Nonlinear Analysis-Hybrid Systems最新文献

英文中文

Sure robust global versus robust global almost sure convergence: Implementing a dynamic random coefficient selection in a quaternion-hysteresis-based distributed hybrid algorithm 鲁棒全局与鲁棒全局几乎肯定收敛：在基于四元数-滞后的分布式混合算法中实现动态随机系数选择

IF 3.7 2区计算机科学 Q2 AUTOMATION & CONTROL SYSTEMS

Nonlinear Analysis-Hybrid Systems

Pub Date : 2025-05-01 Epub Date: 2025-01-31 DOI: 10.1016/j.nahs.2025.101578

Dandan Zhang , Xin Jin , Hongye Su

By employing Lyapunov-like conditions along with the stochastic invariance principle, we develop a quaternion-hysteresis-based distributed stochastic hybrid feedback algorithm aimed at achieving robust global attitude synchronization, addressing both sure and almost sure convergence. The distributed hybrid algorithm integrates a hybrid control variable that experiences continuous changes and instantaneous resets according to a unit quaternion-based reset rule and the associated hysteresis-based conditions. In this hysteresis-based hybrid framework, by treating the reset coefficients as random variables, these coefficients introduce the unique source of randomness; these coefficients are dynamically and randomly selected by the reset rule, leading to varying hysteresis half-widths and, consequently, different nominal levels of robustness; the orientation of the spring force, which reversely pulls the rigid body along the rotation axis to prevent the unwinding phenomenon, is determined by the deterministic sign of the hybrid control variable, whereas the hysteresis half-widths can delay this pulling. By dynamically and randomly adjusting the stochastic hysteresis half-widths, we create a flexible tradeoff between mitigating the amount of unwinding and enhancing the nominal level of robustness to measurement noise. By imposing different constraints on the support domain of random reset coefficients, the hybrid algorithm achieves both sure robust global and robust global almost sure attitude synchronization.

通过采用类李雅普诺夫条件和随机不变性原理，我们开发了一种基于四元数-滞后的分布式随机混合反馈算法，旨在实现鲁棒的全球姿态同步，解决确定性和几乎确定性收敛问题。分布式混合算法集成了一个混合控制变量，该控制变量根据基于单位四元数的重置规则和相关的基于滞后的条件进行连续变化和瞬时重置。在这种基于迟滞的混合框架中，通过将重置系数作为随机变量处理，这些系数引入了唯一的随机性来源；这些系数是由重置规则动态和随机选择的，导致不同的滞后半宽度，因此，不同的名义鲁棒性水平；弹簧力的方向由混合控制变量的确定性符号决定，弹簧力沿着旋转轴反向拉动刚体以防止放卷现象，而滞后半宽度可以延迟这种拉动。通过动态和随机调整随机滞后半宽度，我们在减轻unwind量和增强对测量噪声的标称鲁棒性水平之间创建了一个灵活的权衡。通过对随机重置系数支持域施加不同的约束，混合算法实现了鲁棒全局和鲁棒全局几乎确定的姿态同步。

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引用次数: 0

Chaotic dynamics of three-dimensional piecewise linear systems with sliding heteroclinic cycles 具有滑动异斜周期的三维分段线性系统的混沌动力学

IF 3.7 2区计算机科学 Q2 AUTOMATION & CONTROL SYSTEMS

Nonlinear Analysis-Hybrid Systems

Pub Date : 2025-05-01 Epub Date: 2025-02-13 DOI: 10.1016/j.nahs.2025.101584

Zhe Zhao, Tiantian Wu

This paper explores chaotic dynamics in a class of three-dimensional piecewise linear systems with sliding heteroclinic cycles which are composed of two sliding heteroclinic orbits connecting two saddle-foci or a saddle-focus and a saddle. The system with a sliding heteroclinic cycle connecting two saddle-foci has infinite chaotic invariant sets under an eigenvalue condition, while the existence of chaotic invariant sets for the system with a sliding heteroclinic cycle connecting a saddle-focus and a saddle needs an additional condition except for an eigenvalue condition.

本文研究了一类具有滑动异斜环的三维分段线性系统的混沌动力学，该系统由两个滑动异斜轨道连接两个鞍点或一个鞍点和一个鞍点。连接两个鞍焦点的滑动异斜环系统在特征值条件下具有无限混沌不变量集，而连接鞍焦点和鞍的滑动异斜环系统混沌不变量集的存在性除了特征值条件外还需要一个附加条件。

引用次数: 0

A Floquet–Lyapunov theory for nonautonomous linear periodic differential equations with piecewise constant deviating arguments 具有分段常偏差参数的非自治线性周期微分方程的Floquet-Lyapunov理论

IF 3.7 2区计算机科学 Q2 AUTOMATION & CONTROL SYSTEMS

Nonlinear Analysis-Hybrid Systems

Pub Date : 2025-05-01 Epub Date: 2024-12-30 DOI: 10.1016/j.nahs.2024.101574

Ricardo Torres Naranjo

In this work, we introduce a version of the classic Floquet–Lyapunov theorem for

ω -

periodic nonautonomous linear differential equations with piecewise constant arguments of generalized type (IDEPCAG or DEPCAG). We demonstrate that the nonautonomous linear IDEPCAG is kinematically similar to an autonomous linear ordinary differential equation. Additionally, we provide explicit formulas for the Floquet normal form of the fundamental matrix of IDEPCAG nonautonomous linear systems. These are very useful for analyzing qualitative properties such as the stability and periodicity of the solutions, making the study of IDEPCAG systems more accessible. Finally, we have included examples to demonstrate the effectiveness of our results.

在本文中，我们引入了具有分段常数广义型（IDEPCAG或DEPCAG）的ω -周期非自治线性微分方程的经典Floquet-Lyapunov定理。我们证明了非自治线性IDEPCAG在运动学上类似于一个自治线性常微分方程。此外，我们还给出了IDEPCAG非自治线性系统基本矩阵的Floquet范式的显式公式。这对于分析解的稳定性和周期性等定性性质非常有用，使IDEPCAG体系的研究更加容易。最后，我们列举了一些例子来证明我们的结果的有效性。

引用次数: 0

Strategy optimization of controlled evolutionary games on a two-layer coupled network using Lebesgue sampling 基于Lebesgue抽样的两层耦合网络可控进化博弈策略优化

IF 3.7 2区计算机科学 Q2 AUTOMATION & CONTROL SYSTEMS

Nonlinear Analysis-Hybrid Systems

Pub Date : 2025-05-01 Epub Date: 2024-12-20 DOI: 10.1016/j.nahs.2024.101570

Shihua Fu , Ling Li , Jun-e Feng

This paper studies the strategy optimization for a type of evolutionary games on coupled networks under sampled-data state feedback controls (SDSFCs) with Lebesgue sampling, which is more economical than traditional state feedback controls. Firstly, using the semi-tensor product of matrices, the algebraic expression of a controlled evolutionary game on a two-layer coupled network is established. Secondly, for a given Lebesgue sampling region, a necessary and sufficient condition is presented to detect whether each player’s payoff can ultimately remain at or above its own threshold, and the corresponding SDSFCs are designed. Furthermore, for a given signal of Lebesgue sampling, an approach is provided to obtain a desired sampling region, under which each player’s payoff always meets their threshold condition after a certain time. Finally, an illustrative example is provided to support our new results.

本文研究了一类耦合网络演化博弈在Lebesgue采样数据状态反馈控制（sdsfc）下的策略优化问题，该控制比传统的状态反馈控制更具经济性。首先，利用矩阵的半张量积，建立了两层耦合网络上可控进化对策的代数表达式；其次，对于给定的Lebesgue采样区域，给出了检测每个参与者的收益最终是否能保持在或高于其阈值的充分必要条件，并设计了相应的sdsfc。进一步，对于给定的勒贝格采样信号，给出了一种获得期望采样区域的方法，在该采样区域下，每个参与人的收益在一定时间后总是满足其阈值条件。最后，给出了一个示例来支持我们的新结果。

引用次数: 0

Fixed-time intermittent control for a class of switched chaotic systems 一类切换混沌系统的定时间歇控制

IF 3.7 2区计算机科学 Q2 AUTOMATION & CONTROL SYSTEMS

Nonlinear Analysis-Hybrid Systems

Pub Date : 2025-05-01 Epub Date: 2025-02-27 DOI: 10.1016/j.nahs.2025.101587

Luxia Han, Runzi Luo, Panpan Zhang, Xianzhou Liu, Shuai Liu, Zijun Song

This paper is a pilot study on the fixed-time stability of switched chaotic systems via the intermittent control. Some novel fixed-time stability theorems that generalize some previous related research works and have a broad application prospect, are proposed. According to the proposed fixed-time stability theorems, a new intermittent switching controller for reducing information transmission and saving control energy is provided to achieve the fixed-time stability of the considered switched chaotic systems. In addition, numerical simulations are conducted to verify the correctness of resulting conclusion.

本文是利用间歇控制方法研究切换混沌系统的定时稳定性的初步研究。提出了一些新的固定时稳定性定理，这些定理推广了前人的相关研究成果，具有广阔的应用前景。根据所提出的定时稳定性定理，提出了一种减少信息传输和节省控制能量的间歇切换控制器，以实现所考虑的切换混沌系统的定时稳定性。并通过数值模拟验证了所得结论的正确性。

引用次数: 0

STL and wSTL control synthesis: A disjunction-centric mixed-integer linear programming approach STL和wSTL控制综合：一种以析取为中心的混合整数线性规划方法

IF 3.7 2区计算机科学 Q2 AUTOMATION & CONTROL SYSTEMS

Nonlinear Analysis-Hybrid Systems

Pub Date : 2025-05-01 Epub Date: 2025-01-29 DOI: 10.1016/j.nahs.2025.101576

Gustavo A. Cardona, Disha Kamale, Cristian-Ioan Vasile

This paper introduces an efficient optimization-based control synthesis methodology tailored for Signal Temporal Logic (STL) and its extension, weighted Signal Temporal Logic (wSTL). While STL captures Boolean and temporal operators, wSTL further allows users to express preferences and priorities over concurrent and sequential tasks denoted by weights over logical and temporal operators along with satisfaction times. The proposed approach utilizes Mixed Integer Linear Programming (MILP) for synthesis with both STL and wSTL formulae. We introduce efficient disjunction-centric encodings for STL and wSTL that capture both qualitative and quantitative semantics. This encoding minimizes the number of variables and constraints necessary to represent STL and wSTL formulae by efficiently handling conjunction operations (e.g., conjunction, always operators) and only introducing variables when disjunction operations are used (e.g., disjunction, eventually). Multiple case studies are conducted to demonstrate the proposed methodology’s operation and computational efficiency for the control synthesis with STL and wSTL specifications. While non-linear dynamics and predicates can be considered using piecewise linear functions, this work focuses on linear predicates and dynamics. We show how cost functions involving potentially conflicting objectives expressed in terms of states, controls, and satisfaction robustness impact the solutions to the control synthesis problem for STL and wSTL. We conduct a sensitivity analysis of weights used in wSTL formulae, offering detailed insights into how these weights modulate solutions for given formulae. Finally, the time performance of the disjunction-centric encodings for both STL and wSTL is compared against state-of-the-art frameworks, comprehensively evaluating their efficiency and practical applicability.

本文介绍了一种为信号时序逻辑（STL）及其扩展加权信号时序逻辑（wSTL）量身定制的有效的基于优化的控制综合方法。虽然STL捕获布尔运算符和时间运算符，但wSTL进一步允许用户表达对并发和顺序任务的偏好和优先级，这些任务由逻辑和时间运算符的权重以及满足时间表示。该方法利用混合整数线性规划（MILP）对STL和wSTL公式进行综合。我们为STL和wSTL引入了高效的以析取为中心的编码，以捕获定性和定量语义。这种编码通过有效地处理连接操作（例如，连接，总是操作符）和只在使用分离操作（例如，disjunction，最终）时引入变量来最小化表示STL和wSTL公式所需的变量和约束的数量。进行了多个案例研究，以证明所提出的方法在与STL和wSTL规范的控制综合方面的操作和计算效率。虽然可以使用分段线性函数考虑非线性动态和谓词，但本工作侧重于线性谓词和动态。我们展示了包含以状态、控制和满意度鲁棒性表达的潜在冲突目标的成本函数如何影响STL和wSTL的控制综合问题的解决方案。我们对wSTL公式中使用的权重进行了敏感性分析，提供了这些权重如何调节给定公式的解决方案的详细见解。最后，将以析取为中心的STL和wSTL编码的时间性能与最先进的框架进行了比较，全面评估了它们的效率和实用性。

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引用次数: 0

Disturbance decoupling controller design of switched Boolean control networks in recursion 递归切换布尔控制网络的干扰解耦控制器设计

IF 3.7 2区计算机科学 Q2 AUTOMATION & CONTROL SYSTEMS

Nonlinear Analysis-Hybrid Systems

Pub Date : 2025-05-01 Epub Date: 2024-12-03 DOI: 10.1016/j.nahs.2024.101558

Xiangshan Kong , Haitao Li

This paper studies the disturbance decoupling problem (DDP) of switched Boolean control networks (SBCNs) by the methodology of recursion. All the state nodes of the original SBCNs are split into two parts based on whether or not the state node influences the outputs. By driving the part of state nodes which influence the outputs to the largest control invariant set, the concept of DDP in recursion is proposed. Using the algebraic state space representation (ASSR) method, both mode-independent and mode-dependent state feedback controllers are constructed to solve the DDP in recursion of SBCNs. Furthermore, based on the obtained mode-independent state feedback DDP controllers, the mode-independent output feedback controllers are designed for the DDP in recursion of SBCNs.

本文用递归方法研究了切换布尔控制网络的干扰解耦问题。原始sbcn的所有状态节点根据状态节点是否影响输出分为两部分。通过将影响输出的部分状态节点驱动到最大控制不变量集中，提出了递归中的DDP概念。利用代数状态空间表示（ASSR）方法，构造了模式无关和模式相关的状态反馈控制器来解决sbcn递归中的DDP问题。在此基础上，针对sbcn递归中的DDP，设计了与模式无关的输出反馈控制器。

引用次数: 0

On (θ,T)-periodic solutions of abstract generalized ODEs and applications to Volterra–Stieltjes–type integral equations 抽象广义ode的（θ，T）-周期解及其在volterra - stieltje型积分方程中的应用

IF 3.7 2区计算机科学 Q2 AUTOMATION & CONTROL SYSTEMS

Nonlinear Analysis-Hybrid Systems

Pub Date : 2025-05-01 Epub Date: 2024-12-27 DOI: 10.1016/j.nahs.2024.101573

M. Ap. Silva , E.M. Bonotto , R. Collegari , M. Federson , M.C. Gadotti

It is known that generalized ordinary differential equations (generalized ODEs for short) encompass other types of equations such as impulsive differential equations as well as dynamic equations on time scales. The present paper concerns the theory of

(θ, T)

-periodic solutions in the framework of generalized ODEs in Banach spaces. We exhibit necessary and sufficient conditions for a solution of a generalized ODE to be

(θ, T)

-periodic. Moreover, we develop the Floquet theory of homogeneous linear generalized ODEs and, as a consequence, we present a characterization of fundamental matrices for the finite dimensional case. As an illustration, we apply the main results to Volterra–Stieltjes–type integral equations.

众所周知，广义常微分方程（简称广义微分方程）包含了其他类型的方程，如脉冲微分方程和时间尺度上的动态方程。本文研究了Banach空间中广义ode框架下（θ，T）-周期解的理论。给出了广义ODE解为（θ，T）周期的充分必要条件。此外，我们发展了齐次线性广义ode的Floquet理论，因此，我们给出了有限维情况下基本矩阵的表征。作为说明，我们将主要结果应用于volterra - stieltje型积分方程。

引用次数: 0

Faithful dynamic timing analysis of digital circuits using continuous thresholded mode-switched ODEs 基于连续阈值模式切换ode的数字电路忠实动态时序分析

IF 3.7 2区计算机科学 Q2 AUTOMATION & CONTROL SYSTEMS

Nonlinear Analysis-Hybrid Systems

Pub Date : 2025-05-01 Epub Date: 2025-01-06 DOI: 10.1016/j.nahs.2024.101572

Arman Ferdowsi , Matthias Függer , Thomas Nowak , Ulrich Schmid , Michael Drmota

Thresholded hybrid systems are restricted dynamical systems, where the current mode, and hence the ODE system describing its behavior, is solely determined by externally supplied digital input signals and where the only output signals are digital ones generated by comparing an internal state variable to a threshold value. An attractive feature of such systems is easy composition, which is facilitated by their purely digital interface. A particularly promising application domain of thresholded hybrid systems is digital integrated circuits: Modern digital circuit design considers them as a composition of Millions and even Billions of elementary logic gates, like inverters, OR and AND. Since every such logic gate is eventually implemented as an electronic circuit, however, which exhibits a behavior that is governed by some ODE system, thresholded hybrid systems are ideally suited for making the transition from the analog to the digital world rigorous.

In this paper, we prove that the mapping from digital input signals to digital output signals is continuous for a large class of thresholded hybrid systems. Moreover, we show that, under some mild conditions regarding causality, this continuity also continues to hold for arbitrary compositions, which in turn guarantees that the composition faithfully captures the analog reality. By applying our generic results to some recently developed thresholded hybrid gate models, both for single-input single-output gates like inverters and for a two-input CMOS NOR gate, we show that they are continuous. Moreover, we provide a novel thresholded hybrid model for the two-input NOR gate, which is not only continuous but also, unlike the existing one, faithfully models all multi-input switching effects.

阈值混合系统是受限制的动态系统，其中当前模式以及描述其行为的ODE系统完全由外部提供的数字输入信号决定，其中唯一的输出信号是通过比较内部状态变量与阈值产生的数字信号。这种系统的一个吸引人的特点是易于组成，这是由它们的纯数字接口促进的。阈值混合系统的一个特别有前途的应用领域是数字集成电路：现代数字电路设计认为它们是由数百万甚至数十亿个基本逻辑门组成的，如逆变器，或和与。然而，由于每个这样的逻辑门最终都是作为电子电路实现的，它表现出由某些ODE系统控制的行为，因此阈值混合系统非常适合从模拟世界严格过渡到数字世界。本文证明了一大类阈值混合系统从数字输入信号到数字输出信号的映射是连续的。此外，我们表明，在一些关于因果关系的温和条件下，这种连续性也继续适用于任意组合，这反过来又保证了组合忠实地捕捉模拟现实。通过将我们的一般结果应用于一些最近开发的阈值混合门模型，无论是单输入单输出门，如逆变器还是双输入CMOS NOR门，我们表明它们是连续的。此外，我们还为双输入NOR门提供了一种新的阈值混合模型，该模型不仅是连续的，而且与现有模型不同，它忠实地模拟了所有多输入开关效应。

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引用次数: 0

Reachability analysis of recurrent neural networks 递归神经网络的可达性分析

IF 3.7 2区计算机科学 Q2 AUTOMATION & CONTROL SYSTEMS

Nonlinear Analysis-Hybrid Systems

Pub Date : 2025-05-01 Epub Date: 2025-02-21 DOI: 10.1016/j.nahs.2025.101581

Sung Woo Choi , Yuntao Li , Xiaodong Yang , Tomoya Yamaguchi , Bardh Hoxha , Georgios Fainekos , Danil Prokhorov , Hoang-Dung Tran

The paper proposes a new sparse star set representation and extends the recent star reachability method to verify the robustness of vanilla, long short-term memory (LSTM), and gated recurrent units (GRU) recurrent neural networks (RNNs) for safety-critical applications. RNNs are a popular machine learning method for various applications, but they are vulnerable to adversarial attacks, where slightly perturbing the input sequence can lead to an unexpected result. Recent notable techniques for verifying RNNs include unrolling and invariant inference approaches. The first method has scaling issues since unrolling an RNN creates a large feedforward neural network. The second method, using invariant sets, has better scalability but can produce unknown results due to the accumulation of over-approximation errors over time. This paper introduces a complementary verification method for RNNs that is both sound and complete. A relaxation parameter can be used to convert the method into a fast over-approximation method that still provides soundness guarantees. The vanilla RNN verification method is designed to be used with NNV, a tool for verifying deep neural networks and learning-enabled cyber–physical systems, while the verification approach of LSTM and GRU RNNs are implemented on StarV. Compared to state-of-the-art methods for verifying a vanilla RNN, the extended exact reachability method is

10 \times

faster, and the over-approximation method is

100 \times

5000 \times

faster. Although the sparse star set is slow compared to state-of-the-art methods, it was able to verify more robust cases in general than them.

本文提出了一种新的稀疏星集表示，并扩展了最近的星可达性方法来验证vanilla、长短期记忆（LSTM）和门控循环单元（GRU）递归神经网络（rnn）在安全关键应用中的鲁棒性。rnn是一种流行的机器学习方法，适用于各种应用，但它们容易受到对抗性攻击，其中稍微干扰输入序列可能导致意想不到的结果。最近验证rnn的著名技术包括展开和不变推理方法。第一种方法有缩放问题，因为展开RNN会创建一个大的前馈神经网络。第二种方法使用不变集，具有更好的可伸缩性，但由于随着时间的推移过度逼近误差的积累，可能产生未知的结果。本文介绍了一种既健全又完备的rnn互补验证方法。可以使用松弛参数将该方法转换为快速的过逼近方法，但仍能提供可靠性保证。香草RNN验证方法被设计为与NNV一起使用，NNV是一种验证深度神经网络和支持学习的网络物理系统的工具，而LSTM和GRU RNN的验证方法则在StarV上实现。与最先进的验证香草RNN的方法相比，扩展精确可达性方法快了10倍，过度逼近方法快了100倍到5000倍。尽管与最先进的方法相比，稀疏星集的速度较慢，但总的来说，它能够验证比它们更健壮的情况。

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