Stabilization of a class of switched systems with state constraints via time-varying Lyapunov functions

Ma, Ruicheng; Hua, Lin; Tian, Xiaoyi

doi:10.1177/01423312221086075

Cited by 6 publications

(4 citation statements)

References 32 publications

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“…Lemma 5 ([15]). The shifting function proposed in (8) has the following two properties: a. s(t) is strictly increasing for t ∈ [0, T) and s(0…”

Section: Lemma 3 ([46]) the Following Results Holds For |Z|mentioning

confidence: 99%

“…In the past two or three decades, as a very important and special hybrid dynamic system, switching system has been widely used in power application control systems, aircraft control, intelligent traffic management, intelligent machine control, and other fields [1][2][3][4]. In references [5][6][7][8][9][10], the tracking problems of nonlinear systems with output or state constraints have been studied by many scholars. Using the barrier Lyapunov function (BLF), the switching systems were studied in references [11][12][13][14].…”

Section: Introductionmentioning

confidence: 99%

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Nussbaum gain adaptive fuzzy control for switched nonlinear systems with predefined output and full time‐varying states constraints

Ding

et al. 2023

Asian Journal of Control

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In this paper, the problem of adaptive fuzzy tracking control for a class of uncertain switched nonlinear systems with unknown control direction is studied. Aiming at the problem, an adaptive control scheme with Nussbaum gain technology is constructed by using the average dwell time (ADT) method and the backstepping method to overcome the unknown control direction, and time‐varying asymmetric barrier Lyapunov functions (ABLFs) are adopted to ensure the full‐state constraints satisfaction. The proposed control scheme guarantees that all closed‐loop signals remain bounded under a class of switching signals with ADT, while the output tracking error converges to a small neighborhood of the zero. An important innovation of this design method is that the unknown control direction, asymmetric time‐varying full state constraints, and predefined time‐varying output requirements are simultaneously considered in uncertain switched nonlinear systems for the first time. We set a moment in advance, and make the systems comply with the constraint conditions before running the moment by the shift function nested in the first time‐varying ABLF. Finally, a simulation example verifies the effectiveness of the proposed scheme.

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“…Lemma 5 ([15]). The shifting function proposed in (8) has the following two properties: a. s(t) is strictly increasing for t ∈ [0, T) and s(0…”

Section: Lemma 3 ([46]) the Following Results Holds For |Z|mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Nussbaum gain adaptive fuzzy control for switched nonlinear systems with predefined output and full time‐varying states constraints

Ding

et al. 2023

Asian Journal of Control

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“…The Lyapunov stability theory (Ma et al, 2022) may be used to describe the algorithms for adjusting parameters in the MRAC system. For the systems mentioned above (equations (1) and ( 2)), the controller law is defined by equation ( 5), and the error is given by equation ( 6).…”

Section: Lyapunov Rulementioning

confidence: 99%

Effect of adaptation gain and reference model in MIT and Lyapunov rule–based model reference adaptive control for first- and second-order systems

Gupta,

Kumar,

Giri

2023

Transactions of the Institute of Measurement and Control

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An adaptive control law encompasses a regulating control rule compensating for system dynamics variations by adjusting the controller characteristics to maintain the overall system performance. Recently, some techniques have been developed based on fundamental aspects of the adaptability of living organisms. The adaptive control method is a technique that measures the dynamic characteristics of the plant automatically and continuously to make a comparison with its required output. It utilizes the difference between these two to commute adaptable system parameters to maintain optimal performance regardless of the system variations. The behavior of the adaptation rule is significantly affected by the adaptation gain value. Here, it has also been investigated that the adaptation gain range is wide for the systems with the lower order. The appropriate range of adaptation gain decreases as the order of the system increases. In the present work, the model reference adaptive control (MRAC) for first- and second-order systems has been designed and investigated using a wide range of values for the adaptation gain and variations in the reference model parameters. The MIT (Massachusetts Institute of Technology) and Lyapunov rules are applied for the analyses of systems. On the MATLAB/Simulink platform, all the adaptation process comparisons, variations, and investigations have been carried out by altering the adaptation gain and the reference model parameters. The obtained results present encouraging outcomes.

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“…Because constrained MPC systems are nonlinear, the second stability theorem of Lyapunov is commonly used to prove the nominal stability of the systems (Jiang et al, 2022; Ma et al, 2022).…”

Section: Mo Control Algorithmmentioning

confidence: 99%

Adaptive cruise control method based on hierarchical control and multi-objective optimization

Piao

Gao

Yang

et al. 2022

Transactions of the Institute of Measurement and Control

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Considering the perception of a driver, driving safety, and riding comfort, an adaptive cruise control (ACC) method based on a multi-objective (MO) real-time optimization control algorithm is proposed. The ACC system can be divided into various working modes according to the driver’s perception, as well as the relative state of the host vehicle and the preceding vehicle. To distinguish the driver’s intention in the rapid acceleration, strong deceleration, steady, and larger clearance modes, a fuzzy tool is proposed to solve the problem. To maintain the inter-clearance, velocity, and jerking action in a reasonable region, an MO control algorithm based on model predictive control was used to obtain the optimal control vectors. Moreover, the control vector increment is restricted to suppressing the fluctuation caused by switching among various modes. Simulations were conducted for various scenarios to verify the effectiveness of the ACC method. The simulation results indicated that the driver’s comfort and fuel economy improved by 35.3% and 16.6%, respectively, compared with the linear quadratic algorithm in a complicated driving environment. Various simulation results demonstrated that the MO-ACC controller can reduce fuel consumption while barely sacrificing riding comfort or tracking performance, as compared to the linear quadratic controller.

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Stabilization of a class of switched systems with state constraints via time-varying Lyapunov functions

Cited by 6 publications

References 32 publications

Nussbaum gain adaptive fuzzy control for switched nonlinear systems with predefined output and full time‐varying states constraints

Nussbaum gain adaptive fuzzy control for switched nonlinear systems with predefined output and full time‐varying states constraints

Effect of adaptation gain and reference model in MIT and Lyapunov rule–based model reference adaptive control for first- and second-order systems

Adaptive cruise control method based on hierarchical control and multi-objective optimization

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