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 : 2025-01-31 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

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 : 2025-01-29 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

Multiple circles formation-circumnavigation switching control around a nonstationary target 非静止目标多圆编队-绕航切换控制

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

Nonlinear Analysis-Hybrid Systems

Pub Date : 2025-01-25 DOI: 10.1016/j.nahs.2025.101577

Bo Chen, Wei Zhu

In this study, the problem of multiple circles formation-circumnavigation switching control around a nonstationary target of multiple heterogeneous autonomous underwater vehicle (AUV) systems with intermittent communication among partial individuals is investigated. An intermittent communication-based two-layer control strategy is proposed, comprising finite time observers and finite time controller. Since the communication between individuals is intermittent and only partial AUVs can directly obtain partial information from the target, a distributed adaptive finite-time hybrid observer is designed to estimate the information of the target. Additionally, another observer is developed to estimate the state of cluster leader. Subsequently, based on geometric structure and variable substitution, a distributed finite-time multiple circles formation-circumnavigation switching controller is designed, using the estimated value as the reference signal. The controller enables smooth switching between formation and circumnavigation for multiple AUV systems in intermittent communication scenarios, which can effectively improve the economy and practicality of applications. A homogeneous technique is used to show that the control objective can be achieved in finite time under the proposed controller. Numerical simulations are conducted to illustrate the effectiveness of the proposed control strategy.

研究了局部个体间存在间歇通信的多异构自主水下航行器（AUV）系统围绕非平稳目标的多圆形成-环航切换控制问题。提出了一种基于间歇通信的两层控制策略，包括有限时间观测器和有限时间控制器。由于个体间的通信是断断续续的，并且只有部分auv能够直接获取目标的部分信息，因此设计了一种分布式自适应有限时间混合观测器来估计目标的信息。此外，还建立了另一个观测器来估计集群领导者的状态。随后，基于几何结构和变量替换，以估计值为参考信号，设计了一种分布式有限时间多圆编队-环球切换控制器。该控制器可实现多个AUV系统在间歇通信场景下的编队和绕航平滑切换，有效提高了应用的经济性和实用性。采用齐次技术证明了所提出的控制器能在有限时间内实现控制目标。通过数值仿真验证了所提控制策略的有效性。

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引用次数: 0

Attack-resilient corrective control of nondeterministic asynchronous sequential machines and its application to a space-borne digital system 不确定异步顺序机的抗攻击纠偏控制及其在星载数字系统中的应用

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

Nonlinear Analysis-Hybrid Systems

Pub Date : 2025-01-16 DOI: 10.1016/j.nahs.2025.101575

Jung-Min Yang , Seong Woo Kwak

This article addresses a novel attack-resilient corrective control scheme for nondeterministic input/state asynchronous sequential machines (ASMs) vulnerable to actuator attacks. The considered actuator attack causes ASMs to undergo unauthorized state transitions in both fundamental and non-fundamental mode. In comparison with the case of deterministic ASMs, different control objectives and reachability conditions should be presented to fulfill complete attack detection and recovery. In the framework of corrective control theory with the state-burst feedback, we present the existence condition and design procedure for an attack-resilient corrective controller which harnesses nondeterminism in the machine’s operation. To demonstrate the superiority and applicability of the proposed control strategy, hardware experiments on field-programmable gate array (FPGA) circuits implementing a space-borne digital system are conducted and convincing experimental verifications are provided.

本文针对易受致动器攻击的不确定性输入/状态异步顺序机（asm）提出了一种新的抗攻击纠错控制方案。考虑的执行器攻击导致asm在基本和非基本模式下进行未经授权的状态转换。与确定性asm相比，要实现完整的攻击检测和恢复，需要提出不同的控制目标和可达性条件。在状态突发反馈纠偏控制理论的框架下，给出了一种利用机器运行中的不确定性的抗攻击纠偏控制器的存在条件和设计过程。为了证明所提出的控制策略的优越性和适用性，在实现星载数字系统的现场可编程门阵列（FPGA）电路上进行了硬件实验，并提供了令人信服的实验验证。

引用次数: 0

Reachability analysis for linear systems with uncertain parameters using polynomial zonotopes 参数不确定线性系统的可达性分析

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

Nonlinear Analysis-Hybrid Systems

Pub Date : 2025-01-09 DOI: 10.1016/j.nahs.2024.101571

Yushen Huang , Ertai Luo , Stanley Bak, Yifan Sun

In real world applications, uncertain parameters are the rule rather than the exception. We present a reachability algorithm for linear systems with uncertain parameters and inputs using set propagation of polynomial zonotopes. In contrast to previous methods, our approach is able to tightly capture the non-convexity of the reachable set. Building up on our main result, we show how our reachability algorithm can be extended to handle linear time-varying systems as well as linear systems with time-varying parameters. Moreover, our approach opens up new possibilities for reachability analysis of linear time-invariant systems, nonlinear systems, and hybrid systems. We compare our approach to other state of the art methods, with superior tightness on two benchmarks including a 9-dimensional vehicle platooning system. Moreover, as part of the journal extension, we investigate through a polynomial zonotope with special structure named multi-affine zonotopes and its optimization problem. We provide the corresponding optimization algorithm and experiment over the examples obtained from two benchmark systems, showing the efficiency and scalability comparing to the state of the art method for handling such type of set representation.

在现实世界的应用程序中，不确定的参数是规则而不是例外。利用多项式带拓扑的集合传播，提出了具有不确定参数和输入的线性系统的可达性算法。与以前的方法相比，我们的方法能够很好地捕捉可达集的非凸性。在我们的主要结果的基础上，我们展示了如何将可达性算法扩展到处理线性时变系统以及具有时变参数的线性系统。此外，我们的方法为线性定常系统、非线性系统和混合系统的可达性分析开辟了新的可能性。我们将我们的方法与其他最先进的方法进行了比较，在包括9维车辆队列系统在内的两个基准上具有优越的密封性。此外，作为期刊扩展的一部分，我们研究了一种具有特殊结构的多项式带拓扑——多仿射带拓扑及其优化问题。我们提供了相应的优化算法，并对从两个基准系统中获得的示例进行了实验，与处理此类集合表示的最先进方法相比，显示了效率和可扩展性。

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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 : 2025-01-06 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

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 : 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

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 : 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

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 : 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

Finite bit rate stabilization of switched linear systems with bounded delay based on event-triggering control 基于事件触发控制的有界延迟切换线性系统的有限比特率稳定

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

Nonlinear Analysis-Hybrid Systems

Pub Date : 2024-12-10 DOI: 10.1016/j.nahs.2024.101567

Yihong Tang, Yuan Liu, Qiang Ling

This paper investigates the finite bit rate stabilization of a switched linear system whose feedback packets are transmitted through a communication network with bounded time-varying delays. The unknown network delay and mode switching cause unavoidable asynchronous modes between the sensor and the controller, and greatly complicate the stabilization of that system. To resolve these issues, an event-triggering mechanism and a quantization method with a finite bit rate are proposed to sample, quantize and transmit the feedback signals. Furthermore, state estimation updating methods are designed to eliminate the effects of time-varying delays on state estimation errors. We derive sufficient stabilizing conditions in terms of average dwell time and feedback bit rate through determining the convergence rates of the Lyapunov function at sampling instants under different switching scenarios. Simulations are presented to verify the effectiveness of the proposed strategies.

本文研究了反馈数据包通过有界时变延迟通信网络传输的交换线性系统的有限比特率稳定问题。未知的网络时延和模式切换导致传感器和控制器之间不可避免地出现异步模式，使系统的稳定变得非常复杂。为了解决这些问题，提出了一种事件触发机制和一种有限比特率的量化方法来对反馈信号进行采样、量化和传输。此外，设计了状态估计更新方法，以消除时变延迟对状态估计误差的影响。通过确定李雅普诺夫函数在不同切换场景下采样时刻的收敛速率，我们从平均停留时间和反馈比特率方面得到了足够的稳定条件。仿真结果验证了所提策略的有效性。

引用次数: 0

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