzzy control scheme for a class of nonstrict-feedback nonlinear systems with dead zone outputs and prescribed performance. By utilizing the monotonically increasing property of system bounding functions and the Nussbaum function, the design difficulties caused by the nonstrict-feedback structure and dead zone output are overcome. Combining backstepping technique with prescribed performance algorithm, a feasible adaptive fuzzy controller is designed to guarantee the boundedness of all signals of the closed-loop system and the prescribed tracking performance of the system. Finally, simulation results are depicted to illustrate the effectiveness of the proposed control approach. K E Y W O R D Sadaptive fuzzy control, backstepping technique, dead zone outputs, prescribed performance INTRODUCTIONBy utilizing fuzzy logic systems 1-4 or neural networks 5 to approximate the unknown nonlinear system functions, approximation-based adaptive fuzzy or neural control has received considerable attention in the past decades. In References 6-12, combining with backstepping technique, adaptive fuzzy or neural control was considered for strict-feedback nonlinear systems. In References 13-17, the authors extended the controlled nonlinear systems from deterministic systems to the uncertain stochastic nonlinear systems. However, the results obtained in References 6-17 cannot be directly applied to nonstrict-feedback nonlinear systems. For the strict-feedback systems, the nonlinear functions of the jth subsystem are independent of the latter state variables x i (j + 1 ≤ i ≤ n), and in the nonstrict-feedback systems, each subsystem function contains the whole state variables, which is the major difference between a strict-feedback nonlinear system and a nonstrict-feedback one. If the traditional backstepping control scheme is adopted in a nonstrict-feedback system, virtual control signal designed in the approach is the function of whole state vector, which makes the controller design difficult and leads to algebraic loop problem.Recently, many researchers have paid attention to adaptive fuzzy or neural control of nonstrict-feedback nonlinear systems. In Reference 18, the problem of observer-based adaptive neural output-feedback control was considered for stochastic nonstrict-feedback nonlinear system. In References 19-24, adaptive fuzzy or neural control was extended to nonstrict-feedback nonlinear systems with input nonlinearities such as time delays, 19 dead zones, 20,21 input saturation 22,23

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Adaptive fuzzy asymptotic tracking control of uncertain nonaffine nonlinear systems with non-symmetric dead-zone nonlinearities

Cited by 34 publications

References 62 publications

Improved prescribed performance control for nonaffine pure‐feedback systems with input saturation

Improved prescribed performance control for nonaffine pure‐feedback systems with input saturation

Stability analysis and adaptive control for nonlinear discrete‐time systems with time delays and dead zone via state‐feedback technique

Prescribed performance adaptive fuzzy control for nonstrict‐feedback nonlinear systems with dead zone outputs

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