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Comments on “Innovative non-asymptotic and robust estimation method using auxiliary modulating dynamical systems” [Automatica 152 (2023) 110953] 关于“基于辅助调制动力系统的创新非渐近鲁棒估计方法”的评论[自动化]152 (2023)110953]

IF 6.4 2区计算机科学 Q1 AUTOMATION & CONTROL SYSTEMS

Automatica

Pub Date : 2026-02-03 DOI: 10.1016/j.automatica.2026.112846

Matti Noack, Davi Goncalves Accioli, Johann Reger, Jerome Jouffroy

引用次数: 0

On dissipativity of cross-entropy loss in training ResNets — A turnpike towards architecture search 训练ResNets中交叉熵损失的耗散性——结构搜索的收费公路

IF 5.9 2区计算机科学 Q1 AUTOMATION & CONTROL SYSTEMS

Automatica

Pub Date : 2026-01-27 DOI: 10.1016/j.automatica.2025.112767

Jens Püttschneider , Timm Faulwasser

The training of ResNets and neural ODEs can be formulated and analyzed from the perspective of optimal control. This paper proposes a dissipative formulation of the training of ResNets and neural ODEs for classification problems. Specifically, we consider a variant of the cross-entropy (label smoothing) as a loss function and as a regularization in the stage cost. Based on our dissipative formulation of the training, we prove that the training OCPs for ResNets and neural ODEs alike exhibit the turnpike phenomenon. We illustrate this finding with numerical results for the two spirals and MNIST datasets. Crucially, our training formulation ensures that the transformation of the data from input to output is achieved in the first layers. In the following layers, which constitute the turnpike, the data remains at an equilibrium state and therefore these layers do not contribute to the transformation learned. In principle, these layers can be pruned after training, resulting in a network with only the necessary number of layers thus simplifying tuning of hyperparameters.

resnet和神经ode的训练可以从最优控制的角度进行阐述和分析。本文提出了一种用于分类问题的resnet和神经ode训练的耗散公式。具体来说，我们将交叉熵（标签平滑）的一种变体视为损失函数和阶段成本的正则化。基于我们的训练耗散公式，我们证明了ResNets和神经ode的训练ocp都表现出收费公路现象。我们用两个螺旋和MNIST数据集的数值结果来说明这一发现。至关重要的是，我们的训练公式确保在第一层实现数据从输入到输出的转换。在构成收费公路的以下层中，数据保持在平衡状态，因此这些层对学习到的转换没有贡献。原则上，这些层可以在训练后进行修剪，从而使网络只具有必要的层数，从而简化超参数的调优。

引用次数: 0

Non-overshooting output shaping for switched linear systems under arbitrary switching using eigenstructure assignment 基于特征结构赋值的任意开关线性系统非超调输出整形

IF 5.9 2区计算机科学 Q1 AUTOMATION & CONTROL SYSTEMS

Automatica

Pub Date : 2026-01-21 DOI: 10.1016/j.automatica.2026.112831

Kai Wulff , Maria Christine Honecker , Robert Schmid , Johann Reger

We consider the analytical control design for switched linear multiple-input multiple-output (MIMO) systems subject to arbitrary switching signals. A state feedback controller design method is proposed to obtain an eigenstructure assignment ensuring that the closed-loop switched system is globally asymptotically stable, and the outputs achieve the non-overshooting tracking of a step reference. Our analysis indicates whether non-overshooting or even monotonic tracking is achievable for the given system and considered outputs, and provides a choice of possible eigenstructures to be assigned to the constituent subsystems. We derive a structural condition that verifies the feasibility of the chosen assignment. A constructive algorithm to obtain suitable feedback matrices is provided, and the method is illustrated with numerical examples.

研究了受任意开关信号影响的切换线性多输入多输出（MIMO）系统的解析控制设计。提出了一种状态反馈控制器设计方法来获得特征结构分配，保证闭环切换系统全局渐近稳定，输出实现阶跃参考的非超调跟踪。我们的分析表明，对于给定的系统和考虑的输出，是否可以实现非超调或甚至单调跟踪，并提供了分配给组成子系统的可能特征结构的选择。我们推导了一个结构条件来验证所选赋值的可行性。给出了一种构造算法来获取合适的反馈矩阵，并用数值算例说明了该方法。

引用次数: 0

Quality evaluation-based resilient distributed state estimation over time-varying networks via multi-hop communication 基于质量评估的时变网络多跳通信弹性分布式状态估计

IF 5.9 2区计算机科学 Q1 AUTOMATION & CONTROL SYSTEMS

Automatica

Pub Date : 2026-01-21 DOI: 10.1016/j.automatica.2026.112837

Rui Gao , Guang-Hong Yang , Tianyou Chai

This paper studies the problem of resilient distributed state estimation for a linear system using a set of agents connected through time-varying networks containing some Byzantine agents, where the Byzantine agents can arbitrarily manipulate the messages that they send or relay to other agents. First, an evaluation mechanism is introduced to assess the quality of the estimate generated by each agent at each step. Based on the quality evaluation and the multi-hop communication, a novel resilient distributed state estimation scheme is proposed, which enables each regular agent to evaluate the messages received from its time-varying multi-hop neighbors and discard the suspicious ones in real time. Then, to facilitate the stability analysis, the relationship between the estimates and the corresponding quality evaluations is established and the upper bound of the quality evaluations is derived. Specifically, the graph conditions under which all regular agents can estimate the state of the system exponentially fast at any given rate and even in finite time despite the existence of Byzantine agents are established. Different from the existing results requiring the time-varying networks to contain a sufficient amount of redundancy within bounded adjacent intervals, the proposed scheme can reduce the network redundancy requirement and allow the intervals over which such redundancy is preserved to grow over time. Finally, an example is simulated to validate the effectiveness of the proposed scheme.

本文研究了一个线性系统的弹性分布式状态估计问题，该系统通过包含一些拜占庭代理的时变网络连接一组代理，其中拜占庭代理可以任意操纵它们发送或转发给其他代理的消息。首先，引入了一种评估机制来评估每个agent在每个步骤中生成的估计的质量。基于质量评估和多跳通信，提出了一种新的弹性分布式状态估计方案，该方案使每个规则代理能够实时评估从时变多跳邻居接收的消息，并丢弃可疑的消息。然后，为了便于稳定性分析，建立了估计与相应质量评价之间的关系，并推导了质量评价的上界。具体地说，建立了在拜占庭智能体存在的情况下，所有规则智能体在任何给定速率下，甚至在有限时间内，都能指数级快速估计系统状态的图条件。与现有的结果要求时变网络在有界的相邻间隔内包含足够的冗余不同，该方案可以降低网络冗余要求，并允许保留冗余的间隔随时间增长。最后，通过一个算例验证了所提方案的有效性。

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引用次数: 0

Non-zero-sum games in continuous-time nonlinear systems: Multiplayer cascaded solutions 连续时间非线性系统中的非零和游戏：多人级联解决方案

IF 5.9 2区计算机科学 Q1 AUTOMATION & CONTROL SYSTEMS

Automatica

Pub Date : 2026-01-20 DOI: 10.1016/j.automatica.2026.112828

Yuzhe Chen , Ci Chen , Frank L. Lewis

This paper studies multiplayer nonzero-sum (NZS) games with an infinite horizon for nonlinear continuous-time (CT) systems with an emphasis on addressing the pervasive stability challenges encountered during the application of policy iteration methodologies. Central to this work is the introduction of the framework termed multiplayer cascaded policy iteration (MCPI), devised to iteratively approximate Nash equilibrium solutions within the realm of nonlinear NZS games. A salient feature of MCPI lies in its ability to ensure not only the stability of the iterative process but also its intriguing convergence equivalence with quasi-Newton iteration paradigms. Furthermore, building upon approximate dynamic programming technology, we present an extended effort in the development of an online algorithm. This algorithm leverages input and state data from the system to approximate the optimal solution online, eliminating the need for specific system parameters. Employing the apparatus of the approximation theorem, the algorithm approximates value functions and control policies, with the least squares method serving for weight updates. A rigorous proof of convergence substantiates the efficacy of the approximate solution, ensuring its eventual convergence to optimality. The efficacy of the developed method is validated through a numerical example.

本文研究了具有无限视界的非线性连续时间（CT）系统的多人非零和（NZS）对策，重点解决了策略迭代方法在应用过程中遇到的普遍稳定性挑战。这项工作的核心是引入了称为多人级联策略迭代（MCPI）的框架，该框架旨在迭代地近似非线性NZS博弈领域内的纳什均衡解。MCPI的一个显著特点是它不仅能够保证迭代过程的稳定性，而且具有与拟牛顿迭代范式的有趣的收敛等价性。此外，在近似动态规划技术的基础上，我们提出了一个在线算法开发的扩展努力。该算法利用系统的输入和状态数据在线逼近最优解，消除了对特定系统参数的需要。该算法利用逼近定理的工具，逼近值函数和控制策略，最小二乘法用于权值更新。收敛性的严格证明证实了近似解的有效性，保证了其最终收敛到最优性。通过算例验证了该方法的有效性。

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引用次数: 0

Input–output data-driven sensor selection for cyber-physical systems 网络物理系统的输入-输出数据驱动传感器选择

IF 5.9 2区计算机科学 Q1 AUTOMATION & CONTROL SYSTEMS

Automatica

Pub Date : 2026-01-20 DOI: 10.1016/j.automatica.2026.112829

Filippos Fotiadis , Kyriakos G. Vamvoudakis

In this paper, we consider the problem of input–output data-driven sensor selection for unknown cyber–physical systems (CPS). In particular, out of a large set of sensors available for use, we choose a subset of them that maximizes a metric of observability of the CPS. The considered observability metric is related to the

H_{2}

system norm, which quantifies the average output energy of the selected sensors over a finite or an infinite horizon. However, its computation inherently requires knowledge of the unknown matrices of the system, so we draw connections from the reinforcement learning literature and design an input–output data-driven algorithm to compute it in a model-free manner. We then use the derived data-driven metric expression to choose the best sensors of the system in polynomial time, effectively obtaining a provably convergent model-free sensor selection process. Additionally, we show how the proposed data-driven approach can be exploited to select sensors that optimize volumetric measures of observability, while also noting its applicability to the dual problem of actuator selection. Simulations are performed to demonstrate the validity and effectiveness of the proposed approach.

在本文中，我们考虑了未知网络物理系统（CPS）的输入-输出数据驱动传感器选择问题。特别是，在可供使用的大量传感器中，我们选择其中的一个子集，使CPS的可观察性度量最大化。考虑的可观测性度量与H2系统范数有关，H2系统范数量化了选定传感器在有限或无限范围内的平均输出能量。然而，它的计算本质上需要了解系统的未知矩阵，因此我们从强化学习文献中提取联系，并设计了一个输入输出数据驱动的算法，以无模型的方式计算它。然后，我们使用导出的数据驱动度量表达式在多项式时间内选择系统的最佳传感器，有效地获得了一个可证明收敛的无模型传感器选择过程。此外，我们展示了如何利用所提出的数据驱动方法来选择优化可观测性体积测量的传感器，同时也注意到它适用于执行器选择的双重问题。仿真结果验证了该方法的有效性。

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引用次数: 0

Passivity-based control of a double-pendulum crane using propagation of vibration suppression 基于振动抑制传播的双摆起重机无源控制

IF 5.9 2区计算机科学 Q1 AUTOMATION & CONTROL SYSTEMS

Automatica

Pub Date : 2026-01-19 DOI: 10.1016/j.automatica.2026.112818

Ho Duc Tho , Kazuhiko Terashima , Takanori Miyoshi

The second swing angle information may not be strictly required to fully control the double-pendulum overhead crane (DPOC) system. Such an insight stems from the propagation of vibration suppression principle, which states that if either of the two swing angles is suppressed by control, both pendulums will cease to vibrate altogether. This intuition serves as the basis of the augmented passivity-based control law. The trolley velocity — the default command of most industrial cranes — is chosen as the system’s control input. Passivity properties of the system and the control law design are formulated based on a linearized model. The region of attraction (ROA) of the nonlinear closed-loop system is then computed using the sum-of-square (SOS) programming. The established controller does not require measurements or estimations of any rate or velocity signals. In the absence of the second swing angle information, the proposed approach can achieve similar control performance compared to existing full-state feedback controllers. An experimental result on a small-scale DPOC rig is also provided.

为了完全控制双摆桥式起重机（DPOC）系统，可能不需要严格要求第二摆角信息。这种见解源于振动抑制原理的传播，该原理指出，如果两个摆动角度中的任何一个被控制抑制，两个钟摆将完全停止振动。这种直觉作为增强型被动控制律的基础。小车速度-大多数工业起重机的默认指令-被选择作为系统的控制输入。基于线性化模型确定了系统的无源特性和控制律设计。然后用平方和规划法计算非线性闭环系统的吸引区域（ROA）。所建立的控制器不需要测量或估计任何速率或速度信号。在没有第二摆角信息的情况下，与现有的全状态反馈控制器相比，所提出的方法可以获得相似的控制性能。并给出了在小型DPOC钻机上的实验结果。

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引用次数: 0

Optimal advertising and product durability decisions in new product diffusion 新产品扩散中的最优广告和产品耐久性决策

IF 5.9 2区计算机科学 Q1 AUTOMATION & CONTROL SYSTEMS

Automatica

Pub Date : 2026-01-16 DOI: 10.1016/j.automatica.2026.112826

Adrian P. Kennedy , Ashutosh Prasad , Suresh P. Sethi , Chi Chung Siu , Sheung Chi Phillip Yam

This paper studies the optimal advertising policy over the product life cycle of a semi-durable good whose failure rate is a design decision. The product’s adoption process draws from three sources of consumers, viz., innovators who find the product directly, consumers influenced by advertising, and loyal customers making replacements. The revenue stream is composed of the sales of new products, maintenance fees, and replacement sales. We propose a product diffusion model with both durable and non-durable properties and solve it using optimal control. The guidelines for advertising during new product diffusion are simple to implement due to explicit solutions. We make recommendations for the design of product durability and observe cases where higher failure rates are optimal. Finally, we extend our analysis to a game-theoretic framework, showcasing that the optimal advertising decisions remain tractable even in the context of competing manufacturers.

研究了一种半耐用商品在产品生命周期内的最优广告策略，其故障率是一个设计决策。产品的采用过程有三个消费者来源，即直接找到产品的创新者，受广告影响的消费者，以及更换产品的忠实客户。收入流由新产品的销售、维护费用和更换销售组成。提出了一种同时具有耐用性和非耐用性的产品扩散模型，并用最优控制方法对其进行求解。由于有明确的解决方案，新产品传播期间的广告指导方针易于实施。我们对产品耐久性的设计提出建议，并观察高故障率的最佳情况。最后，我们将分析扩展到博弈论框架，表明即使在竞争制造商的背景下，最佳广告决策仍然是可处理的。

引用次数: 0

MAKO: Meta-Adaptive Koopman Operators for learning-based model predictive control of parametrically uncertain nonlinear systems 参数不确定非线性系统基于学习模型预测控制的元自适应Koopman算子

IF 5.9 2区计算机科学 Q1 AUTOMATION & CONTROL SYSTEMS

Automatica

Pub Date : 2026-01-16 DOI: 10.1016/j.automatica.2026.112827

Minghao Han , Kiwan Wong , Adrian Wing-Keung Law , Xunyuan Yin

In this work, we propose a meta-learning-based Koopman modeling and predictive control approach for nonlinear systems with parametric uncertainties. An adaptive deep meta-learning-based modeling approach, called Meta Adaptive Koopman Operator (MAKO), is proposed. Without knowledge of the parametric uncertainty, the proposed MAKO approach can learn a meta-model from a multi-modal dataset and efficiently adapt to new systems with previously unseen parameter settings by using online data. Based on the learned meta Koopman model, a predictive control scheme is developed, and the stability of the closed-loop system is ensured even in the presence of previously unseen parameter settings. Through extensive simulations, our proposed approach demonstrates superior performance in both modeling accuracy and control efficacy as compared to competitive baselines.

在这项工作中，我们提出了一种基于元学习的具有参数不确定性的非线性系统的Koopman建模和预测控制方法。提出了一种基于深度元学习的自适应建模方法——元自适应库普曼算子（MAKO）。在不知道参数不确定性的情况下，所提出的MAKO方法可以从多模态数据集中学习元模型，并通过使用在线数据有效地适应具有先前未见参数设置的新系统。基于学习到的meta Koopman模型，提出了一种预测控制方案，即使存在先前未知的参数设置，也能保证闭环系统的稳定性。通过广泛的仿真，与竞争基线相比，我们提出的方法在建模精度和控制效率方面都表现出优越的性能。

引用次数: 0

A linearly convergent distributed heavy-ball GNE seeking algorithm for aggregative games over weight-unbalanced digraphs via finite-time consensus 基于有限时间共识的权重不平衡有向图上聚集博弈的线性收敛分布式重球GNE搜索算法

IF 5.9 2区计算机科学 Q1 AUTOMATION & CONTROL SYSTEMS

Automatica

Pub Date : 2026-01-15 DOI: 10.1016/j.automatica.2026.112830

Xiaomeng Chen , Kemi Ding , Subhrakanti Dey , Ling Shi

In this paper, we study the generalized Nash equilibrium (GNE) seeking problem for aggregative games with affine coupling constraints in a partial-decision information scenario. In this scenario, all players attempt to seek the GNE by exchanging messages with neighbors over strongly connected and weight-unbalanced directed graphs. To overcome the challenges posed by the asymmetric nature of communication matrices, we propose a novel accelerated distributed discrete-time primal–dual algorithm, which integrates finite-time exact ratio consensus (FTERC) and heavy-ball acceleration. Moreover, it is designed to accommodate uncoordinated stepsizes and momentum parameters, enhancing convergence rate. Despite the challenges introduced by uncoordinated elements and an additional momentum term, we present a rigorous analysis demonstrating that the proposed primal–dual algorithm achieves linear convergence to the GNE with constant uncoordinated stepsizes. Finally, we validate our theoretical results with numerical examples on two different communication graphs, demonstrating the effectiveness of the algorithm and how the momentum term enhances acceleration.

研究了部分决策信息场景下具有仿射耦合约束的聚集对策的广义纳什均衡问题。在这种情况下，所有玩家都试图通过与邻居在强连接和权重不平衡的有向图上交换信息来寻找GNE。为了克服通信矩阵的不对称特性带来的挑战，我们提出了一种新的加速分布式离散时间原对偶算法，该算法集成了有限时间精确比率一致性（FTERC）和重球加速。此外，该方法还可以适应不协调的步长和动量参数，提高收敛速度。尽管不协调元素和额外的动量项带来了挑战，但我们提出了一个严格的分析，表明所提出的原始对偶算法在恒定的不协调步长下实现了对GNE的线性收敛。最后，我们在两个不同的通信图上用数值例子验证了我们的理论结果，证明了算法的有效性以及动量项如何增强加速度。

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