Journal of The Franklin Institute-engineering and Applied Mathematics最新文献

英文中文

Inverse compensation-based optimized intelligent control for nonlinear systems driven by hysteretic actuators 基于逆补偿的迟滞非线性系统优化智能控制

IF 4.2 3区计算机科学 Q2 AUTOMATION & CONTROL SYSTEMS

Journal of The Franklin Institute-engineering and Applied Mathematics

Pub Date : 2026-01-17 DOI: 10.1016/j.jfranklin.2026.108435

Li Zhou , Yonghua Wang , Guanyu Lai , Yongwei Zhang

This paper proposes an adaptive optimized intelligent control strategy for nonlinear strict-feedback systems with asymmetric hysteretic actuators by integrating reinforcement learning with backstepping. Although inverse hysteresis compensation is commonly employed, its performance is inherently limited by modeling inaccuracies, leading to non-negligible residual error. To address this issue, a dual-stage control framework is developed. First, an inverse asymmetric shifted Prandtl-Ishlinskii hysteresis compensator is applied to counteract the dominant hysteresis nonlinearity. Subsequently, an optimized backstepping controller is designed using a reinforcement learning-based identifier-critic-actor architecture with the dynamic surface technique to further suppress the residual error, thereby ensuring system stability and tracking performance. The main contributions of this work are threefold: 1) A simplified reinforcement learning mechanism is established, where the weight update laws for the actor and critic networks are designed to relax the persistent excitation condition while reducing computational complexity; 2) The dynamic surface technique is introduced to effectively circumvent the “differential explosion” problem inherent in conventional backstepping; 3) Adaptive parameters are incorporated to compensate for the residual error following inverse compensation. A rigorous Lyapunov-based stability analysis demonstrates that all closed-loop signals are semiglobally uniformly ultimately bounded. Simulation results confirm the effectiveness and robustness of the proposed controller.

针对具有非对称滞后作动器的非线性严格反馈系统，提出了一种将强化学习与反演相结合的自适应优化智能控制策略。逆滞回补偿是一种常用的补偿方法，但其性能受到建模误差的固有限制，导致剩余误差不可忽略。为了解决这一问题，开发了一种双级控制框架。首先，采用逆不对称移位的Prandtl-Ishlinskii迟滞补偿器来抵消占主导地位的迟滞非线性。随后，采用基于强化学习的辨识器-关键-参与者结构和动态曲面技术设计了优化后的反步控制器，进一步抑制残差，从而保证系统的稳定性和跟踪性能。本工作的主要贡献有三个方面：1)建立了一种简化的强化学习机制，其中设计了演员和评论家网络的权重更新规律，以放松持续激励条件，同时降低计算复杂度；2)引入动态面技术，有效规避了常规退步所固有的“差爆”问题；3)引入自适应参数对逆补偿后的残差进行补偿。一个严格的lyapunov稳定性分析证明了所有闭环信号都是半全局一致最终有界的。仿真结果验证了所提控制器的有效性和鲁棒性。

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引用次数: 0

Two-stage gradient-based iterative algorithms for the Hammerstein nonlinear systems with non-uniform sampling using the key term separation 基于关键项分离的非均匀采样Hammerstein非线性系统的两阶段梯度迭代算法

IF 4.2 3区计算机科学 Q2 AUTOMATION & CONTROL SYSTEMS

Journal of The Franklin Institute-engineering and Applied Mathematics

Pub Date : 2026-01-16 DOI: 10.1016/j.jfranklin.2026.108416

Hongchen Qin , Yan Ji

This study develops a parameter estimation method for Hammerstein nonlinear systems under non-uniform sampling conditions, utilizing the key term separation techniques. The core of this technique lies in the reformulation of the system output, transforming it into a linear-in-the-parameters form. As a result, a complex system is broken down into several subsystems with reduced variable dimensions, making the parameter estimation process more manageable. A key term separation auxiliary model gradient-based iterative algorithm was derived based on the principle of the negative gradient search. Meanwhile, to further enhance the efficiency of parameter estimation, by applying the hierarchical identification principle, an enhanced two-stage gradient-based iterative algorithm was developed. Ultimately, numerical simulations verify the efficacy of the developed algorithms.

利用关键项分离技术，研究了非均匀采样条件下Hammerstein非线性系统的参数估计方法。该技术的核心在于对系统输出进行重新表述，将其转化为参数线性形式。因此，一个复杂的系统被分解成几个子系统，减少了可变维度，使参数估计过程更易于管理。基于负梯度搜索原理，推导了一种基于关键项分离辅助模型梯度的迭代算法。同时，为了进一步提高参数估计的效率，应用层次辨识原理，提出了一种增强的基于两阶段梯度的迭代算法。最后，通过数值仿真验证了所开发算法的有效性。

引用次数: 0

Decentralized data-driven control of large-scale discrete-time delayed systems with application to vehicle formations 大规模离散时滞系统的分散数据驱动控制及其在车辆编队中的应用

IF 4.2 3区计算机科学 Q2 AUTOMATION & CONTROL SYSTEMS

Journal of The Franklin Institute-engineering and Applied Mathematics

Pub Date : 2026-01-16 DOI: 10.1016/j.jfranklin.2026.108417

Jin Zhang , Ziqi Cao , Chen Peng , Songlin Hu

This paper studies the stabilization problem of large-scale discrete-time systems with state delays. Recently, a data-driven approach to design a state feedback controller via data-based formulas is proposed in a centralized manner. In this paper, we extend this design to large-scale discrete-time delay systems. First, we present data-based formulas to represent the original subsystem by using its own input-state data and the state data of its neighbors. Then, by applying the Lyapunov-Krasovskii (L-K) approach, data-based sufficient conditions are obtained in terms of linear matrix inequalities (LMIs) that ensure the exponential stability of large-scale systems. Then, a criterion for designing state feedback controllers that stabilize the system is presented through a set of solvable LMIs. In addition, we incorporate cost control and H_∞ control into the controller design. Finally, the efficiency of the proposed method is validated through two examples including a platoon of heavy-duty vehicles (HDVs).

研究了具有状态时滞的大规模离散系统的镇定问题。最近，提出了一种数据驱动的方法，通过基于数据的公式集中设计状态反馈控制器。在本文中，我们将这种设计推广到大规模离散时滞系统。首先，我们提出了基于数据的公式，通过使用原始子系统自身的输入状态数据和相邻子系统的状态数据来表示原始子系统。然后，应用Lyapunov-Krasovskii （L-K）方法，从线性矩阵不等式（lmi）的角度，得到了保证大系统指数稳定性的基于数据的充分条件。然后，通过一组可解lmi给出了设计状态反馈控制器使系统稳定的判据。此外，我们在控制器设计中加入了成本控制和H∞控制。最后，通过一个重型车辆排算例验证了该方法的有效性。

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引用次数: 0

Stochastic false data injection attacks against distributed state estimation in interconnected large-scale systems 大规模互联系统分布式状态估计下的随机假数据注入攻击

IF 4.2 3区计算机科学 Q2 AUTOMATION & CONTROL SYSTEMS

Journal of The Franklin Institute-engineering and Applied Mathematics

Pub Date : 2026-01-15 DOI: 10.1016/j.jfranklin.2026.108434

Chuanyi Ning, Fei Hao

In this paper, a novel distributed estimator has been designed for the interconnected large-scale systems (LSSs). In LSSs, the interconnection property of the subsystems makes it difficult to design a distributed estimator. Therefore, an unknown-input observer (UIO)-like observer is introduced to handle the unknown system information. Combined with the Kalman filter, the optimal estimation under Gaussian noises has also been guaranteed. Moreover, the vulnerability of the proposed estimation algorithm under malicious attacks has been investigated, including the conditions of the existence of stealthy false data injection (FDI) attacks. Note that the existing researches mainly focus on the attacks targeted at the wireless channels between the cyber layer and the physical layer in general cyber-physical system (CPS) model. However, as one kind of CPSs, a special feature of the LSS is that the distributed estimators need exchange data through wireless channels in the cyber layer. Motivated by the consideration above, the problem of designing optimal FDI attacks in cyber layer has also been addressed. Finally, simulation results are provided based on the three-area interconnected power system to illustrate the feasibility and advantages of the theoretical results.

本文针对大型互联系统设计了一种新的分布式估计器。在lss中，由于子系统的互连性，使得分布式估计器的设计变得困难。因此，引入一个类似于未知输入的观测器来处理未知的系统信息。结合卡尔曼滤波，保证了在高斯噪声下的最优估计。此外，研究了所提估计算法在恶意攻击下的脆弱性，包括存在隐形虚假数据注入（FDI）攻击的条件。需要注意的是，现有的研究主要集中在一般网络物理系统（CPS）模型中针对网络层和物理层之间无线通道的攻击。然而，作为cps的一种，LSS的一个特点是分布式估计器需要在网络层通过无线信道交换数据。基于上述考虑，本文还研究了网络层FDI攻击的最优设计问题。最后，给出了基于三区互联电力系统的仿真结果，说明了理论结果的可行性和优越性。

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引用次数: 0

Complete stability analysis and optimal design for dual-state-feedback delayed resonator 双态反馈延迟谐振器稳定性分析及优化设计

IF 4.2 3区计算机科学 Q2 AUTOMATION & CONTROL SYSTEMS

Journal of The Franklin Institute-engineering and Applied Mathematics

Pub Date : 2026-01-15 DOI: 10.1016/j.jfranklin.2026.108432

Qingbin Gao , Jiazhi Cai , Hao Wu , Kai Zhou , Libor Pekař

We propose a dual-state-feedback delayed resonator (DFDR) by incorporating an additional acceleration-based feedback into the classical DR design. The optimal tuning of its feedback parameters is guided by two objectives: enhancing vibration suppression at a specified target frequency and maintaining overall system stability. First, we extend the Advanced Clustering with Frequency Sweeping (ACFS) methodology from the delay-only domain to the combined delay-gain domain, enabling a rigorous and complete stability analysis where feedback gains and delays interact. Second, we develop the optimal parameter tuning procedure and demonstrate that the proposed DFDR achieves improved stability margins, enhanced robustness to frequency variations, and superior vibration suppression performance compared to the classical DR. These results highlight the practical potential of DFDR as an effective and robust solution for active vibration suppression systems.

我们提出了一种双状态反馈延迟谐振器（DFDR），通过在经典DR设计中加入一个额外的基于加速度的反馈。其反馈参数的最优调谐以两个目标为指导：在指定的目标频率下增强振动抑制和保持系统的整体稳定性。首先，我们将带频率扫描的高级聚类（ACFS）方法从仅延迟域扩展到组合延迟增益域，从而实现反馈增益和延迟相互作用的严格而完整的稳定性分析。其次，我们开发了最优参数调整程序，并证明了与经典dr相比，所提出的DFDR实现了更好的稳定裕度，增强了对频率变化的鲁棒性，并且具有更好的振动抑制性能。这些结果突出了DFDR作为主动振动抑制系统的有效鲁棒解决方案的实际潜力。

引用次数: 0

Fuzzy adaptive prescribed performance control for stochastic nonlinear non-strict feedback systems with multiple delays and unmodeled dynamics 多时滞未建模随机非线性非严格反馈系统模糊自适应规定性能控制

IF 4.2 3区计算机科学 Q2 AUTOMATION & CONTROL SYSTEMS

Journal of The Franklin Institute-engineering and Applied Mathematics

Pub Date : 2026-01-14 DOI: 10.1016/j.jfranklin.2026.108407

Xin Jin , Jiuxiang Dong

This article investigates the fuzzy adaptive prescribed performance control problem for stochastic nonlinear systems in non-strict feedback form with state delays, input delays and unmodeled dynamics. Firstly, by constructing intermediate variables and adopting the Padé approximation method, the original system is transformed into a system only perturbed by state delays. Secondly, aiming at the characteristic of the system’s non-strict feedback structure, a Lyapunov-Krasovskii functional associated with all the state variables is constructed to compensate for the state delay terms. Auxiliary dynamic signals are introduced to deal with the uncertainties arising from unmodeled dynamics. Then, an improved adaptive prescribed performance control strategy is proposed based on the properties of the hyperbolic tangent functions combined with the backstepping method. This strategy achieves higher convergence accuracy and superior tracking performance compared to traditional methods. Analysis demonstrates that all variables in the controlled system are semi-globally bounded in probability, and the tracking error can converge to the preset performance range. A simulation example is conducted to validate the efficacy of the proposed method.

研究了具有状态时滞、输入时滞和未建模动力学的非严格反馈随机非线性系统的模糊自适应规定性能控制问题。首先，通过构造中间变量，采用pad近似方法，将原系统转化为只有状态时滞的扰动系统。其次，针对系统非严格反馈结构的特点，构造了一个包含所有状态变量的Lyapunov-Krasovskii泛函来补偿状态延迟项。引入辅助的动态信号来处理未建模的动态所带来的不确定性。然后，基于双曲正切函数的特性，结合反演方法，提出了一种改进的自适应规定性能控制策略。与传统方法相比，该策略具有更高的收敛精度和更好的跟踪性能。分析表明，被控系统中所有变量在概率上都是半全局有界的，跟踪误差能够收敛到预设的性能范围内。通过仿真算例验证了该方法的有效性。

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引用次数: 0

Saturation control for fractional-order power systems with electric vehicles integration using sampling mechanism and actuator faults 基于采样机构和执行器故障的电动汽车集成分数阶电力系统饱和控制

IF 4.2 3区计算机科学 Q2 AUTOMATION & CONTROL SYSTEMS

Journal of The Franklin Institute-engineering and Applied Mathematics

Pub Date : 2026-01-13 DOI: 10.1016/j.jfranklin.2026.108421

R. Samidurai , M. Yazhini , M. Baskar

The increasing penetration of electric vehicles (EVs) and renewable sources introduces significant challenges to power system stability, including load fluctuations, renewable intermittency, actuator saturation, and possible actuator faults. Existing control approaches often treat these issues separately and fail to capture the memory and hereditary effects inherent in such systems. This paper proposes a resilient fault-tolerant saturation control framework for fractional-order power systems with EV and photovoltaic integration, explicitly considering actuator faults, input saturation, and sampling mechanisms in a unified manner. A fractional-order state-space model combined with a Takagi-Sugeno fuzzy approach is developed to represent nonlinearities and uncertainties. Based on an indirect fractional-order Lyapunov method, less conservative LMI-based stability conditions are derived to guarantee robust asymptotic stability. Numerical simulations demonstrate that the proposed strategy achieves enhanced robustness and reliability against sampling irregularities, actuator failures, and saturation effects, significantly improving the stability and resilience of modern EV-integrated fractional-order power systems.

电动汽车和可再生能源的日益普及给电力系统的稳定性带来了重大挑战，包括负荷波动、可再生能源间歇性、致动器饱和和可能的致动器故障。现有的控制方法通常将这些问题分开处理，无法捕捉到这些系统中固有的记忆和遗传效应。本文提出了一种针对电动汽车和光伏集成的分数阶电力系统的弹性容错饱和控制框架，该框架明确地统一考虑了执行器故障、输入饱和和采样机制。提出了一种分数阶状态空间模型，结合Takagi-Sugeno模糊方法来表示非线性和不确定性。基于间接分数阶Lyapunov方法，导出了保证鲁棒渐近稳定的少保守性lmi稳定性条件。数值仿真结果表明，该策略对采样不规则性、致动器故障和饱和效应具有较强的鲁棒性和可靠性，显著提高了现代电动汽车集成分数阶电力系统的稳定性和弹性。

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引用次数: 0

Trajectory tracking control for quadrotor under wind disturbance based on four-quadrant switch and NMPC 基于四象限开关和NMPC的风扰动四旋翼飞行器轨迹跟踪控制

IF 4.2 3区计算机科学 Q2 AUTOMATION & CONTROL SYSTEMS

Journal of The Franklin Institute-engineering and Applied Mathematics

Pub Date : 2026-01-13 DOI: 10.1016/j.jfranklin.2026.108420

Jialiang Liu, Lipeng Wang, Donghui Yuan, Zhenyao Fan

This paper proposes a composite nonlinear control method for trajectory tracking of a quadrotor unmanned aerial vehicle (UAV) subject to strong wind disturbances. Initially, the dynamic model of the quadrotor UAV, along with turbulent and shear wind models, are established. Subsequently, for the position subsystem of the quadrotor UAV, a four-quadrant switching-based sliding mode controller (FQS-SMC) is designed. For the control allocation segment, a nonlinear programming (NP)-based control allocator is developed. Finally, for the attitude subsystem, a barrier Lyapunov global sliding mode control based nonlinear model predictive controller (BLGSMC-NMPC) is proposed. The performance of the proposed method is evaluated through three simulation scenarios: planar trajectory, spatial trajectory, as well as a complex trajectory under different wind conditions. The experimental results demonstrate that the composite control method proposed in this paper significantly outperforms the comparative methods in terms of dynamic performance, disturbance rejection, and control smoothness.

提出了一种针对强风干扰下四旋翼无人机轨迹跟踪的复合非线性控制方法。首先，建立了四旋翼无人机的动力学模型，以及湍流和切变风模型。随后，针对四旋翼无人机的位置子系统，设计了基于四象限切换的滑模控制器（FQS-SMC）。针对控制分配段，提出了一种基于非线性规划的控制分配器。最后，针对姿态子系统，提出了一种基于障垒Lyapunov全局滑模控制的非线性模型预测控制器（BLGSMC-NMPC）。通过平面轨迹、空间轨迹和不同风况下的复杂轨迹三种模拟场景对该方法的性能进行了评价。实验结果表明，本文提出的复合控制方法在动态性能、抗扰性和控制平滑性方面明显优于比较方法。

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引用次数: 0

Adaptive control for stochastic high-order nonlinear systems with guaranteed tracking performance 具有保证跟踪性能的随机高阶非线性系统自适应控制

IF 4.2 3区计算机科学 Q2 AUTOMATION & CONTROL SYSTEMS

Journal of The Franklin Institute-engineering and Applied Mathematics

Pub Date : 2026-01-13 DOI: 10.1016/j.jfranklin.2026.108419

Gang Chen, Arong Xue

This paper investigates the adaptive tracking control for stochastic high-order nonlinear systems with actuator faults and time-varying input delay. A novel fault-tolerant control scheme with ensured tracking performance is proposed and analyzed. More specially, the prescribed finite-time performance (PFTP) function is integrated into the controller design to achieve the prescribed transient performance. To deal with the problem of complexity explosion for the controller design, the extended high-order error compensation mechanism combined with the dynamic surface control approach is presented, which possesses enhanced robustness and broader applicability compared to existing methods. Additionally, an efficient high-order auxiliary system (HOAS) is constructed to handle the system inputs limited by faults and time delays concurrently. By combining the PFTP function with the asymptotic tracking control, the proposed control scheme first ensures that the tracking errors reach the prescribed range within the prescribed time and then achieve asymptotic convergence in probability. Finally, two simulation examples are employed to demonstrate the effectiveness of the designed control scheme.

研究了具有执行器故障和时变输入延迟的随机高阶非线性系统的自适应跟踪控制。提出并分析了一种保证跟踪性能的容错控制方案。更具体地说，将规定的有限时间性能（PFTP）功能集成到控制器设计中，以实现规定的瞬态性能。针对控制器设计复杂性激增的问题，提出了与动态曲面控制方法相结合的扩展高阶误差补偿机制，与现有方法相比具有更强的鲁棒性和更广泛的适用性。此外，还构建了一个高效的高阶辅助系统（HOAS）来同时处理受故障和时延限制的系统输入。该控制方案将PFTP函数与渐近跟踪控制相结合，首先保证跟踪误差在规定时间内达到规定范围，然后在概率上实现渐近收敛。最后，通过两个仿真实例验证了所设计控制方案的有效性。

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引用次数: 0

A fuzzy weighted self-allocation sliding mode controller for UAV trajectory tracking 无人机轨迹跟踪的模糊加权自分配滑模控制器

IF 4.2 3区计算机科学 Q2 AUTOMATION & CONTROL SYSTEMS

Journal of The Franklin Institute-engineering and Applied Mathematics

Pub Date : 2026-01-13 DOI: 10.1016/j.jfranklin.2026.108418

Lin Xiao, Yuyang Liu, Qiuyue Zuo, Mengrui Cao, Wangqiu Kuang

Sliding mode control has been extensively applied in unmanned aerial vehicle control for its robustness to nonlinear systems. However, its performance is sensitive to initial conditions and controller parameters, particularly reaching time. To address this, this paper proposes a Fuzzy Weighted Self-Allocation Sliding Mode Controller (FWSASMC) for quadrotor UAV trajectory tracking under bounded disturbances. By leveraging zeroing neural dynamics, the FWSASMC achieves fixed-time convergence through a fuzzy-weighted self-allocation scheme and an adaptive parameter. The scheme identifies varying effects of components in the conventional activation function during neural dynamics and uses fuzzy-optimized weights to coordinate them, accelerating convergence. The improved activation function is smoothed to construct a non-singular sliding surface, while the adaptive parameter refines the reaching law. Theoretical analysis and simulations verify convergence, demonstrating superior trajectory tracking performance and highlighting its potential for UAV applications, particularly in time-varying target tracking.

滑模控制以其对非线性系统的鲁棒性在无人机控制中得到了广泛的应用。但其性能对初始条件和控制器参数敏感，尤其是到达时间。针对这一问题，提出了一种模糊加权自分配滑模控制器（FWSASMC），用于四旋翼无人机在有界扰动下的轨迹跟踪。该算法利用归零神经动力学，通过模糊加权自分配方案和自适应参数实现固定时间收敛。该方案识别了传统激活函数中各分量在神经动力学过程中的不同影响，并使用模糊优化权值对其进行协调，加快了收敛速度。对改进的激活函数进行平滑处理，构造非奇异滑动曲面，自适应参数细化逼近规律。理论分析和仿真验证了收敛性，展示了卓越的轨迹跟踪性能，并突出了其在无人机应用中的潜力，特别是在时变目标跟踪方面。

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