Backstepping control of multi‐input non‐linear systems

Chung, Chien-Wen; Chang, Yao‐Ting

doi:10.1049/iet-cta.2012.0529

Cited by 15 publications

(12 citation statements)

References 34 publications

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“…U sing the Laplace transform we obtain the analog PI controller in the frequency domain (10) By applying the bilinear transform.5 = (2/T)((z+1)/(z -1)), where T > 0 is the sampling period, we obtain the discrete version By taking and then using the inverse z-transform, we obtain UPI(k) = uPI(k -1) + T6.. uPI(k) (12) Where (13) In Equation (12), T6.. uPI(k) represents the incremental output of a conventional PI controller.…”

Section: Gener Alized Predictive Control Methodsmentioning

confidence: 99%

“…This feature makes advanced control approaches operate in a new atmosphere without any trouble. On the other hand, classical control approaches such as sliding mode control strategy [10], [11], backstepping [12] and active control method [13], have shown inflexible behavior when they are applied in new environments. This kind of controllers needs improvements, and for each problem, a specific algorithm must be designed.…”

Section: Introductionmentioning

confidence: 99%

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Generalized predictive control based on fuzzy sliding-mode control strategy and fuzzy PI controller for synchronization of uncertain chaotic systems

Driss

Mansouri

2015

2015 IEEE International Conference on Fuzzy Systems (FUZZ-IEEE)

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In this paper, we consider the synchronization of uncertain chaotic systems using a generalized predictive control (GPC) algorithm based on fuzzy sliding-mode control (FSMC) strategy and fuzzy PI controller respectively. Optimization per formance and synchronization error are the criteria used to distinguish between the two approaches. The control chattering problem affects negatively on the accuracy of FSMC which needs improvements to avoid this problem. The improvements make FSMC more complex to use. Nonetheless, fuzzy PI controller performs better without any improvement, which makes it easier to use. The performances of the two methods are tested considering the synchronization of two uncertain Duffing systems.To illustrate the effectiveness of the described approaches, some numerical results are given.

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Section: Gener Alized Predictive Control Methodsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Generalized predictive control based on fuzzy sliding-mode control strategy and fuzzy PI controller for synchronization of uncertain chaotic systems

Driss

Mansouri

2015

2015 IEEE International Conference on Fuzzy Systems (FUZZ-IEEE)

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“…In [24], a revised adaptive backstepping design scheme for the strict‐feedback system with parametric uncertainties, unknown nonlinearities, and unmodelled dynamics is developed. In [25–28], a hybrid adaptive backstepping sliding mode control algorithm is developed. Adhami‐Mirhoseini and Yazdanpanah designed a robust nested sliding mode controller using a continuous sliding controller with nonlinear sliding surfaces in every step [29].…”

Section: Introductionmentioning

confidence: 99%

“…The critical assumption in [24–29] on the unmatched and matched uncertain terms (i.e.,

δ_{i}, i = 1, 2, \dots n false)

is that they are constrained by known positive functions of states

x_{1}, x_{2}, . ., x_{i}

(i.e

, false| δ_{i} false| \leq ρ_{i} false(x_{1}, x_{2}, . ., x_{i} false), ρ_{i} false(x_{1}, x_{2}, . ., x_{i} false) > 0

).…”

Section: Introductionmentioning

confidence: 99%

Integral backstepping Lyapunov redesign control of uncertain nonlinear systems

Jalalabadi

Paylakhi

Rahimi-Kian

et al. 2021

IET Control Theory & Appl

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This paper intends to design an integral backstepping Lyapunov redesign controller (IBLRC) for various uncertain strict‐feedback‐form nonlinear systems. The pros and cons of backstepping Lyapunov redesign resulted in the design idea. An integral term is incorporated in conventional backstepping with Lyapunov redesign to indirectly decrease chattering and steady‐state error of a reference signal tracking when unknown static parameters and matched and unmatched dynamic uncertainties exist. The closed‐loop system is mathematically confirmed as stable in a Lyapunov frame, and we ultimately reach uniformly semi‐global boundedness of all signals. Simulation results of the proposed IBLRC are juxtaposed with those of the classic backstepping with the Lyapunov redesign. The proposed IBLRC realizes excellent tracking and enhanced robust performance than the BLRC for time‐varying and step tracking references.

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“…As a control technique, it has found diverse applications as in multi-agent problems [2], multi-input systems [3], neural networks [4], proportional-integral-derivative control [5], chaos control [6] and synchronisation [7].…”

Section: Introductionmentioning

confidence: 99%