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Practical adaptive control of state constrained system via zone barrier Lyapunov function 基于区势垒Lyapunov函数的状态约束系统实用自适应控制

IF 2.5 3区计算机科学 Q3 AUTOMATION & CONTROL SYSTEMS

Systems & Control Letters

Pub Date : 2025-12-22 DOI: 10.1016/j.sysconle.2025.106333

Xiaoling Liang , Dan Bao , Shuzhi Sam Ge

This paper has investigated the stability proof, robustness design and applications on practical adaptive control for state constraints. Even though adaptive control and backstepping have been around for a while and are generally regarded as stable at this point, there is still a lot of work being done to improve them and apply them to new scenarios. The theoretical challenge of this topic lies in identifying methods to mitigate the effects of area adaptation dynamics, while the practical significance of this issue arises from the fact that constraints are ubiquitous in physical and technical systems. Motivated by the idea of zone barrier Lyapunov function, the control of strict feedback systems is studied along with full and partial states constraints scenarios wherein parametric uncertainties. In contrast to traditional Lyapunov functions, which are well-defined over the whole domain and radially unbounded for global stability, adaptive zone barrier Lyapunov function (zBLF) not only has the unique property of finite escape if the values of their arguments approach certain bounds, but also offers more freedom space for the states. For the presence of uncertainty in the nonlinear system, under specific feasibility criteria, a practical area is obtained regarding the scenario involving full-state constraints. The zone stability and robustness design guarantee non-violation of constraints via rigorous theory proof. Furthermore, it has been demonstrated that feasibility conditions for partial state constraints with linearly parameterized system nonlinearities exist and similar results of practical stability can be achieved with state satisfactions. Numerical simulations are conducted to validate the theoretical findings obtained.

研究了状态约束自适应控制的稳定性证明、鲁棒性设计及其在实际控制中的应用。尽管自适应控制和后退已经存在了一段时间，并且在这一点上通常被认为是稳定的，但仍有许多工作要做，以改进它们并将它们应用于新的场景。本课题的理论挑战在于寻找减轻区域适应动态影响的方法，而该问题的现实意义在于物理和技术系统中普遍存在约束。基于区域势垒Lyapunov函数的思想，研究了具有参数不确定性的全状态约束和部分状态约束的严格反馈系统的控制问题。传统Lyapunov函数在整个域上定义良好，全局稳定径向无界，与之相反，自适应区垒Lyapunov函数（zBLF）不仅具有当其参数值接近某一边界时有限逃逸的独特性质，而且为状态提供了更大的自由空间。对于非线性系统中存在的不确定性，在特定的可行性准则下，得到了涉及全状态约束的实际区域。区域稳定性和鲁棒性设计通过严格的理论证明保证了约束的不违反。进一步证明了线性参数化系统非线性存在部分状态约束的可行性条件，并且在状态满足的情况下可以得到类似的实际稳定性结果。数值模拟验证了理论结果。

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引用次数: 0

Fixed-time containment control by non-eternally adaptive estimation for nonlinear dynamical systems with irregular disturbance 带有不规则扰动的非线性动力系统的非永恒自适应定时控制

IF 2.5 3区计算机科学 Q3 AUTOMATION & CONTROL SYSTEMS

Systems & Control Letters

Pub Date : 2025-12-22 DOI: 10.1016/j.sysconle.2025.106331

Kexing Yan, Shigen Gao

This paper investigates an adaptive fixed-time containment control problem for a class of inherently nonlinear dynamical multi-agent systems (MASs) in the presence of irregularly external disturbances. The inherent nonlinearity of the considered MASs arises from nonlinear functions that cannot be addressed through a simple Lipschitz continuous assumption. To address irregularly external disturbances, a novel non-eternally (NE) adaptive distributed fixed-time observer and tracking controller are designed with constrained leader states. The concept of NE refers to a system where, by employing an instinct-inspired convergence confirmed-or-not logic, pioneering adaptive fixed-time containment control (AFTCC) can switch to deterministic mode, maintaining the MASs’ adaptive parameters as constant values and enabling the online monitoring of control performance metrics. Once poor control performance is detected, signaling an irregular disturbance, the system reverts from deterministic fixed-time containment control (DFTCC) to AFTCC to promptly handle the disturbance. Theoretical analysis shows that the proposed controller achieves containment control within a fixed-time period, independent of the initial states, even in the presence of external disturbances. In addition, the proposed approach circumvents high-frequency chattering. Comparative simulation results are provided to validate the effectiveness and advantages of the proposed non-eternally adaptive estimation-based fixed-time containment control scheme.

研究了一类存在不规则外部扰动的固有非线性动态多智能体系统的自适应定时控制问题。所考虑的质量的固有非线性是由非线性函数引起的，不能通过简单的利普希茨连续假设来解决。为了解决非规则的外部干扰，设计了一种新颖的非永恒（NE）自适应分布式固定时间观测器和具有约束领导状态的跟踪控制器。NE的概念是指这样一种系统，通过采用本能启发的收敛确认或不确定逻辑，开创性的自适应固定时间遏制控制（AFTCC）可以切换到确定性模式，使MASs的自适应参数保持恒定值，并能够在线监测控制性能指标。一旦检测到控制性能不佳，表明存在不规则干扰，系统将从确定性固定时间遏制控制（DFTCC）恢复到AFTCC，以及时处理干扰。理论分析表明，即使在存在外部干扰的情况下，所提出的控制器也能在固定的时间段内实现与初始状态无关的包含控制。此外，该方法还可以避免高频抖振。对比仿真结果验证了所提出的基于非永久自适应估计的定时包容控制方案的有效性和优越性。

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引用次数: 0

Stubborn observers for infinite-dimensional systems in abstract form with application to parabolic PDEs with boundary measurement 抽象形式无限维系统的顽固观测器及其在具有边界测量的抛物型偏微分方程中的应用

IF 2.5 3区计算机科学 Q3 AUTOMATION & CONTROL SYSTEMS

Systems & Control Letters

Pub Date : 2025-12-22 DOI: 10.1016/j.sysconle.2025.106323

Salim Zekraoui, Daniele Astolfi, Vincent Andrieu

Building upon the recently developed “stubborn” observer construction for finite-dimensional systems, we present a novel observer structure for abstract linear infinite-dimensional systems. A key feature of our design is the use of nonlinear output injection terms with an adjustable dynamical saturation function. This approach not only ensures the input-to-state stability (ISS) of the error system in the presence of measurement disturbances but also demonstrates significant resilience to impulsive noise. We illustrate the effectiveness of our method by applying it to a class of parabolic partial differential equations (PDEs).

基于最近发展的有限维系统的“顽固”观测器结构，我们提出了一种新的抽象线性无限维系统观测器结构。我们设计的一个关键特征是使用具有可调动态饱和函数的非线性输出注入项。这种方法不仅保证了误差系统在存在测量干扰时的输入到状态稳定性，而且对脉冲噪声具有显著的弹性。我们通过将该方法应用于一类抛物型偏微分方程（PDEs）来说明该方法的有效性。

引用次数: 0

Adaptive boundary prescribed-performance MPC for 3-D UAV formation with obstacle/collision avoidance 具有避障/避碰的三维无人机编队自适应边界规定性能MPC

IF 2.5 3区计算机科学 Q3 AUTOMATION & CONTROL SYSTEMS

Systems & Control Letters

Pub Date : 2025-12-18 DOI: 10.1016/j.sysconle.2025.106327

Chengzhen Yu , Kairui Chen , C.L. Philip Chen , Zhi Liu , Jianhui Wang

This brief aims to address the contradiction between prescribed performance constraint and the obstacle/collision avoidance for the multiple unmanned aerial vehicles. Firstly, a prescribed-time performance function with adaptive slack variable is proposed to improve the prescribed performance strategy, prioritizing safety while detecting obstacles or neighbor unmanned aerial vehicles. Based on the proposed performance function, a homeomorphic transformation is applied to restrict the formation error within a certain range, mitigating undesired overshoot. By introducing avoidance function into the cost function, a model predictive control framework based formation algorithm is designed for unmanned aerial vehicles to avoid obstacle/collision in 3-D scenarios.

本文旨在解决多架无人机规定性能约束与避障/避碰之间的矛盾。首先，提出一种带有自适应松弛变量的规定时间性能函数，改进规定性能策略，在检测障碍物或相邻无人机时优先考虑安全；基于所提出的性能函数，应用同胚变换将形成误差限制在一定范围内，减轻了不期望的超调。通过在代价函数中引入避障函数，设计了一种基于模型预测控制框架的无人机避障编队算法。

引用次数: 0

Data-driven certified control barrier functions 数据驱动的认证控制屏障功能

IF 2.5 3区计算机科学 Q3 AUTOMATION & CONTROL SYSTEMS

Systems & Control Letters

Pub Date : 2025-12-16 DOI: 10.1016/j.sysconle.2025.106325

Ali Kashani , Amy K. Strong , Leila J. Bridgeman , Claus Danielson

Control barrier functions and invariant sets are fundamental to constraint enforcement in safety–critical applications. To ensure safety, data-driven control methods based on nonlinear system identification often assume the existence of a barrier function computed from data. This paper presents a wide artificial neural network trained under constrained output evolution to synthesize barrier functions that characterize invariant sets for locally Lipschitz continuous nonlinear systems. We embed safety guarantees in the training, in contrast to probabilistic guarantees often given by scenario optimization or post-hoc verification in trial-and-error methods. Further, guaranteeing invariance for nonlinear systems generally requires solving a model-based nonlinear and often non-convex program. Conversely, we formulate our approach as a linear program for nonlinear systems. To demonstrate the versatility of our method, we approximate the invariant set of the Julia map, a chaotic system known for its complex behavior and fractal invariant sets.

控制屏障函数和不变量集是安全关键应用中约束执行的基础。为了保证安全，基于非线性系统辨识的数据驱动控制方法通常假定存在由数据计算的障碍函数。针对局部Lipschitz连续非线性系统，提出了一种基于约束输出进化训练的广义人工神经网络，用于合成具有不变集特征的障函数。我们在训练中嵌入了安全保证，而不是通常由场景优化或事后验证在试错方法中给出的概率保证。此外，保证非线性系统的不变性通常需要求解基于模型的非线性和非凸规划。相反，我们将我们的方法表述为非线性系统的线性规划。为了证明我们方法的通用性，我们近似Julia映射的不变量集，这是一个以其复杂行为和分形不变量集而闻名的混沌系统。

引用次数: 0

Asymptotic stability equals exponential stability—while you twist your eyes 当你转动眼睛时，渐近稳定性等于指数稳定性

IF 2.5 3区计算机科学 Q3 AUTOMATION & CONTROL SYSTEMS

Systems & Control Letters

Pub Date : 2025-12-15 DOI: 10.1016/j.sysconle.2025.106324

Wouter Jongeneel

Suppose that two vector fields on a smooth manifold render some equilibrium point globally asymptotically stable (GAS). We show that there exists a homotopy between the corresponding semiflows such that this point remains GAS along this homotopy.

假设光滑流形上的两个向量场具有全局渐近稳定的平衡点。我们证明了在相应的半流之间存在一个同伦，使得该点沿着这个同伦保持GAS。

引用次数: 0

Pollution free eigenvalue bounds for the Gramian operator Gramian算子的无污染特征值界

IF 2.5 3区计算机科学 Q3 AUTOMATION & CONTROL SYSTEMS

Systems & Control Letters

Pub Date : 2025-12-11 DOI: 10.1016/j.sysconle.2025.106308

Luka Grubišic , Martin Lazar

In this paper we study eigenvalue estimates for solutions of the Lyapunov equation with a non-compact control operator. We compute eigenvalue estimates from Galerkin discretizations of Lyapunov equations and discuss the appearance of a spurious branch in the discrete spectrum. In this work we focus on providing estimates for the eigenvalues of the Gramian based on the monotonicity of the spectrum (with respect to the Löwner order) so that constants in the estimate do not depend on the dimension of the approximating matrices. We provide criteria for determining the part of the spectrum of the finite-dimensional Gramian which is localized by the same bounds as the spectrum of the full Gramian (pollution free part of the spectrum). Our main tools, which are of independent interest in their own right, are new improved asymptotic estimates for the eigenvalue decay in the case of control operators of large or infinite rank (dimension of the image space). We test our results numerically on an academic prototype problem using spectral element discretizations.

本文研究了具有非紧控制算子的Lyapunov方程解的特征值估计。我们计算了李雅普诺夫方程的伽辽金离散化的特征值估计，并讨论了离散谱中伪分支的出现。在这项工作中，我们专注于基于谱的单调性（相对于Löwner阶）提供格拉曼特征值的估计，以便估计中的常数不依赖于近似矩阵的维数。我们提供了确定有限维格拉姆谱的部分的标准，该部分的谱与全格拉姆谱（谱的无污染部分）的谱具有相同的边界。我们的主要工具是在大秩或无限秩（图像空间的维数）的控制算子的情况下，对特征值衰减的新改进的渐近估计。我们使用谱元离散在一个学术原型问题上对我们的结果进行了数值测试。

引用次数: 0

Fully distributed leader–follower consensus of multiagent systems by observer based linear time-varying protocol 基于观测器的线性时变协议的多智能体系统的完全分布式leader-follower一致性

IF 2.5 3区计算机科学 Q3 AUTOMATION & CONTROL SYSTEMS

Systems & Control Letters

Pub Date : 2025-12-08 DOI: 10.1016/j.sysconle.2025.106311

Di Lu, Bin Zhou, Kai Zhang

This paper proposes a fully distributed, observer based protocol using linear time-varying feedback for the leader–follower consensus problem in linear multi-agent systems. The protocol is inherently distributed, relying solely on local information without requiring knowledge of the global communication topology. For practical implementability, the protocol features a bounded protocol gain and highly tunable parameters, which allow designers to strike a deliberate balance among different performance criteria for specific objectives. The permissible ranges for these parameters are rigorously derived to ensure both consensus and performance. Furthermore, the dimension of the observer is not fixed but is allowed to vary within a certain range. Consensus is formally analyzed within a time-varying Lyapunov framework, and the theoretical findings are validated through numerical simulations that demonstrate the method’s efficacy.

针对线性多智能体系统中的领导者-追随者共识问题，提出了一种基于线性时变反馈的完全分布式观测器协议。该协议本质上是分布式的，仅依赖于本地信息，而不需要了解全局通信拓扑。对于实际的可实现性，该协议具有有限的协议增益和高度可调的参数，这使得设计人员能够在特定目标的不同性能标准之间达到故意的平衡。这些参数的允许范围是严格推导的，以确保一致性和性能。此外，观察者的尺寸不是固定的，而是允许在一定范围内变化。共识在时变Lyapunov框架内进行了正式分析，并通过数值模拟验证了理论结果，证明了该方法的有效性。

引用次数: 0

State feedback Φ∞ synthesis of multivariable linear systems 多变量线性系统的状态反馈Φ∞综合

IF 2.5 3区计算机科学 Q3 AUTOMATION & CONTROL SYSTEMS

Systems & Control Letters

Pub Date : 2025-12-08 DOI: 10.1016/j.sysconle.2025.106312

Xiaokan Yang , Dan Wang , Wei Chen

In this paper, we formulate a

Φ_{\infty}

synthesis problem for multivariable linear time-invariant (LTI) systems, i.e., controller synthesis with closed-loop phase constraints, which complements the

H_{\infty}

synthesis problem. A direct imitation of the solution of

H_{\infty}

synthesis would generally lead to complex-valued controllers for

Φ_{\infty}

synthesis, which are not physically realizable. We derive a necessary and sufficient condition for solvability of the state feedback

Φ_{\infty}

synthesis, formulated through a linear matrix inequality (LMI) subject to a rank condition. An algorithm is proposed to handle the difficulty caused by the rank condition. To overcome the limitation of the algorithm in lacking global convergence, we further derive a sufficient solvability condition with a clear geometric interpretation, expressed in terms of a real-coefficient LMI that ensures the resulting controller is real-valued.

本文提出了多变量线性时不变（LTI）系统的Φ∞综合问题，即具有闭环相位约束的控制器综合问题，它是对H∞综合问题的补充。直接模仿H∞综合的解通常会导致Φ∞综合的复值控制器，这在物理上是不可实现的。我们推导了状态反馈Φ∞综合的可解性的充分必要条件，该条件由服从秩条件的线性矩阵不等式（LMI）表述。提出了一种处理排序条件带来的困难的算法。为了克服算法缺乏全局收敛性的限制，我们进一步推导了一个充分的可解性条件，该条件具有清晰的几何解释，用实系数LMI表示，以确保得到的控制器是实值的。

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引用次数: 0

Integration admissibility for structural controllability in linear networked systems 线性网络系统结构可控性的积分容许性

IF 2.5 3区计算机科学 Q3 AUTOMATION & CONTROL SYSTEMS

Systems & Control Letters

Pub Date : 2025-12-07 DOI: 10.1016/j.sysconle.2025.106314

Qitian Chen, Shaoyuan Li

This article investigates the structural controllability of networked systems composed of interconnected linear subsystems. Focusing on heterogeneous networks where subsystems may differ in state dimension and dynamics, we study the integration of a new subsystem into an existing controllable network and define the concept of integration admissibility, which refers to the existence of suitable interconnection matrices that preserve structural controllability after integration. From a graph-theoretic perspective, we derive a necessary and sufficient condition for integration admissibility in general heterogeneous networks and develop an efficient verification algorithm that relies only on local and adjacent subsystem dynamics. Furthermore, for the special case of homogeneous networks where all subsystems share identical dynamics, we establish sufficient conditions for structural controllability scalability. The proposed framework improves the computational efficiency of structural controllability analysis and verification in large-scale networked systems.

本文研究了由互联线性子系统组成的网络系统的结构可控性。针对异构网络中子系统的状态维数和动力学可能存在差异的问题，研究了将一个新的子系统集成到现有的可控网络中，并定义了集成容许性的概念，即存在合适的互连矩阵，在集成后保持结构的可控性。从图论的角度出发，推导了一般异构网络积分可容许性的充分必要条件，并开发了一种仅依赖局部和相邻子系统动态的有效验证算法。此外，对于所有子系统共享相同动态的同构网络的特殊情况，我们建立了结构可控性可扩展性的充分条件。该框架提高了大规模网络系统结构可控性分析与验证的计算效率。

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全部化学•材料生命科学医学物理工程技术环境•农林材料科学地球科学法学管理学化学环境科学与生态学计算机科学教育学经济学农林科学人文科学生物学数学物理与天体物理心理学综合性期刊其他工业工程理学历史学农学文学信息工程

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Systems & Control Letters

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