Adaptive quantized tracking control for a class of uncertain nonlinear systems with guaranteed transient performance

Jing, Yan-Hui; Yang, Guang‐Hong

doi:10.1016/j.jfranklin.2018.06.001

Cited by 9 publications

(12 citation statements)

References 32 publications

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“…The sector bound approach and the hyperbolic tangent function property are used to deal with the quantization error, and an output feedback controller is designed to guarantee the stability of the uncertain nonlinear quantized system. This result extends the existing state feedback quantized controls to the output feedback control of nonlinear systems with unknown output functions and unknown control directions (see Section 5).…”

Section: Introductionsupporting

confidence: 57%

“…Next, employing the Lemma and the inequality property of hyperbolic tangent function

| x | - x \tanh (\frac{x}{ς}) \leq 0.2785 ς

used by Jing and Yang, we have

\begin{align} ξ_{n prefix- 1} q false(u false) & = ξ_{n prefix- 1} ((), q false(u false) prefix- u + u) \leq ξ_{n prefix- 1} u + δ false| ξ_{n prefix- 1} u false| \\ \leq ξ_{n prefix- 1} u + δ ξ_{n prefix- 1} u normaltanh ((), \frac{ξ_{n prefix- 1} u}{ς false(t false)}) + 0.2785 δ ς false(t false), \end{align}

where ς( t ) is a positive time‐varying function and satisfies

\lim_{t \to + \infty} \int_{0}^{t} ς (s) d s \leq \overline{ς}

with

\overline{ς}

being a positive constant.…”

Section: Further Results For Nonlinear Quantized Systemmentioning

confidence: 99%

“…Proof Let

Φ (t) = - \int_{k (0)}^{k (t)} (g_{\infty} | h_{+}^{^{'}} | N (k) - τ) d k

. Inspired by the work of Wang et al and Jing and Yang, we prove the boundedness of k ( t ) on the interval [0, T f ) by contradiction. If k ( t ) is unbounded, two cases should be considered.…”

Section: Stability Analysismentioning

confidence: 92%

“…is the virtual controller defined in (23). By combining (16) to (21), it can be directly verified that the upper derivative of…”

Section: Output Feedback Controller Designmentioning

confidence: 99%

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Global output feedback control for nonlinear cascade systems with unknown output functions and unknown control directions

Wang

Sun

2020

Intl J Robust & Nonlinear

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Summary This paper investigates the output feedback control for the uncertain nonlinear system with the integral input‐to‐state stable (iISS) cascade subsystem, which allow not only the unknown control direction but also the unknown output function. The unknown output function only needs to have a generalized derivative (which may not be derivable), and the upper and lower bounds of the generalized derivative need not to be known. To deal with the challenge raised by the unknown output function and the unknown control direction, we choose a special Nussbaum function with a faster growth rate to ensure the integrability for the derivative of the selected Lyapunov function. Then, a dynamic output feedback controller is designed to drive the system states to the origin while keeping the boundedness for all other closed‐loop signals. Moreover, via some appropriate transformations, the proposed control scheme is extended to deal with more general uncertain nonlinear cascade systems with quantized input signals. Finally, two simulation examples are given to show the effectiveness of the control scheme.

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Section: Introductionsupporting

confidence: 57%

“…Next, employing the Lemma and the inequality property of hyperbolic tangent function

| x | - x \tanh (\frac{x}{ς}) \leq 0.2785 ς

used by Jing and Yang, we have

\begin{align} ξ_{n prefix- 1} q false(u false) & = ξ_{n prefix- 1} ((), q false(u false) prefix- u + u) \leq ξ_{n prefix- 1} u + δ false| ξ_{n prefix- 1} u false| \\ \leq ξ_{n prefix- 1} u + δ ξ_{n prefix- 1} u normaltanh ((), \frac{ξ_{n prefix- 1} u}{ς false(t false)}) + 0.2785 δ ς false(t false), \end{align}

where ς( t ) is a positive time‐varying function and satisfies

\lim_{t \to + \infty} \int_{0}^{t} ς (s) d s \leq \overline{ς}

with

\overline{ς}

being a positive constant.…”

Section: Further Results For Nonlinear Quantized Systemmentioning

confidence: 99%

“…Proof Let

Φ (t) = - \int_{k (0)}^{k (t)} (g_{\infty} | h_{+}^{^{'}} | N (k) - τ) d k

. Inspired by the work of Wang et al and Jing and Yang, we prove the boundedness of k ( t ) on the interval [0, T f ) by contradiction. If k ( t ) is unbounded, two cases should be considered.…”

Section: Stability Analysismentioning

confidence: 92%

“…is the virtual controller defined in (23). By combining (16) to (21), it can be directly verified that the upper derivative of…”

Section: Output Feedback Controller Designmentioning

confidence: 99%

See 2 more Smart Citations

Global output feedback control for nonlinear cascade systems with unknown output functions and unknown control directions

Wang

Sun

2020

Intl J Robust & Nonlinear

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show abstract

“…An adaptive control strategy was developed for finite time input quantization in the other works . A fuzzy adaptive approach for stochastic strict‐feedback nonlinear systems with quantized input signal was discussed in the work of Niu et al Three adaptive control schemes with input or state quantization were investigated for uncertain systems with unknown control direction and guaranteed transient performance in the other works . Adaptive output feedback control was presented for a class of nonlinear systems with quantized input and output in the other works .…”

Section: Introductionmentioning

confidence: 99%

Adaptive neural output feedback control for uncertain nonlinear systems with input quantization and output constraints

Wang

Zhang

Yang

2020

Adaptive Control & Signal

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Summary In this paper, we are concerned with the problem of adaptive output‐feedback tracking control for nonlinear systems with input quantization, unmodeled dynamics, and output constraints. A novel quantizer with the advantages of hysteresis and uniform quantizer is introduced to handle input signals. A barrier Lyapunov function is employed to solve the output constraints. The state unmodeled dynamics is solved by using a Lyapunov description, and neural networks are used to approximate the unknown smooth functions produced in the adaptive control design process. The controller design is simplified by combining the new quantizer with dynamic surface control method. The mathematical derivation shows the stability of the closed‐loop system and the effectiveness of output constraints. Simulation illustrates and clarifies the theoretical findings.

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Adaptive robust design for nonlinear switched systems with unmodeled dynamics and input quantization

Zhang

et al. 2021

Asian Journal of Control

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In this paper, we focus on the adaptive robust input quantized control problem for a class of uncertain nonlinear switched systems under a state‐dependent switching law. The considered systems admit the non‐ISS unmodeled dynamics, the unknown virtual control coefficients, and an unknown parameter. In order to reduce the conservativeness of the common Lyapunov function, the multiple Lyapunov functions method is used to design a state‐dependent switching law. Besides, to overcome the design difficulty arising from the quantization behavior, a nonlinear decomposition method is used to establish the relationship between the control signal and the quantized signal. We put forward the adaptive robust controllers for the individual subsystems, based on which the resulted closed‐loop system is uniformly ultimately bounded. Finally, to verify the effectiveness of the proposed control scheme, two examples are given to construct the adaptive robust controllers.

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Adaptive quantized tracking control for a class of uncertain nonlinear systems with guaranteed transient performance

Cited by 9 publications

References 32 publications

Global output feedback control for nonlinear cascade systems with unknown output functions and unknown control directions

Global output feedback control for nonlinear cascade systems with unknown output functions and unknown control directions

Adaptive neural output feedback control for uncertain nonlinear systems with input quantization and output constraints

Adaptive robust design for nonlinear switched systems with unmodeled dynamics and input quantization

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