Robust Adaptive Control of Nonholonomic Systems with Nonlinear Parameterization

Wang, Qiangde; Wei, Chunling

doi:10.1360/aas-007-0399

Cited by 32 publications

(9 citation statements)

References 19 publications

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“…If p i = q i = 1and f i = 0, system (1) reduces to a uncertain chained system with strong nonlinear uncertainties was studied in [10][11][12]. In the case, where d i = (1) becomes a linearly parameterized system whose adaptive control problem was solved in [13,14,17,18]; where the low order nonlinearly parameterized systems, i.e., p i = q i = 1, was considered in [15,16].…”

Section: Problem Formulationmentioning

confidence: 99%

“…By use of a novel switching scheme, this result has been extended to both Lyapunov stability and exponential convergence in [11] and [12]. Recently, adaptive control strategies were proposed to stabilize the dynamic nonholonomic systems with modeling or parametric uncertainties, for instance, adaptive state feedback control was considered in [13][14][15][16] and output feedback control in [17,18].…”

Section: Introductionmentioning

confidence: 99%

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Adaptive stabilization of high order nonholonomic systems with strong nonlinear drifts

Gao

Yuan

et al. 2011

Applied Mathematical Modelling

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a b s t r a c tThis paper investigates the problem of adaptive stabilization control design for a class of high order nonholonomic systems in power chained form with strong nonlinear drifts, including unmodeled dynamics, and dynamics modeled with unknown nonlinear parameters. A parameter separation technique is introduced to transform the nonlinear parameterized system into a linear-like parameterized system. Then, by the use of input-state scaling technique and adding a power integrator backstepping approach, an adaptive state feedback controller is obtained. The adaptive control based switching strategy is proposed to eliminate the phenomenon of uncontrollability. Global asymptotic regulation of the closed-loop system states and the boundedness of other signals are guaranteed. Simulation examples demonstrate the effectiveness of the proposed scheme.

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Section: Problem Formulationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Adaptive stabilization of high order nonholonomic systems with strong nonlinear drifts

Gao

Yuan

et al. 2011

Applied Mathematical Modelling

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show abstract

“…In order to overcome this obstruction, several approaches have been proposed for the problem, such as discontinuous time-invariant stabilization [2,3], smooth timevarying stabilization [4][5][6], and hybrid stabilization [7]. Using the valid approaches, the asymptotic stabilization or exponential regulation for nonholonomic systems has been extensively studied [8][9][10][11][12][13][14][15][16][17][18].…”

Section: Introductionmentioning

confidence: 99%

Adaptive Stabilization for a Class of Stochastic Nonlinearly Parameterized Nonholonomic Systems with Unknown Control Coefficients

Gao¹,

Yuan²,

Wu³

2013

Asian Journal of Control

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This paper investigates the problem of adaptive state feedback stabilization for a class of stochastic nonlinearly parameterized nonholonomic systems in chained form with unknown control coefficients. By defining two new unknown parameters whose dynamic updating laws are properly chosen and also by skilfully using the parameter separation, input-statescaling, and integrator backstepping techniques, an adaptive state feedback controller is successfully designed, which guarantees that the closed-loop system is asymptotically stabilized in probability. A simulation example is provided to illustrate the effectiveness of the proposed approach.

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“…By the results of Brockett [1], the nonholonomic system cannot be stabilized at a single equilibrium point by any static smooth pure state-feedback controller. To solve this problem, lots of novel approaches have been considered: discontinuous feedback control [2][3][4], smooth time-varying feedback controller [5], and the method of LMI [6]. The control of nonholonomic mobile robots plays an important role in that of nonholonomic systems because they are a benchmark for these systems.…”

Section: Introductionmentioning

confidence: 99%

Adaptive State-Feedback Stabilization for Stochastic Nonholonomic Mobile Robots with Unknown Parameters

Feng

Sun

Cao

et al. 2013

Discrete Dynamics in Nature and Society

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The stabilizing problem of stochastic nonholonomic mobile robots with uncertain parameters is addressed in this paper. The nonholonomic mobile robots with kinematic unknown parameters are extended to the stochastic case. Based on backstepping technique, adaptive state-feedback stabilizing controllers are designed for nonholonomic mobile robots with kinematic unknown parameters whose linear velocity and angular velocity are subject to some stochastic disturbances simultaneously. A switching control strategy for the original system is presented. The proposed controllers that guarantee the states of closed-loop system are asymptotically stabilized at the zero equilibrium point in probability.

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Robust Adaptive Control of Nonholonomic Systems with Nonlinear Parameterization

Cited by 32 publications

References 19 publications

Adaptive stabilization of high order nonholonomic systems with strong nonlinear drifts

Adaptive stabilization of high order nonholonomic systems with strong nonlinear drifts

Adaptive Stabilization for a Class of Stochastic Nonlinearly Parameterized Nonholonomic Systems with Unknown Control Coefficients

Adaptive State-Feedback Stabilization for Stochastic Nonholonomic Mobile Robots with Unknown Parameters

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