String Exponential Stability With Mode Constraint of Stochastic Vehicle Following Systems

Xu, Xiaolong; Zhang, Jiye; Lan, Tian-Syung

doi:10.1115/1.4024888

Cited by 4 publications

(10 citation statements)

References 16 publications

(36 reference statements)

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“…We note that the criteria for exponential mean‐square stability of nonlinear continuous time stochastic string nonhybrid systems with parametric Gaussian white noises obtained by are not useful to study the stability of nonlinear with strong coupling interconnected systems. To omit this problem the vector Lyapunov function method (VLFM) was successfully used in . It seems to be an efficient mathematical tool in the study of stability of string systems.…”

Section: Conclusion and Final Remarksmentioning

confidence: 99%

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Exponential Mean‐Square Stability of Stochastic String Hybrid Systems Under Continuous Non‐Gaussian Excitation

Socha

2018

Asian Journal of Control

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The problem of the exponential mean-square stability for nonlinear stochastic string hybrid system under parametric (multiplicative) Gaussian and external (additive) continuous non-Gaussian excitations is considered. The string hybrid system is treated as an infinite-dimensional family of strings (subsystems) with a switching rule that has the form of a right continuous Markov chain. It is described by infinite-dimension Ito stochastic differential equations. The excitations are assumed to be parametric Gaussian white noises and the continuous non-Gaussian processes modeled by polynomials of a Gaussian process. The nonlinear strings under external continuous non-Gaussian excitation are transformed to extended dimensional nonlinear strings with a special structure under a parametric Gaussian excitation. Using the methodology of the stability analysis of nonlinear hybrid systems with Markovian switchings the sufficient conditions of the exponential mean-square stability of nonlinear stochastic string systems under parametric Gaussian and external continuous non-Gaussian excitation with a Markovian switching are derived. The detailed calculations are given for linear systems.

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Section: Conclusion and Final Remarksmentioning

confidence: 99%

“…First, stability criteria were derived in by application of the scalar Lyapunov functions. A generalization of these criteria was proposed in where the vector Lyapunov function method was used.…”

Section: Introductionmentioning

confidence: 99%

Exponential Mean‐Square Stability of Stochastic String Hybrid Systems Under Continuous Non‐Gaussian Excitation

Socha

2018

Asian Journal of Control

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“…Definition 3 (see [13]). The zero solution of system (2) = 0 ( ∈ N) is string exponentially stable with mode constraint in the mean square sense if = 0 is string exponentially stable in the mean square sense, and the inequality ‖…”

Section: Model Descriptionmentioning

confidence: 99%

“…Hence the vector Lyapunov function method is more efficient. The research team led by Professor Zhang has studied the stability of some infinite dimensional nonlinear interconnected systems with stochastic disturbances based on the vector Lyapunov function approach and obtained some important stability results; see [12][13][14].…”

Section: Introductionmentioning

confidence: 99%

“…The Lyapunov stability in the general sense cannot describe the stability with mode constraint condition, and the existing Lyapunov function methods cannot be used to analyze the stability with mode constraint for the systems directly. The motivation for the stability problem with mode constraint comes from the analysis and the design of controllers for automated highway system [13], multirobot operation system [15], formation flying of unmanned aerial vehicles [16], and so on. In a formation one wants controllers to be designed so that any shock-wave arising from disturbance propagation should dampen as it travels away from the source.…”

Section: Introductionmentioning

confidence: 99%

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Stability of Infinite Dimensional Interconnected Systems with Impulsive and Stochastic Disturbances

Yin

Zhang

et al. 2014

Abstract and Applied Analysis

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Some research on the stability with mode constraint for a class of infinite dimensional look-ahead interconnected systems with impulsive and stochastic disturbances is studied by using the vector Lyapunov function approach. Intuitively, the stability with mode constraint is the property of damping disturbance propagation. Firstly, we derive a set of sufficient conditions to assure the stability with mode constraint for a class of general infinite dimensional look-ahead interconnected systems with impulsive and stochastic disturbances. The obtained conditions are less conservative than the existing ones. Secondly, the controller for a class of look-ahead vehicle following systems with the above uncertainties is constructed by the sliding mode control method. Based on the obtained new stability conditions, the domain of the control parameters of the systems is proposed. Finally, a numerical example with simulations is given to show the effectiveness and correctness of the obtained results.

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Exponential mean‐square string stability of vehicular platoon with stochastic disturbance and time delay

Sui,

Zhang,

Dai

2024

Intl J Robust & Nonlinear

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Platooning is an effective way to reduce air resistance and fuel consumption in vehicular transportation. However, stochastically generated disturbances can significantly impact the string stability of platoons. This article proposes a novel control law, based on sliding mode control and leader‐predecessor communications, designed to improve the exponential mean‐square string stability of platoons with Ito‐type stochastic disturbances that consider friction force. Specifically, our approach employs a third‐order nonlinear dynamic model to capture the relevant spatiotemporal correlations present in vehicle platoons. The proposed longitudinal control strategy effectively stabilizes the platoons with time delay and was verified through simulation experimentation. In this study, the stability of sliding mode motion is thoroughly investigated by means of sub‐reachable and practical stability analysis with sliding mode control. The findings of this study provide a theoretical foundation for further research on vehicle platoons with increasingly complicated interference and time delays. Overall, our results demonstrate that our approach can achieve significant improvements in both fuel economy and exhaust emissions while maintaining high levels of string stability, further contributing to the development of efficient and sustainable transportation systems.

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String Exponential Stability With Mode Constraint of Stochastic Vehicle Following Systems

Cited by 4 publications

References 16 publications

Exponential Mean‐Square Stability of Stochastic String Hybrid Systems Under Continuous Non‐Gaussian Excitation

Exponential Mean‐Square Stability of Stochastic String Hybrid Systems Under Continuous Non‐Gaussian Excitation

Stability of Infinite Dimensional Interconnected Systems with Impulsive and Stochastic Disturbances

Exponential mean‐square string stability of vehicular platoon with stochastic disturbance and time delay

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