Adaptive backstepping quantized control for a class of unknown nonlinear systems

Aslmostafa, Ehsan; Ghaemi, Sehraneh; Badamchizadeh, Mohammad Ali; Ghiasi, Amir Rikhtehgar

doi:10.1016/j.isatra.2021.06.009

Cited by 41 publications

(14 citation statements)

References 23 publications

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“…Proof. According to (24) and the Lemmas 1-4, u satisfies the Lipschitz condition with respect to zn . Thus, there exists a constant L u > 0, such that…”

Section: Backstepping-based Arc With Quantized States and Inputmentioning

confidence: 99%

“…Theorem 1. Consider the system (1) with quantized state feedback under the control law (24) and the adaptive law ˙θ = γτ qn . (…”

Section: Consider the Lyapunov Candidate Functionmentioning

confidence: 99%

“…Ignoring the state quantization, the designed controller (24) degrades into the ARC law proposed in [8], in which the bounds that the states of the system converge to and the convergence rate are determined by the control parameters k i and ε i ; the converge rates of the parameter estimators are determined by the adaptive parameter matrix γ. Moreover, β i = α i , i.e., the Lyapunov function V n (t) becomes the traditional form in [5,8].…”

Section: Consider the Lyapunov Candidate Functionmentioning

confidence: 99%

“…The packet losses and time delay were considered by Wang et al in [16]. Although there have been many results for networked control systems in strictfeedback form, few results aim at signal quantization, especially state quantization [22][23][24]. In the past decades, input quantization has been widely concerned.…”

Section: Introductionmentioning

confidence: 99%

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Adaptive Robust Control for Networked Strict-Feedback Nonlinear Systems with State and Input Quantization

et al. 2021

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Backstepping method is a successful approach to deal with the systems in strict-feedback form. However, for networked control systems, the discontinuous virtual law caused by state quantization introduces huge challenges for its applicability. In this article, a quantized adaptive robust control approach in backsetpping framework is developed in this article for networked strict-feedback nonlinear systems with both state and input quantization. In order to prove the efficiency of the designed control scheme, a novel form of Lyapunov candidate function was constructed in the process of analyzing the stability, which is applicable for the systems with nondifferentiable virtual control law. In particular, the state and input quantizers can be in any form as long as they meet the sector-bound condition. The theoretic result shows that the tracking error is determined by the pregiven constants and quantization errors, which are also verified by the simulation results.

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“…Proof. According to (24) and the Lemmas 1-4, u satisfies the Lipschitz condition with respect to zn . Thus, there exists a constant L u > 0, such that…”

Section: Backstepping-based Arc With Quantized States and Inputmentioning

confidence: 99%

“…Theorem 1. Consider the system (1) with quantized state feedback under the control law (24) and the adaptive law ˙θ = γτ qn . (…”

Section: Consider the Lyapunov Candidate Functionmentioning

confidence: 99%

Section: Consider the Lyapunov Candidate Functionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Adaptive Robust Control for Networked Strict-Feedback Nonlinear Systems with State and Input Quantization

et al. 2021

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“…In [15,16], the backstepping control method was applied to construct the adaptive neural network control law. In [17], an adaptive backstepping quantized control scheme was presented to ensure the stability of the given system. In [18], a command filterbased adaptive finite-time backstepping control law was designed that ensured that the position tracking error converged to the desired neighborhood in finite time.…”

Section: Introductionmentioning

confidence: 99%

Adaptive Neural Tracking Control for Nonstrict-Feedback Nonlinear Systems with Unknown Control Gains via Dynamic Surface Control Method

et al. 2022

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This paper addresses the tracking control problem of nonstrict-feedback systems with unknown control gains. The dynamic surface control method, Nussbaum gain function control technique, and radial basis function neural network are applied for the design of virtual control laws, and adaptive control laws. Then, an adaptive neural tracking control law is proposed in the last step. By using the dynamic surface control method, the “explosion of complexity” problem of conventional backstepping is avoided. Based on the application of the Nussbaum gain function control technique, the unknown control gain problem is well solved. With the help of the radial basis function neural network, the unknown nonlinear dynamics are approximated. Furthermore, through Lyapunov stability analysis, it is proved that the proposed control law can guarantee that all signals in the closed-loop system are bounded and the tracking error can converge to an arbitrarily small domain of zero by adjusting the design parameters. Finally, two examples are provided to illustrate the effectiveness of the proposed control law.

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Disturbance observer based adaptive heading control for unmanned surface vehicle with event‐triggered and signal quantization

Ma,

Li,

Ning

et al. 2024

Adaptive Control & Signal

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SummaryThis article delves into the adaptive heading tracking control of unmanned surface vehicle (USV) by incorporating an event‐triggered mechanism and signal quantization. The primary objective is to save communication resources while alleviating the burden of signal transmission. To address time‐varying external perturbations inherent in the control system, a disturbance observer is employed for precise estimation. Additionally, a linear model is introduced to delineate the procedure of quantization. By furnishing the controller with purpose‐designed quantized control input, the adaptive tracking control system can effectively track desired input without requiring any prior knowledge of the quantized parameters. The article substantiates its claims by demonstrating the system's stability in the absence of quantization considerations and the bounded nature of quantization errors through a series of presented lemmas. Further, the stability of the USV heading control system, integrated with an event‐triggered mechanism and signal quantization, is proofed in accordance with Lyapunov stability theory. Finally, the proposed strategy's efficacy and practical applicability are validated through experimental simulations.

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Adaptive backstepping quantized control for a class of unknown nonlinear systems

Cited by 41 publications

References 23 publications

Adaptive Robust Control for Networked Strict-Feedback Nonlinear Systems with State and Input Quantization

Adaptive Robust Control for Networked Strict-Feedback Nonlinear Systems with State and Input Quantization

Adaptive Neural Tracking Control for Nonstrict-Feedback Nonlinear Systems with Unknown Control Gains via Dynamic Surface Control Method

Disturbance observer based adaptive heading control for unmanned surface vehicle with event‐triggered and signal quantization

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