Nonlinear Analysis-Hybrid Systems最新文献

英文中文

Efficient strategy synthesis for switched stochastic systems with distributional uncertainty 具有分布不确定性的开关随机系统的高效策略合成

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

Nonlinear Analysis-Hybrid Systems

Pub Date : 2024-11-14 DOI: 10.1016/j.nahs.2024.101554

Ibon Gracia , Dimitris Boskos , Morteza Lahijanian , Luca Laurenti , Manuel Mazo Jr.

We introduce a framework for the control of discrete-time switched stochastic systems with uncertain distributions. In particular, we consider stochastic dynamics with additive noise whose distribution lies in an ambiguity set of distributions that are

ɛ -

close, in the Wasserstein distance sense, to a nominal one. We propose algorithms for the efficient synthesis of distributionally robust control strategies that maximize the satisfaction probability of reach-avoid specifications with either a given or an arbitrary (not specified) time horizon, i.e., unbounded-time reachability. The framework consists of two main steps: finite abstraction and control synthesis. First, we construct a finite abstraction of the switched stochastic system as a robust Markov decision process (robust MDP) that encompasses both the stochasticity of the system and the uncertainty in the noise distribution. Then, we synthesize a strategy that is robust to the distributional uncertainty on the resulting robust MDP. We employ techniques from optimal transport and stochastic programming to reduce the strategy synthesis problem to a set of linear programs, and propose a tailored and efficient algorithm to solve them. The resulting strategies are correctly refined into switching strategies for the original stochastic system. We illustrate the efficacy of our framework on various case studies comprising both linear and non-linear switched stochastic systems.

我们为具有不确定分布的离散时间切换随机系统的控制引入了一个框架。特别是，我们考虑了具有加性噪声的随机动力学，其分布位于一个模糊集合中，从瓦瑟斯坦距离意义上讲，该集合中的分布与标称分布ɛ接近。我们提出了高效合成分布稳健控制策略的算法，这些策略能在给定或任意（未指定）时间跨度（即无时间限制可达性）内最大化可达-避免规格的满足概率。该框架包括两个主要步骤：有限抽象和控制合成。首先，我们将开关随机系统有限抽象为鲁棒马尔可夫决策过程（鲁棒 MDP），其中包含系统的随机性和噪声分布的不确定性。然后，我们综合出一种策略，该策略对由此产生的鲁棒马尔可夫决策过程的分布不确定性具有鲁棒性。我们采用最优传输和随机编程的技术，将策略综合问题简化为一组线性程序，并提出了一种量身定制的高效算法来解决它们。由此产生的策略被正确地提炼为原始随机系统的切换策略。我们通过线性和非线性切换随机系统的各种案例研究来说明我们的框架的有效性。

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引用次数: 0

Sustainable solution for hybrid differential game with regime shifts and random duration 具有制度转换和随机持续时间的混合微分博弈的可持续解决方案

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

Nonlinear Analysis-Hybrid Systems

Pub Date : 2024-11-12 DOI: 10.1016/j.nahs.2024.101553

Yilun Wu, Anna Tur, Peichen Ye

Switching phenomena are ubiquitous in real-world applications. An

n

-player hybrid pollution-control problem is considered with switching behavior and uncertain game duration. The payoff functional with a random duration is converted to a payoff functional in the infinite horizon, which is discounted by a heterogeneous discounting function. By applying Pontryagin’s maximum principle and analyzing the structure of the adjoint variable, the sustainable equilibria in cooperative and noncooperative games are uniquely determined. The convergence of the corresponding state variable in cooperative and noncooperative games is proved. Furthermore, a unique state trajectory represented by a hybrid limit cycle is found to compute the players’ payoffs in cooperative and noncooperative scenarios. Finally, a reasonable, cooperative solution that employs the Shapley value as a single-point solution is proposed. All results are derived analytically and demonstrated with a numerical example.

切换现象在实际应用中无处不在。本文考虑了一个 n 人混合污染控制问题，该问题具有切换行为和不确定的博弈持续时间。随机持续时间的报酬函数被转换为无限视界的报酬函数，并通过异质贴现函数进行贴现。通过应用庞特里亚金最大原则和分析邻接变量的结构，唯一确定了合作博弈和非合作博弈中的可持续均衡。证明了合作博弈和非合作博弈中相应状态变量的收敛性。此外，还找到了一个由混合极限循环代表的唯一状态轨迹，用于计算合作和非合作情况下博弈者的报酬。最后，还提出了一种合理的合作解，它采用夏普利值作为单点解。所有结果都是通过分析得出的，并通过一个数值示例进行了演示。

引用次数: 0

Asymptotic synchronization in coupled Boolean and probabilistic Boolean networks with delays 有延迟的耦合布尔和概率布尔网络中的渐近同步性

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

Nonlinear Analysis-Hybrid Systems

Pub Date : 2024-11-09 DOI: 10.1016/j.nahs.2024.101552

Yong Wang , Bowen Li , Qinyao Pan , Jie Zhong , Ning Li

This paper addresses the delay output synchronization in a coupled system of a Boolean network and a probabilistic Boolean network with state delays. We model the system as a Markov chain-based augmented system, simplifying the synchronization problem to a delay set stability issue. Analysis of the Markov chain’s transition matrix through positive recurrent closed sets yields synchronization criteria, both in probability and in probability one, based on Boolean matrix characteristics and matrix splitting techniques. These methods avoid the cumulative multiplication of high-dimensional matrices and reduce the complexity of the computation. Besides, the study progresses to explore asymptotic output synchronization, employing these methods. To demonstrate the practicality and effectiveness of the proposed methodology, several illustrative examples are provided.

本文探讨了布尔网络和具有状态延迟的概率布尔网络耦合系统中的延迟输出同步问题。我们将系统建模为基于马尔可夫链的增强系统，将同步问题简化为延迟集稳定性问题。根据布尔矩阵特征和矩阵分割技术，通过正循环闭集分析马尔可夫链的转换矩阵，可获得概率和概率一的同步标准。这些方法避免了高维矩阵的累加乘法，降低了计算的复杂性。此外，研究还利用这些方法探索渐近输出同步。为了证明所提方法的实用性和有效性，我们提供了几个示例。

引用次数: 0

Asynchronous intermittent sampled-data control for delayed complex dynamical networks with Lévy noise 具有莱维噪声的延迟复杂动态网络的异步间歇采样数据控制

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

Nonlinear Analysis-Hybrid Systems

Pub Date : 2024-11-01 DOI: 10.1016/j.nahs.2024.101550

Hui Zhou , Jingheng Feng , Ju H. Park , Wenxue Li

The article researches the synchronization issue of delayed multilink complex dynamical networks with Lévy noise (DMCNL) via asynchronously intermittent sampled-data decentralized control (AISDC). Asynchronous intermittent decentralized control, compared to synchronous intermittent control, is a policy that enables individual node-system to operate with distinct work and rest periods, thereby offering a higher degree of adaptability. Considering that continuous sampling in the control segment may result in resource wastage, a novel policy called AISDC is proposed by integrating the policy above and intermittent sampled-data control. Then, an auxiliary timer is designed for every node-system to make a compromise between regulating work intervals and controlling the rest interval. Moreover, graph theory and the Lyapunov method are combined to establish several synchronization criteria. Finally, numerical examples on a second-order Kuramoto model verify the feasibility of the proposed results.

文章通过异步间歇采样数据分散控制（AISDC）研究了具有莱维噪声的延迟多链路复杂动力学网络（DMCNL）的同步问题。与同步间歇控制相比，异步间歇分散控制是一种能使单个节点系统在不同的工作和休息时间内运行的策略，从而提供更高的适应性。考虑到控制部分的连续采样可能会造成资源浪费，我们将上述策略与间歇采样数据控制相结合，提出了一种名为 AISDC 的新型策略。然后，为每个节点系统设计了一个辅助定时器，以便在调节工作间隔和控制休息间隔之间做出折中。此外，图论和 Lyapunov 方法相结合，建立了多个同步标准。最后，二阶仓本模型的数值实例验证了所提结果的可行性。

引用次数: 0

Barrier function-based adaptive continuous higher-order sliding mode controllers 基于势垒函数的自适应连续高阶滑模控制器

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

Nonlinear Analysis-Hybrid Systems

Pub Date : 2024-10-31 DOI: 10.1016/j.nahs.2024.101551

Yacine Chitour , Hussein Obeid , Salah Laghrouche , Leonid Fridman

In this paper, two classes of continuous higher order adaptive sliding mode controllers based on barrier functions are developed for a perturbed chain of integrators with perturbations bounded by unknown functions. Both classes provide finite-time convergence of the state of the system to a predefined domain using a continuous control signal. The first class of adaptive controllers require few assumptions about the perturbation. However, it can provide unbounded control gains in general. To ensure bounded control gains in the case of a Lipschitz perturbation, a second class of adaptive controllers, called the adaptive higher order Super-Twisting (HOST) algorithm, is developed. The effectiveness of the proposed adaptive controllers is specifically assessed for a cart-pendulum system. Simulation results illustrate high performance in achieving stabilization, even in cases where the disturbance upper bound and its derivative are unknown.

本文针对由未知函数约束扰动的积分器扰动链，开发了两类基于障碍函数的连续高阶自适应滑模控制器。这两类控制器都能利用连续控制信号使系统状态在有限时间内收敛到预定域。第一类自适应控制器对扰动的假设很少。不过，它一般可以提供无界控制增益。为了确保在 Lipschitz 摄动情况下的有界控制增益，我们开发了第二类自适应控制器，称为自适应高阶超扭曲（HOST）算法。针对小车摆系统，对所提出的自适应控制器的有效性进行了具体评估。仿真结果表明，即使在扰动上限及其导数未知的情况下，也能实现高性能的稳定。

引用次数: 0

Exponential stability of positive implicit dynamic equations with constant coefficients 带常数系数的正隐式动态方程的指数稳定性

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

Nonlinear Analysis-Hybrid Systems

Pub Date : 2024-10-23 DOI: 10.1016/j.nahs.2024.101549

Do Duc Thuan

In this paper, the problem of positivity and stability for linear time-invariant implicit dynamic equations is generally studied. We provide necessary and sufficient conditions for positivity of these equations. This characterization can be considered as a unification and generalization for some previous results. On the other hand, we study the exponential stability of positive implicit dynamic equations. Previously, this issue was not completely addressed. By using Krein–Rutman theorem, we show that a positive implicit dynamic equation on a time scale is uniformly exponentially stable if and only if the characteristic polynomial of the matrix pair defining the equation has all its coefficients of the same sign.

本文一般性地研究了线性时变隐式动态方程的实在性和稳定性问题。我们为这些方程的正定性提供了必要和充分条件。这一表征可视为对之前一些结果的统一和概括。另一方面，我们研究了正隐式动态方程的指数稳定性。在此之前，这个问题并没有得到彻底解决。我们利用 Krein-Rutman 定理证明，当且仅当定义方程的矩阵对的特征多项式的所有系数都是同号时，时间尺度上的正隐式动态方程是均匀指数稳定的。

引用次数: 0

New results on finite-time stability of singular Markovian jump systems with time-varying delay 关于具有时变延迟的奇异马尔可夫跃迁系统有限时间稳定性的新结果

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

Nonlinear Analysis-Hybrid Systems

Pub Date : 2024-10-21 DOI: 10.1016/j.nahs.2024.101548

Shaohua Long , Mei Huang , Shouming Zhong

In this paper, we focus on the finite-time stability problem of singular Markovian jump systems with time-varying delay. Firstly, this paper presents some new inequalities which are very important to the finite-time stability problem of the considered systems. Secondly, by employing these new inequalities and the Lyapunov–Krasovskii functional approach, this paper derives some sufficient conditions that guarantee the considered systems to be regular, impulse-free and finite-time stable. Finally, three numerical examples are given to illustrate the effectiveness and advantage of the proposed methods.

本文主要研究具有时变延迟的奇异马尔可夫跃迁系统的有限时间稳定性问题。首先，本文提出了一些对所考虑系统的有限时间稳定性问题非常重要的新不等式。其次，通过利用这些新的不等式和 Lyapunov-Krasovskii 函数方法，本文推导出一些充分条件，以保证所考虑的系统是正则、无脉冲和有限时间稳定的。最后，本文给出了三个数值示例，以说明所提方法的有效性和优势。

引用次数: 0

Cluster synchronization of complex dynamic networks under pinning control via a limited capacity communication channel 通过容量有限的通信信道实现钉控条件下复杂动态网络的集群同步

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

Nonlinear Analysis-Hybrid Systems

Pub Date : 2024-09-25 DOI: 10.1016/j.nahs.2024.101547

Haifeng Wu , Shuai Liu , Licheng Wang

In this paper, the cluster synchronization pinning control problem is investigated for the continuous-time-directed complex dynamic networks under the bit rate constraint. Firstly, a node selection scheme based on differences in node degrees is proposed to achieve cluster synchronization. Subsequently, a coding–decoding scheme is designed during data transmission through digital communication channels where only a limited number of encoded signal sequences are sent to the controller side. Further, regarding the unreliability of the channel, the phenomenon of packet dropouts is considered during the encoding process, which is modeled by using a series of independent Bernoulli distributed random variables. The pinning controller is then designed based on the received decoding information. By means of the convex optimization method, a sufficient condition is established to ensure that the cluster synchronization error is ultimately bounded and the desired controller gain is determined based on the solution to matrix inequalities. Finally, the effectiveness of the obtained results is validated through a simulation example.

本文研究了比特率约束下连续时间定向复杂动态网络的簇同步钉控问题。首先，提出了一种基于节点度差异的节点选择方案，以实现簇同步。随后，在通过数字通信信道进行数据传输时，设计了一种编码-解码方案，其中只有数量有限的编码信号序列被发送到控制器端。此外，考虑到信道的不稳定性，在编码过程中考虑了丢包现象，并使用一系列独立的伯努利分布式随机变量对其进行建模。然后根据接收到的解码信息设计引脚控制器。通过凸优化方法，建立了确保集群同步误差最终有界的充分条件，并根据矩阵不等式的解确定了所需的控制器增益。最后，通过一个仿真实例验证了所获结果的有效性。

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引用次数: 0

Globally convergent path-aware optimization with mobile robots 利用移动机器人进行全局收敛路径感知优化

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

Nonlinear Analysis-Hybrid Systems

Pub Date : 2024-09-13 DOI: 10.1016/j.nahs.2024.101546

T. Sântejudean , Ş. Ungur , R. Herzal , I.-C. Morărescu , V.S. Varma , L. Buşoniu

Consider a mobile robot that must navigate as quickly as possible to the global maxima of a function (e.g. density of seabed litter, pollutant concentration, wireless signal strength) defined over its operating area. This objective function is initially unknown and is assumed to be Lipschitz continuous. The limited velocity of the robot restricts the next samples to neighboring positions, and to avoid wasting time and energy, the robot’s path must be adapted as new information becomes available. The paper proposes two methods that use an upper bound on the objective to iteratively change the position targeted by the robot as new samples are acquired. The first method is FTW, which Turns When the best value seen so far of the objective Function is larger than the bound of the current target position. The second is FTWD, an extension of FTW that takes into account the Distance to the target. Convergence guarantees are provided for both methods, and a convergence rate is proven to characterize how fast the FTW suboptimality decreases as the number of samples grows. In a numerical study, FTWD greatly improves performance compared to FTW, outperforms two representative source-seeking baselines, and obtains results similar to a much more computationally intensive method that does not guarantee convergence. The relationship between FTW and FTWD is also confirmed in real-robot experiments, where a TurtleBot3 seeks the darkest point on a 2D grayscale map.

考虑一个移动机器人，它必须尽可能快地航行到一个函数（如海底垃圾密度、污染物浓度、无线信号强度）的全球最大值，该函数定义在其运行区域内。该目标函数最初是未知的，并假定为 Lipschitz 连续函数。由于机器人的速度有限，下一次采样只能在邻近位置进行，为了避免浪费时间和精力，机器人的路径必须在获得新信息时进行调整。本文提出了两种方法，在获取新样本时，利用目标上界迭代改变机器人的目标位置。第一种方法是 FTW，当目前看到的目标函数的最佳值大于当前目标位置的边界时，机器人就会改变目标位置。第二种是 FTWD，它是 FTW 的扩展，考虑了与目标的距离。这两种方法都提供了收敛保证，并证明了收敛速率，以表征 FTW 次优性随着样本数量的增加而降低的速度。在数值研究中，与 FTW 相比，FTWD 极大地提高了性能，优于两种具有代表性的寻源基线，并获得了与计算量更大但不能保证收敛的方法类似的结果。FTW 和 FTWD 之间的关系在实际机器人实验中也得到了证实，TurtleBot3 在二维灰度地图上寻找最暗的点。

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引用次数: 0

Predefined-time convergence strategies for multi-cluster games in hybrid heterogeneous systems 混合异构系统中多集群博弈的预定义时间收敛策略

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

Nonlinear Analysis-Hybrid Systems

Pub Date : 2024-09-04 DOI: 10.1016/j.nahs.2024.101537

Fuxi Niu, Xiaohong Nian

This paper explores the problem of (generalized) Nash equilibrium search in multi-cluster games with heterogeneous dynamics and multiple constraints. Within this research framework, each agent acquires information solely through local interactions with its neighbors and forms clusters based on similarity of interests. These clusters manifest dual relationships of cooperation and competition: agents within the same cluster enhance decision-making capabilities through cooperation, while different clusters compete to maximize their respective benefits. To delve into these complex interactions among clusters and the learning and evolution processes among agents, four distributed control algorithms suitable for various scenario requirements are designed and implemented. These algorithms ensure that each agent converges to a Nash equilibrium (NE) or generalized Nash equilibrium (GNE) of the multi-cluster system within predefined time points. Finally, we apply these algorithms to the connectivity control problem of unmanned aerial vehicle swarms with diverse dynamics, validating the theoretical results through comprehensive simulations.

本文探讨了在具有异质动态和多重约束条件的多群组博弈中寻找（广义）纳什均衡的问题。在这一研究框架中，每个代理仅通过与其邻居的局部互动来获取信息，并根据利益相似性形成集群。这些集群表现出合作与竞争的双重关系：同一集群中的代理通过合作提高决策能力，而不同集群则通过竞争实现各自利益的最大化。为了深入研究集群之间的复杂互动关系以及代理之间的学习和进化过程，我们设计并实施了四种适合不同场景要求的分布式控制算法。这些算法确保每个代理在预定的时间点内收敛到多集群系统的纳什均衡（NE）或广义纳什均衡（GNE）。最后，我们将这些算法应用于具有不同动力学特性的无人机群的连接控制问题，并通过综合模拟验证了理论结果。

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