Adaptive backstepping sliding mode control for feedforward uncertain systems

Koshkouei, Ali J.; Burnham, Keith J.

doi:10.1080/00207721.2011.617059

Cited by 22 publications

(35 citation statements)

References 21 publications

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“…with state x [1] ∈ R, v [1] being designed to asymptotically stabilize the system (38) at an equilibrium x [1] * . Introduce an error variableθ 1 =θ 1 − θ 1 and choose a virtual controller v [1] expressed as follows:…”

Section: Robust Adaptive Control Designmentioning

confidence: 99%

“…[1][2][3][4][5][6][7][8][9][10][11][12][13][14] In spite of highly rich literature, it is surprising to notice that a Lyapunov function is required to obtain the virtual control law and the parameter updated law at each step of the design. In general, backstepping algorithm is taken as a core for control design of nonlinear systems in strict feedback form and is combined with other techniques like adaptive control, fuzzy or neural network control, and sliding mode control to yield some new control methods for both academic and industrial communities.…”

Section: Introductionmentioning

confidence: 99%

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Mapping filtered forwarding‐based robust adaptive control for uncertain nonlinear systems with input constraint

Zhang

Huang

et al. 2017

Adaptive Control & Signal

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This work develops a robust adaptive control algorithm for uncertain nonlinear systems with parametric uncertainties and external disturbances satisfying an extended matching condition. This control method is implemented in the framework of a mapping filtered forwarding-based technique. As an attractive alternative of the adaptive backstepping method, this bottom-up strategy forms a virtual controller and a parameter updated law at each step of the design, where Lyapunov functions and the prior knowledge of system parameters are not required. The boundedness of all signals is guaranteed by using Barbalat's lemma. According to immersion relationship, a compliant behavior of systems behaves accordingly to the lower-order target dynamics. Furthermore, input constraints are handled by estimating a saturated scaling. A spring, mass, and damper system is used to demonstrate the controller performances via simulation results. KEYWORDS adaptive control, filters, input saturation, mapping filtered forwarding control, uncertain nonlinear systems 248 ;32:248-264. ZHANG ET AL. 249error as z =θ − θ + β(x), where β(x) is a continuous term, and utilizing the uncertainty equivalence principle to design parameter update laws for lower triangular systems. Although researchers used this method to design parameter update laws in some practical systems, the achievements strictly depend on an assumption satisfying the partial differential inequality to obtain β(x). 20,21 In essence, the solvability of this inequality strongly relies on the structure of the regressor, and as system order increases, the implementation will be limited. Therefore, it could not be feasible to achieve I&I adaptive stabilization for high-order nonlinear systems with extended matching uncertainties. 22,23 Furthermore, control input saturation severely limits system performance in many physical systems, giving rise to undesirable properties or leading instability. 24,25 The hyperbolic tangent function is used to approximate the saturated nonlinearity, 12 where the approximated error is considered as an augmented external disturbance. Although this algorithm is easy to be carried out, the problem of the definition domain of artanh(·) is encountered while tuning controller gains. It can be shown that the bound of the nonlinear function we derive must be restricted to (−1, 1). 26 The problem of the controller design for the nonlinear systems with input saturation and parametric uncertainties has not been addressed adequately under a mapping filtered forwarding-based framework.In this paper, we will study the robust adaptive control design for nonlinear systems subject to input saturation and uncertainties under the mapping filtered forwarding-based framework. A new bottom-up control scheme from a manifold's perspective, namely, mapping filtered adaptive forwarding, which consists of virtual control laws and parameter updated laws, will be presented. With the proposed controller architecture, manifolds are guaranteed to be insensitive to uncertainties, and the iss...

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Section: Robust Adaptive Control Designmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Mapping filtered forwarding‐based robust adaptive control for uncertain nonlinear systems with input constraint

Zhang

Huang

et al. 2017

Adaptive Control & Signal

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“…Dealing with the robust control of nonlinear systems with parametric uncertainties, the adaptive backstepping control (ABC) is one of the popular design methods for a large class of uncertain nonlinear systems, and various reports for the ABC have been proposed (Chang & Chen 2010;Kanelakopoulos, Kokotovic, & Morse, 1991;Koshkouei & Burnham 2011;Kristic, Kanellakopoulos, & Kokotovic, 1992;Pan & Basar, 1998;Yao & Tomuzuka, 2001). The ABC much contributes to improve the global robustness and the stabilisation for the uncertain nonlinear systems, but the explosion of complexity problem due to the necessity to perform repeated differentiations of nonlinear functions provides relatively complicated algorithms of the ABC.…”

Section: Introductionmentioning

confidence: 98%

Design of a simplified adaptive fuzzy backstepping control for uncertain discrete-time nonlinear systems

Yoshimura

2014

International Journal of Systems Science

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This paper presents a simplified adaptive fuzzy backstepping control for uncertain discrete-time nonlinear systems. It is assumed that the systems are described by a discrete-time equation with nonlinear uncertainties to be viewed as the modelling errors and the unknown external disturbances, and the states are observed with measurement noises. To design the simplified adaptive fuzzy backstepping control, the modelling errors are approximated by using the fuzzy inference approach based on the extended single-input rule modules, and the estimates for the unmeasurable states and the adjustable parameters are derived by using the weighted and its simplified weighted least squares estimators. It is proved that the states are ultimately bounded, and the estimation errors remain in the vicinity of zero. The effectiveness of the proposed approach is indicated through the simulation experiment of a simple numerical system.

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“…With external disturbances and uncertain parameters, adaptive backstepping sliding mode control schemes are developed, which have been applied in uncertain systems [23]. It introduces the sliding mode control in backstepping design to modify the last step of backstepping algorithm and simplify the design of controller.…”

Section: Adaptive Backstepping Sliding Mode Controlmentioning

confidence: 99%

Attitude Analysis and Robust Adaptive Backstepping Sliding Mode Control of Spacecrafts Orbiting Irregular Asteroids

Liang

2014

Mathematical Problems in Engineering

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Attitude stability analysis and robust control algorithms for spacecrafts orbiting irregular asteroids are investigated in the presence of model uncertainties and external disturbances. Rigid spacecraft nonlinear attitude models are considered and detailed attitude stability analysis of spacecraft subjected to the gravity gradient torque in an irregular central gravity field is included in retrograde orbits and direct orbits using linearized system model. The robust adaptive backstepping sliding mode control laws are designed to make the attitude of the spacecrafts stabilized and responded accurately to the expectation in the presence of disturbances and parametric uncertainties. Numerical simulations are included to illustrate the spacecraft performance obtained using the proposed control laws.

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Adaptive backstepping sliding mode control for feedforward uncertain systems

Cited by 22 publications

References 21 publications

Mapping filtered forwarding‐based robust adaptive control for uncertain nonlinear systems with input constraint

Mapping filtered forwarding‐based robust adaptive control for uncertain nonlinear systems with input constraint

Design of a simplified adaptive fuzzy backstepping control for uncertain discrete-time nonlinear systems

Attitude Analysis and Robust Adaptive Backstepping Sliding Mode Control of Spacecrafts Orbiting Irregular Asteroids

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