Nonlinear Analysis-Hybrid Systems最新文献

英文中文

Minimum time problem for the double integrator with a loss-of-control region 具有失去控制区域的双积分器的最小时间问题

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

Nonlinear Analysis-Hybrid Systems

Pub Date : 2026-01-30 DOI: 10.1016/j.nahs.2026.101681

Térence Bayen , Anas Bouali , Loïc Bourdin

In this paper we address the minimum time problem for the double integrator, but here, in contrast with the classical version of this problem, the control is constrained to remain constant as long as the state belongs to a given region of the state space called loss-of-control region. This situation prevents switches from occurring in the loss-of-control region and, therefore, a new analysis has to be performed. For this purpose we prove an appropriate version of the Pontryagin maximum principle in which the necessary conditions comprise two key components. The first is an averaged Hamiltonian gradient condition to determine the optimal constant values of the control in the loss-of-control region. The second is, similarly to hybrid maximum principles found in the literature, that the costate admits discontinuity jumps at the interface between the loss-of-control region and its complement. We then highlight the theoretical use of these necessary conditions by solving analytically the minimum time problem for the double integrator with an illustrative loss-of-control region (precisely, the left vertical half-space). New behaviors are observed such as the lack of dynamic programming principle, of feedback expression and of saturation of the control constraint set. Finally we further illustrate these aspects by solving numerically the same minimum time problem for the double integrator but with two other illustrative loss-of-control regions (first a sloped half-space, then a disk).

在本文中，我们解决了二重积分器的最小时间问题，但在这里，与该问题的经典版本相反，只要状态属于状态空间的给定区域（称为失去控制区域），控制就被约束为保持恒定。这种情况防止开关发生在失去控制的区域，因此，必须执行新的分析。为此，我们证明了一个适当版本的庞特里亚金极大原理，其中必要条件包括两个关键组成部分。首先是一个平均哈密顿梯度条件，用于确定失去控制区域的最优控制常数值。第二种是，与文献中发现的混合极大值原理类似，状态允许在失去控制区域与其补充区域之间的界面处出现不连续跳跃。然后，我们通过解析解决具有说明性失去控制区域（准确地说，是左侧垂直半空间）的双积分器的最小时间问题，突出了这些必要条件的理论应用。发现了缺乏动态规划原理、反馈表达式和控制约束集饱和等新行为。最后，我们通过在数值上解决相同的双积分器的最小时间问题来进一步说明这些方面，但使用另外两个示范性的失去控制区域（首先是倾斜的半空间，然后是磁盘）。

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引用次数: 0

Input-to-state stability in discrete-time stochastic delay systems featuring Markovian switching and impulsive effects 具有马尔可夫切换和脉冲效应的离散随机延迟系统的输入-状态稳定性

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

Nonlinear Analysis-Hybrid Systems

Pub Date : 2026-01-28 DOI: 10.1016/j.nahs.2026.101685

Ting Cai , Pei Cheng , Xin Liu

This paper primarily investigates the

p

th moment exponential input-to-state stability (ISS) of nonlinear discrete-time (DT) impulse random delayed systems with Markovian switching. Firstly, by using the Lyapunov functional, some

p

th moment exponential ISS criteria are presented, which simultaneously consider the unstable and stable effects of switching behavior and impulses. These criteria demonstrate that, regardless of the original system’s stability, proper coordination of impulses, switching, and the original system can achieve stability. Secondly, we apply these theoretical results to assess the ISS of a specific class of neural networks (NNs) subjected to random disturbances. The findings are further substantiated by numerical examples that demonstrate their effectiveness. The research in this paper is of significant importance for addressing stability issues in DT impulse random delayed systems with Markovian switching. It provides valuable insights for control and optimization problems in practical applications.

本文主要研究具有马尔可夫切换的非线性离散时间（DT）脉冲随机时滞系统的第p阶指数输入状态稳定性。首先，利用Lyapunov泛函，给出了同时考虑开关行为和脉冲的不稳定和稳定效应的若干p阶矩指数ISS判据。这些准则表明，无论原系统是否稳定，适当地协调脉冲、开关和原系统都可以达到稳定。其次，我们应用这些理论结果来评估受随机干扰的特定类别的神经网络（nn）的ISS。数值算例进一步证实了上述结论的有效性。本文的研究对于解决具有马尔可夫切换的DT脉冲随机时滞系统的稳定性问题具有重要意义。它为实际应用中的控制和优化问题提供了有价值的见解。

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引用次数: 0

Perfect stationary solutions of reaction–diffusion equations on lattices and regular graphs 格和正则图上反应扩散方程的完全平稳解

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

Nonlinear Analysis-Hybrid Systems

Pub Date : 2026-01-27 DOI: 10.1016/j.nahs.2026.101684

Vladimír Švígler, Jonáš Volek

In this work, we introduce a notion of perfect stationary solutions of reaction–diffusion differential equations on lattices and regular graphs and show its elementary properties. The perfect stationary solutions – a special class of finite-range solutions in which the neighborhood values are determined by the value of the central vertex – generalize periodic stationary solutions. The focus on the solution which attain a finite number of values enables us to reduce the stationary problem from a countable algebraic system of equations to a finite one. However, the possible absence of periodicity in the solutions allows for richer structure of the solutions and their abundance compared to the periodic stationary solutions. We further present results from the theory of perfect colorings in order to prove the existence of the solutions on the square, triangular, and hexagonal grid. As a byproduct, the existence of uncountable number of two-valued stationary solutions on these grids is shown. These two-valued solutions alone can form highly aperiodic and highly irregular patterns. Finally, an application to a bistable reaction–diffusion equation on the square grid is presented.

在本文中，我们引入了反应扩散微分方程在格和正则图上的完全平稳解的概念，并给出了它的基本性质。完美平稳解是一类特殊的有限范围解，其邻域值由中心顶点的值决定。关注获得有限个值的解，使我们能够将平稳问题从可数代数方程组简化为有限代数方程组。然而，与周期性平稳解相比，解中可能不存在周期性，这使得解具有更丰富的结构和丰度。我们进一步给出了完全着色理论的结果，以证明在正方形、三角形和六边形网格上解的存在性。作为副产物，证明了在这些网格上存在不可数的二值平稳解。仅这两值解就可以形成高度非周期性和高度不规则的图案。最后给出了在方形网格上双稳态反应扩散方程的一个应用。

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引用次数: 0

Controller redesign to minimize uniform quantization errors in uncertain linear systems with fixed hardware constraints 在具有固定硬件约束的不确定线性系统中，重新设计控制器以最小化均匀量化误差

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

Nonlinear Analysis-Hybrid Systems

Pub Date : 2026-01-27 DOI: 10.1016/j.nahs.2026.101683

Mircea Şuşcă , Vlad Mihaly , Zsófia Lendek , Irinel-Constantin Morărescu , Petru Dobra

We consider the classical emulation paradigm in which a controller is already designed for a linear time-invariant plant. Motivated by implementation constraints in real applications, we analyze the effects of ubiquitous low-cost quantizers on the closed-loop dynamics. Consequently, we address the robust control problem of an uncertain discrete-time linear process using a regulator affected by the effects of uniform quantization performed by the input–output converters and arithmetical unit. In this setup with fixed hardware resolutions, the regulator’s state-space realization is balanced to minimize the process’ state quantization error while simultaneously maintaining its desired transient response. To characterize the quantization error, we provide an ultimate bound for its worst-case scenario using the input-to-state stability framework. The minimization is performed using off-the-shelf tools, with a characterization of the resulting problem. Finally, a comparative numeric case study showing the tightness of the computed bound is discussed.

我们考虑经典的仿真范例，其中控制器已经为线性定常对象设计。基于实际应用中的实现约束，我们分析了无处不在的低成本量化器对闭环动力学的影响。因此，我们使用受输入输出转换器和算术单元执行的均匀量化影响的调节器来解决不确定离散线性过程的鲁棒控制问题。在这种固定硬件分辨率的设置中，调节器的状态空间实现是平衡的，以最小化过程的状态量化误差，同时保持其所需的瞬态响应。为了表征量化误差，我们使用输入到状态稳定性框架为其最坏情况提供了一个最终边界。最小化是使用现成的工具执行的，并对所产生的问题进行描述。最后，讨论了一个比较的数值研究，说明了计算界的严密性。

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引用次数: 0

Linear dynamical systems with weight functions 具有权函数的线性动力系统

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

Nonlinear Analysis-Hybrid Systems

Pub Date : 2026-01-25 DOI: 10.1016/j.nahs.2026.101680

Rajab Aghamov , Christel Baier , Toghrul Karimov , Joël Ouaknine , Jakob Piribauer

In discrete-time linear dynamical systems (LDSs), a linear map is repeatedly applied to an initial vector yielding a sequence of vectors called the orbit of the system. A weight function assigning weights to the points in the orbit can be used to model quantitative aspects, such as resource consumption, of a system modelled by an LDS. This paper addresses the problems of how to compute the mean payoff, the total accumulated weight, and the discounted accumulated weight of the orbit under continuous weight functions as well as polynomial weight functions as a special case. Additionally, weight functions that are definable in an o-minimal extension of the theory of the reals with exponentiation, which can be shown to be piecewise continuous, are considered. In particular, good ergodic properties of o-minimal weight functions, instrumental to the computation of the mean payoff, are established. Besides general LDSs, the special cases of stochastic LDSs and LDSs with bounded orbits are addressed. Finally, the problem of deciding whether an energy constraint is satisfied by the weighted orbit, i.e., whether the accumulated weight never drops below a given bound, is analysed.

在离散时间线性动力系统（lds）中，将线性映射反复应用于初始向量，得到称为系统轨道的一系列向量。为轨道上的点分配权重的权重函数可用于模拟由LDS建模的系统的定量方面，例如资源消耗。本文讨论了连续权函数和多项式权函数下轨道的平均收益、总累积权和折现累积权的计算问题。此外，还考虑了在幂实数理论的0 -极小扩展中可定义的权函数，它可以被证明是分段连续的。特别是，建立了o最小权函数的良好遍历性质，有助于计算平均收益。除了一般的lds外，还讨论了随机lds和有界轨道lds的特殊情况。最后，分析了加权轨道是否满足能量约束的判定问题，即累积的权值是否不低于给定的边界。

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引用次数: 0

Passivity preservation in interconnections of linear cone complementarity systems with state jumps 具有状态跳变的线性锥互补系统互连的无源保持

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

Nonlinear Analysis-Hybrid Systems

Pub Date : 2026-01-24 DOI: 10.1016/j.nahs.2026.101682

Bernard Brogliato , Aneel Tanwani

This article is largely concerned with generic interconnections of a class of passive nonsmooth nonlinear dynamical systems, namely linear cone complementarity systems (LCCS). We stipulate that each subsystem admits a positive definite storage function that characterizes the passivity of an underlying nonsmooth mapping. We provide algebraic criteria in terms of these individual storage functions to find the storage function which guarantees passivity of the overall interconnected system. State jumps in the interconnections are studied in detail. Examples from dynamic feedback control, switching DAEs, interconnected sweeping processes, and nonsmooth circuits are included as an illustration of the theoretical developments.

本文主要研究一类被动非光滑非线性动力系统，即线性锥互补系统（LCCS）的一般互连问题。我们规定，每个子系统承认一个正定的存储函数，表征底层非光滑映射的无源性。我们根据这些单独的存储函数提供代数准则，以找到保证整个互联系统无源性的存储函数。详细研究了互连中的状态跳变。从动态反馈控制，开关DAEs，互连扫描过程，和非光滑电路的例子包括作为理论发展的例证。

引用次数: 0

Data-driven stability and optimality certificates for hybrid dynamical systems 混合动力系统的数据驱动稳定性和最优性证明

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

Nonlinear Analysis-Hybrid Systems

Pub Date : 2026-01-22 DOI: 10.1016/j.nahs.2026.101678

Carlos A. Montenegro G., Santiago J. Leudo, Ricardo G. Sanfelice

In this paper, we develop a learning-based approach for hybrid systems with a twofold purpose: (i) the construction of Lyapunov functions and (ii) the computation of upper bounds on the cost of system solution. Our approach enforces stability and cost conditions on a finite collection of states and then, by exploiting regularity properties of the system dynamics and stage-cost maps, extends these conditions to all relevant unsampled states. Neural networks are used to learn both a Lyapunov function surrogate and a value-like function whose regularity properties allow us to certify stability (in a practical sense) of a compact set or to find an upper bound on the cost of solutions, which are not required to be unique. We illustrate the approach on nonlinear continuous-time and discrete-time systems, as well as on a hybrid system modeled by set-valued dynamics.

在本文中，我们开发了一种基于学习的混合系统方法，具有双重目的：(i) Lyapunov函数的构造和（ii）系统解代价上界的计算。我们的方法在有限的状态集合上强制执行稳定性和成本条件，然后通过利用系统动力学和阶段成本映射的规律性，将这些条件扩展到所有相关的未采样状态。神经网络用于学习李雅普诺夫函数代理和类值函数，其正则性允许我们证明（在实际意义上）紧集的稳定性或找到解决方案成本的上界，而不需要是唯一的。我们在非线性连续时间系统和离散时间系统以及集值动力学建模的混合系统上说明了这种方法。

引用次数: 0

Switched-gain observer and stabilization of positive complex networks 正复杂网络的开关增益观测器与镇定

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

Nonlinear Analysis-Hybrid Systems

Pub Date : 2026-01-09 DOI: 10.1016/j.nahs.2026.101676

Qingquan Xu , Haoyue Yang , Tarek Raïssi , Junfeng Zhang

This paper presents a switched-gain observer and the corresponding observer-based controller for positive complex networks. An observer-based control approach is proposed using co-positive Lyapunov function and linear programming. A switching rule is established for the resulting hybrid observation system. The designed observer gain can be dynamically adjusted according to the change of state. State estimation is utilized to generate control signals. Under the designed observer and controller, the positivity and stability of the system are guaranteed. The main novelties of this paper lie in that: (i) A novel switched-gain observer is designed for positive complex networks, (ii) An observer-based controller is proposed, and (iii) A tractable design and analysis approach is developed using a co-positive Lyapunov function and linear programming. Finally, several illustrated examples are given to verify the validity of the proposed observer and controller.

针对正复杂网络，提出了一种开关增益观测器和相应的基于观测器的控制器。利用协正李雅普诺夫函数和线性规划，提出了一种基于观测器的控制方法。建立了混合观测系统的切换规则。所设计的观测器增益可以根据状态的变化进行动态调整。利用状态估计产生控制信号。在设计的观测器和控制器下，保证了系统的正性和稳定性。本文的主要新颖之处在于：(i)为正复杂网络设计了一种新的开关增益观测器，（ii）提出了一种基于观测器的控制器，以及（iii）使用协正Lyapunov函数和线性规划开发了一种易于处理的设计和分析方法。最后，通过实例验证了所提观测器和控制器的有效性。

引用次数: 0

Interval estimation for continuous-time linear switched systems via ellipsoidal analysis 基于椭球分析的连续时间线性切换系统区间估计

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

Nonlinear Analysis-Hybrid Systems

Pub Date : 2026-01-04 DOI: 10.1016/j.nahs.2026.101675

Fan Zhang , Zhenhua Wang , Nacim Meslem , Tarek Raïssi , Yi Shen

This paper proposes a two-step interval estimation approach for continuous-time linear switched systems with unknown but bounded uncertainties. First, a robust observer design method is proposed to obtain point estimation and attenuate the effects of the system uncertainties. Second, based on a system split method, an ellipsoidal analysis method is introduced to provide the smallest enclosures of the estimation error. By merging the interval evaluation of the estimation error with the point estimate provided by the robust observer, the proposed method allows one to obtain a tight interval estimation of the actual state vector with less restrictive and simple design conditions. The proposed method solves the interval estimation problem for switched systems in two cases: switched systems under an arbitrary switching signal and switched systems under an average dwell time switching condition. In terms of accuracy, comparison studies show that the proposed method outperforms some existing methods in the literature.

针对具有未知但有界不确定性的连续时间线性切换系统，提出了一种两步区间估计方法。首先，提出了一种鲁棒观测器设计方法，以获得点估计并减弱系统不确定性的影响。其次，在系统分裂方法的基础上，引入椭球面分析法，给出了估计误差的最小范围；通过将估计误差的区间估计与鲁棒观测器提供的点估计相结合，该方法可以在较少的限制和简单的设计条件下获得实际状态向量的紧密区间估计。该方法解决了任意切换信号下切换系统和平均停留时间切换条件下切换系统两种情况下切换系统的区间估计问题。在准确性方面，对比研究表明，本文提出的方法优于文献中已有的一些方法。

引用次数: 0

Maximum period construction and nonsingularity analysis of NFSR with fault resistance 带故障电阻的NFSR最大周期构造及非奇异性分析

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

Nonlinear Analysis-Hybrid Systems

Pub Date : 2026-01-03 DOI: 10.1016/j.nahs.2026.101677

Jiangying Li , Hao Zhang , Chengye Zou , Feifei Yang , Haonan Li

Nonlinear feedback shift register (NFSR) is an important method to generate pseudorandom sequences and its robustness needs to be acknowledged. This paper investigates the robustness of NFSR with fault detection and handling capabilities via semi-tensor product (STP). Firstly, the NFSR model with fault is constructed and the nonsingularity criteria of this model are derived. Secondly, an efficient fault detection mechanism is designed to find the fault node and controllers are introduced to eliminate the impact of fault. Thus, the studied NFSR maintains nonsingular after control. Finally, the period of the controlled NFSR is optimized to the maximum, such that the pseudorandomness of generated sequence has been enhanced.

非线性反馈移位寄存器（NFSR）是生成伪随机序列的一种重要方法，其鲁棒性有待进一步研究。本文通过半张量积（STP）研究了具有故障检测和处理能力的NFSR的鲁棒性。首先，建立了带故障的NFSR模型，并推导了该模型的非奇异准则；其次，设计了有效的故障检测机制来查找故障节点，并引入控制器来消除故障的影响；因此，研究的NFSR在控制后保持非奇异。最后，将控制的NFSR周期优化到最大，增强了生成序列的伪随机性。

引用次数: 0

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