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

{"title":"Decentralized optimized finite-time backstepping control of large-scale high-order fully actuated strict-feedback nonlinear systems via reinforcement learning","authors":"Xiaofeng Xu,&nbsp;Weihao Pan,&nbsp;Xianfu Zhang","doi":"10.1016/j.jfranklin.2025.108083","DOIUrl":"10.1016/j.jfranklin.2025.108083","url":null,"abstract":"<div><div>This paper studies the problem of finite-time optimized tracking control for large-scale high-order fully actuated strict-feedback nonlinear systems for the first time. Notably, reinforcement learning (RL)-based backstepping approach is employed for achieving the optimized control, such that the corresponding cost function is minimized and uncertain nonlinearities are allowed in the considered system. The control design incorporates a finite-time high-order Levant differentiator to estimate high-order derivatives, effectively solving the issue of “explosion of complexity”. Additionally, the finite-time error compensation signals are integrated to minimize filtering errors. The proposed scheme ensures that all signals of the closed-loop system are bounded and the tracking error can converge to a bounded neighborhood of the origin in a finite time.</div></div>","PeriodicalId":17283,"journal":{"name":"Journal of The Franklin Institute-engineering and Applied Mathematics","volume":"362 16","pages":"Article 108083"},"PeriodicalIF":4.2,"publicationDate":"2025-09-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145222526","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Dynamic event-triggered adaptive fuzzy command filtered asymptotic containment control for flexible robotic manipulator multiagent systems","authors":"Yulong Li ,&nbsp;Jihang Sui ,&nbsp;Huilin Yang ,&nbsp;Ben Niu ,&nbsp;Chenguang Ning ,&nbsp;Limin Han","doi":"10.1016/j.jfranklin.2025.108101","DOIUrl":"10.1016/j.jfranklin.2025.108101","url":null,"abstract":"<div><div>This paper presents the adaptive fuzzy asymptotic containment control scheme for flexible robotic manipulator multiagent systems (MASs) based on a novel dynamic event-triggered mechanism (DETM). Firstly, a two-step coordinate transformation method is presented based on the command filtered technique and the backstepping method, which effectively works out the issue of “explosion of complexity”. Secondly, it should be worth stressing that the controller design is particularly challenging because of the unknown nonlinearities that appear in the actual flexible robotic manipulator MASs. Therefore, the fuzzy logic systems (FLSs) are introduced to deal with the unknown nonlinearities. Based on an auxiliary dynamic variable, a DETM is designed to save communication resources without the Zeno phenomenon. The proposed control scheme not only ensures that all variables in the closed-loop system are uniformly ultimately bounded (UUB), but also the outputs of the followers can evolve within the dynamic convex hull formed by the multiple leaders, and the containment errors can eventually tend to zero. Finally, the simulation results indicate the feasibility of the proposed control scheme.</div></div>","PeriodicalId":17283,"journal":{"name":"Journal of The Franklin Institute-engineering and Applied Mathematics","volume":"362 16","pages":"Article 108101"},"PeriodicalIF":4.2,"publicationDate":"2025-09-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145222528","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Energy-aware task mapping combining DVFS and task duplication for multicore networked systems","authors":"Lei Mo ,&nbsp;Jingyi Zhang ,&nbsp;Minyu Cui ,&nbsp;Xiaoyong Yan ,&nbsp;Shuang Wang ,&nbsp;Xiaojun Zhai","doi":"10.1016/j.jfranklin.2025.108097","DOIUrl":"10.1016/j.jfranklin.2025.108097","url":null,"abstract":"<div><div>Integrating high-performance communication and computation capabilities, multicore embedded platforms have become key components to realize applications of networked systems, e.g., Cyber-Physical Systems (CPS). Such systems usually consist of multiple dependent and real-time tasks that can be executed in parallel on different cores of the nodes and have timing, energy, and reliability constraints. Designing efficient task mapping methods to transmit and process task data under multiple constraints is challenging. Existing works seldom consider the joint design problem under timing, energy, and reliability constraints, which are coupled with each other, introducing complexity in designing efficient task mapping methods. In this paper, we first formulate the joint design problem as a complex combinational optimization problem and design a linearization method to find the optimal solution. To reduce computation complexity and enhance scalability, we design a decomposition-based heuristic method. Then, a refinement method based on feedback control is added to enhance task schedulability. The results show that the optimal solution obtained by the proposed method achieves the desired system performance. Moreover, the proposed heuristic provides a feasible solution with negligible computing time (reduces <span><math><mrow><mn>99.9</mn><mspace></mspace><mo>%</mo></mrow></math></span> computation time but with <span><math><mrow><mn>24.3</mn><mspace></mspace><mo>%</mo></mrow></math></span> performance loss). Compared with the existing works, our method can optimize the usage of system resources to balance energy, timing, and reliability requirements.</div></div>","PeriodicalId":17283,"journal":{"name":"Journal of The Franklin Institute-engineering and Applied Mathematics","volume":"362 16","pages":"Article 108097"},"PeriodicalIF":4.2,"publicationDate":"2025-09-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145222533","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Safe collaborative control for UAH formation based on improved SODO and tracking differentiator under dynamic boundary constraints","authors":"Yongkang Guo ,&nbsp;Ting Wang ,&nbsp;Chunyu Zhang ,&nbsp;Tao Li","doi":"10.1016/j.jfranklin.2025.108098","DOIUrl":"10.1016/j.jfranklin.2025.108098","url":null,"abstract":"<div><div>This paper investigates the problem of safe collaborative control for unmanned aerial helicopter (UAH) formation under dynamic boundary constraints and external disturbances. Firstly, an improved boundary protection algorithm (IBPA) is proposed to tackle the issue on dynamic boundary constraints of the UAH formation, which instantaneously constructs the dynamic security trajectories for the follower UAHs. Secondly, for each UAH, an improved second-order disturbance observer (SODO) is proposed by incorporating state prediction error to achieve efficient and accurate estimation under lower gain. Thirdly, to achieve safe efficient tracking, a dual-layer control strategy is presented: the first layer introduces a virtual UAH and presents a force fast tracking differentiator (FFTD), effectively smoothing the severe deflection generated when the dynamic safe trajectories approach the constraint boundaries and suppressing high-frequency oscillation within the safe boundaries; the second layer adopts the trajectory switching algorithm (TSA) and proposes the controller design based on backstepping method, which further improves the tracking accuracy and reduces computational complexity. Fourthly, by borrowing Lyapunov theory, the stability for overall closed-loop system composed of estimation errors and tracking errors is analyzed, thus establishing the method of deriving observer gains and controller ones. Finally, the effectiveness and superiority of the proposed scheme is verified by resorting to simulated results.</div></div>","PeriodicalId":17283,"journal":{"name":"Journal of The Franklin Institute-engineering and Applied Mathematics","volume":"362 16","pages":"Article 108098"},"PeriodicalIF":4.2,"publicationDate":"2025-09-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145222535","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Optimal state feedback control for port-Hamiltonian systems : A shifted Hamiltonian approach integrating disturbance attenuation and adaptive parameter estimation","authors":"Tao Xu ,&nbsp;Haisheng Yu ,&nbsp;Jinpeng Yu ,&nbsp;Aiyun Zhu ,&nbsp;Baozeng Fu","doi":"10.1016/j.jfranklin.2025.108078","DOIUrl":"10.1016/j.jfranklin.2025.108078","url":null,"abstract":"<div><div>This paper addresses the optimal control problem for Port-Hamiltonian (PH) systems, focusing to minimize state error and control energy, where the desired state is not necessarily at the origin. By leveraging the Hamilton-Jacobi-Bellman (HJB) equation, an improved optimal state feedback control law is derived to minimize a quadratic cost function. First, departing from conventional energy-shaping paradigms, this work develops a shifted Hamiltonian function that decouples stability analysis from optimality constraints, effectively resolving the conflict between asymptotic stabilization and performance metrics. Second, by incorporating disturbance <span><math><msub><mi>L</mi><mn>2</mn></msub></math></span>-gain attenuation, the proposed framework achieves asymptotic stability under external perturbations. Third, a parameter estimator with adaptive law is established for uncertain parameters. Simulation results verify that the proposed control scheme is feasible and effective.</div></div>","PeriodicalId":17283,"journal":{"name":"Journal of The Franklin Institute-engineering and Applied Mathematics","volume":"362 16","pages":"Article 108078"},"PeriodicalIF":4.2,"publicationDate":"2025-09-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145156831","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"MRAC for H∞ tracking of TUAV based on improved AED-ADT method","authors":"Dawei Wu ,&nbsp;Xiaoqi Huang ,&nbsp;Yonghui Sun ,&nbsp;Kenan Yong","doi":"10.1016/j.jfranklin.2025.108081","DOIUrl":"10.1016/j.jfranklin.2025.108081","url":null,"abstract":"<div><div>This paper addresses the transition mode tracking control problem of the tilt-rotor UAV(TUAV). And a new adaptive robust control approach is proposed, leveraging the improved admissible edge-dependent average dwell time(AED-ADT) framework, which integrates the model reference adaptive control(MRAC) method with <span><math><msub><mi>H</mi><mi>∞</mi></msub></math></span> control technique. The TUAV’s variable structure and strong coupling result in complex aerodynamic behavior and modeling uncertainties. To resolve the aforementioned issues, an improved AED-ADT method is proposed for the first time. This method significantly relaxes the constraints on the Lyapunov functions for any two subsystems, providing a more flexible framework for the design of variable-structure aircraft control systems. Benefiting from the flexible framework, a modified MRAC is integrated to address substantial modeling uncertainties, featuring a more flexible adaptive law design. In addition, the robust <span><math><msub><mi>H</mi><mi>∞</mi></msub></math></span> control is introduced and combined with the improved MRAC and AED-ADT methods, which further improves the robustness of the controlled system against external disturbances. Ultimately, the simulation results presented validate the effectiveness of the proposed method.</div></div>","PeriodicalId":17283,"journal":{"name":"Journal of The Franklin Institute-engineering and Applied Mathematics","volume":"362 16","pages":"Article 108081"},"PeriodicalIF":4.2,"publicationDate":"2025-09-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145156830","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"New perspective on sampled-data control for persistent dwell-time switched PDE systems with 2D spatial diffusion","authors":"Shuo Han ,&nbsp;Xiaona Song ,&nbsp;Shuai Song ,&nbsp;Zenglong Peng ,&nbsp;Vladimir Stojanovic ,&nbsp;Inés Tejado","doi":"10.1016/j.jfranklin.2025.108075","DOIUrl":"10.1016/j.jfranklin.2025.108075","url":null,"abstract":"<div><div>Existing research has rarely focused on sampled-data control for switched partial differential equation (PDE) systems with two-dimensional (2D) spatial diffusion and a persistent dwell-time (PDT) switching rule, despite their strong application background in science and engineering. Therefore, a novel sampled-data control scheme for a class of switched PDE systems in 2D space is proposed in this paper. First, to accurately describe the fast and slow switching phenomena of the systems, PDT switching rule is used to model target switched PDE systems. The main advantage of PDT switching rule is being able to overcome the strict switching frequency limitations of dwell-time and average dwell-time switching rules. Moreover, a 2D spatial sampled-data control strategy, where the system’s continuous state <span><math><mrow><mi>z</mi><mo>(</mo><mi>t</mi><mo>,</mo><msub><mi>x</mi><mn>1</mn></msub><mo>,</mo><msub><mi>x</mi><mn>2</mn></msub><mo>)</mo></mrow></math></span> is sampled as discrete states <span><math><mrow><mi>z</mi><mo>(</mo><msub><mi>t</mi><mi>k</mi></msub><mo>,</mo><msub><mi>x</mi><mrow><mn>1</mn><mo>,</mo><mover><mi>m</mi><mo>˜</mo></mover></mrow></msub><mo>,</mo><msub><mi>l</mi><mn>2</mn></msub><mo>)</mo></mrow></math></span> and <span><math><mrow><mi>z</mi><mo>(</mo><msub><mi>t</mi><mi>k</mi></msub><mo>,</mo><msub><mi>l</mi><mn>1</mn></msub><mo>,</mo><msub><mi>x</mi><mrow><mn>2</mn><mo>,</mo><mover><mi>m</mi><mo>^</mo></mover></mrow></msub><mo>)</mo></mrow></math></span>, is employed to achieve system stabilization. This ensures system stability while reducing control costs compared to distributed control. Then, to address the asynchronous difficulties caused by switching and sampling when analyzing the systems’ stability, iteration, recursion, and equiprobable summation are used and sufficient conditions are obtained to ensure the closed-loop system’s stability. Finally, the effectiveness of the proposed method is verified through two simulations.</div></div>","PeriodicalId":17283,"journal":{"name":"Journal of The Franklin Institute-engineering and Applied Mathematics","volume":"362 16","pages":"Article 108075"},"PeriodicalIF":4.2,"publicationDate":"2025-09-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145222532","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Stabilization of LTI systems via derivative feedback and time delay effects","authors":"Lifei Xie,&nbsp;Xueyan Zhao,&nbsp;Feiqi Deng","doi":"10.1016/j.jfranklin.2025.108079","DOIUrl":"10.1016/j.jfranklin.2025.108079","url":null,"abstract":"<div><div>This study investigates the output derivative feedback control issue for linear time-invariant (LTI) systems and introduces the novel concept of derivative-induced stability. By imposing structural assumptions on the system, we establish a category of systems that fail to be stabilised by conventional output feedback control. Subsequently, to achieve stability under derivative feedback, two parameterization methods for designing feedback gains are proposed, involving algebraic analysis and Lyapunov theory. Furthermore, to overcome the practical challenges of measuring derivatives and reduce noise sensitivity, a difference feedback control framework based on finite-difference approximation was introduced. It was shown that by incorporating a properly selected delay, the system not only achieves effective derivative estimation but also benefits from improved stability, this phenomenon aligns with the theory of delay-induced stability. Using Lyapunov functional analysis, sufficient conditions are established to ensure asymptotic stability under difference feedback control. Finally, the proposed method is validated through two numerical examples, which also highlight the beneficial impact of output derivatives and time delays on system stability.</div></div>","PeriodicalId":17283,"journal":{"name":"Journal of The Franklin Institute-engineering and Applied Mathematics","volume":"362 16","pages":"Article 108079"},"PeriodicalIF":4.2,"publicationDate":"2025-09-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145156835","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Trajectory planning and tracking control for cable-driven continuum robots with dynamic obstacles","authors":"Yanan Qin,&nbsp;Qi Chen","doi":"10.1016/j.jfranklin.2025.108089","DOIUrl":"10.1016/j.jfranklin.2025.108089","url":null,"abstract":"<div><div>To obtain safe and optimal trajectory planning and high-performance tracking control for cable-driven continuum robots (CDCRs) with dynamic obstacles, a novel two-layer model predictive control (MPC) based trajectory planning and tracking controller is designed. In the outer layer, a soft constraint is incorporated into the cost function via a penalty term and integrated into MPC, thereby ensuring the safety of CDCR obstacle avoidance while effectively mitigating the issue of infeasible solutions that arise from hard constraints. Additionally, an improved grey wolf optimizer (IGWO) is introduced into MPC-based trajectory planner to achieve optimal obstacle avoidance. Particularly, to obtain the motion estimation of dynamic obstacles, a super-twisting observer (STO) is combined with the MPC-based trajectory planner to predict the state of moving obstacles. In the inner layer, the IGWO is merged into MPC to attain high precision and rapid convergence in trajectory tracking control. Both simulation and experimental results show that the proposed two-layer MPC achieves excellent effectiveness in trajectory planning and tracking for the CDCR navigating dynamic obstacles within uncertain environments.</div></div>","PeriodicalId":17283,"journal":{"name":"Journal of The Franklin Institute-engineering and Applied Mathematics","volume":"362 16","pages":"Article 108089"},"PeriodicalIF":4.2,"publicationDate":"2025-09-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145120474","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Synthesizing a negative-imaginary system with a specified L2-performance bound via nonlinear static output feedback control","authors":"Pravin Behera ,&nbsp;Arnab Dey ,&nbsp;Sourav Patra","doi":"10.1016/j.jfranklin.2025.108087","DOIUrl":"10.1016/j.jfranklin.2025.108087","url":null,"abstract":"<div><div>In this paper, an iterative algorithm is proposed for synthesizing a nonlinear negative-imaginary (NI) system by designing a stabilizing nonlinear static output feedback (SOF) controller for input-affine polynomial systems. Additionally, <span><math><msub><mi>L</mi><mn>2</mn></msub></math></span>-performance of the closed-loop system is ensured in local sense. This scheme can handle robustness in the face of NI and <span><math><msub><mi>L</mi><mn>2</mn></msub></math></span>-norm bounded uncertainties of the system. Since the design of nonlinear SOF control ensuring closed-loop NI property is inherently a bilinear matrix inequality (BMI) problem, a set of sufficient conditions is derived in polynomial optimization framework using the Lyapunov-based approach with no structural constraints imposed on the Lyapunov function, contrary to the existing result. To solve this optimization problem, a computationally tractable sum of squares (SOS) decomposition technique is applied. The effectiveness of the developed results is demonstrated through numerical examples, highlighting the favorable features of the proposed synthesis scheme.</div></div>","PeriodicalId":17283,"journal":{"name":"Journal of The Franklin Institute-engineering and Applied Mathematics","volume":"362 16","pages":"Article 108087"},"PeriodicalIF":4.2,"publicationDate":"2025-09-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145222577","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}