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

{"title":"Formation tracking control for unmanned vehicles using enhanced sequential convex programming-based model predictive control","authors":"Xiaoming Liu ,&nbsp;Fuchun Wu ,&nbsp;Yunshan Deng ,&nbsp;Ming Wang ,&nbsp;Yuanqing Xia","doi":"10.1016/j.jfranklin.2025.107571","DOIUrl":"10.1016/j.jfranklin.2025.107571","url":null,"abstract":"<div><div>This paper proposes an enhanced sequential convex programming-based model predictive control (ESCPMPC) scheme for formation tracking control problems. Considering coupled input constraints, a tracking error dynamic equation is established based on the position error between the leader and the follower, and a model predictive controller (MPC) is formulated for formation tracking. To improve the real-time control capability, we integrate MPC with sequential convex programming (SCP) by linearizing kinematics and convexifying obstacle avoidance constraints, thereby transforming the nonconvex optimization into a series of convex subproblems. While this approach efficiently approximates the solution to the original nonconvex problem, the linearization errors introduced during each SCP iteration can accumulate and potentially make the optimization problem infeasible. To address this issue, we propose an enhanced SCP (ESCP) method, which corrects these linearization errors. To ensure system stability, a terminal controller and a corresponding terminal set are computed. The recursive feasibility and stability of the proposed method are theoretically demonstrated. Finally, numerical simulations validate the effectiveness and computational efficiency of the proposed method in achieving formation tracking control for unmanned vehicles.</div></div>","PeriodicalId":17283,"journal":{"name":"Journal of The Franklin Institute-engineering and Applied Mathematics","volume":"362 6","pages":"Article 107571"},"PeriodicalIF":3.7,"publicationDate":"2025-02-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143601039","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":"An iterative method for solving the constrained tensor equations with the Einstein product","authors":"Bentelhoda Zali,&nbsp;Saeed Karimi","doi":"10.1016/j.jfranklin.2025.107592","DOIUrl":"10.1016/j.jfranklin.2025.107592","url":null,"abstract":"<div><div>In this paper, we present an iterative method for solving tensor equations, specifically multilinear systems of the form <span><math><mrow><mi>A</mi><msub><mrow><mo>∗</mo></mrow><mrow><mi>N</mi></mrow></msub><mi>X</mi><msub><mrow><mo>∗</mo></mrow><mrow><mi>M</mi></mrow></msub><mi>B</mi><mo>+</mo><mi>C</mi><msub><mrow><mo>∗</mo></mrow><mrow><mi>N</mi></mrow></msub><mi>X</mi><msub><mrow><mo>∗</mo></mrow><mrow><mi>M</mi></mrow></msub><mi>D</mi><mo>=</mo><mi>E</mi></mrow></math></span> with one of the constraints <span><math><mrow><mi>X</mi><mo>=</mo><msup><mrow><mi>X</mi></mrow><mrow><mi>T</mi></mrow></msup></mrow></math></span>, <span><math><mrow><mi>X</mi><mo>=</mo><mi>P</mi><msub><mrow><mo>∗</mo></mrow><mrow><mi>N</mi></mrow></msub><mi>X</mi><msub><mrow><mo>∗</mo></mrow><mrow><mi>M</mi></mrow></msub><mi>Q</mi></mrow></math></span>, <span><math><mrow><mi>X</mi><mo>=</mo><mo>−</mo><mi>P</mi><msub><mrow><mo>∗</mo></mrow><mrow><mi>N</mi></mrow></msub><mi>X</mi><msub><mrow><mo>∗</mo></mrow><mrow><mi>M</mi></mrow></msub><mi>Q</mi></mrow></math></span> and <span><math><mrow><mi>X</mi><mo>=</mo><mi>P</mi><msub><mrow><mo>∗</mo></mrow><mrow><mi>N</mi></mrow></msub><mi>X</mi><msub><mrow><mo>∗</mo></mrow><mrow><mi>N</mi></mrow></msub><mi>P</mi></mrow></math></span>, where <span><math><mi>P</mi></math></span> and <span><math><mi>Q</mi></math></span> are reflexive tensors. The proposed method is grounded in the generalized least squares method with the Einstein product. To address the constrained tensor equation using the global least squares method, we introduce a multilinear operator and its adjoint. For a more detailed survey, we compare the proposed method for solving the constrained tensor equation with one of the matrix format methods for the associated matrix equation. We also use the new method to solve the image restoration problem with a symmetrical structure, as a special case of constrained tensor equation. Finally, we give some examples to illustrate the effectiveness of the proposed method.</div></div>","PeriodicalId":17283,"journal":{"name":"Journal of The Franklin Institute-engineering and Applied Mathematics","volume":"362 6","pages":"Article 107592"},"PeriodicalIF":3.7,"publicationDate":"2025-02-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143511009","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":"Merging rules for strong structural controllability and minimum input problem in undirected networks","authors":"Nam-Jin Park ,&nbsp;Seong-Ho Kwon ,&nbsp;Yoo-Bin Bae ,&nbsp;Byeong-Yeon Kim ,&nbsp;Kevin L. Moore ,&nbsp;Hyo-Sung Ahn","doi":"10.1016/j.jfranklin.2025.107589","DOIUrl":"10.1016/j.jfranklin.2025.107589","url":null,"abstract":"<div><div>This paper explores the conditions for strong structural controllability in structured networks determined by the zero/non-zero patterns of edges. For undirected networks, starting with the fundamental unit for controllability, the path graph, we investigate the strong structural controllability of larger components such as cycles, trees, and ultimately, a pactus (a generalization of the well-known cactus graph) through the merging rules. In this process, we introduce the notion of a component input node, which functions identically to an external input node, providing a new perspective on how internal nodes can facilitate controllability. Furthermore, we offer an intuitive interpretation by decomposing complex graph structures into simpler path graphs and applying merging rules to understand how disjoint controllable components can merge to maintain overall controllability. Finally, we present an algorithm to solve the minimum input problem in a pactus, which leverages the concept of component input nodes to optimize the number of external inputs for strong structural controllability.</div></div>","PeriodicalId":17283,"journal":{"name":"Journal of The Franklin Institute-engineering and Applied Mathematics","volume":"362 6","pages":"Article 107589"},"PeriodicalIF":3.7,"publicationDate":"2025-02-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143526616","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":"Selective segmentation of inhomogeneous images based on local clustering and global smoothness","authors":"Lihua Min,&nbsp;Zhe Zhang,&nbsp;Zhengmeng Jin","doi":"10.1016/j.jfranklin.2025.107591","DOIUrl":"10.1016/j.jfranklin.2025.107591","url":null,"abstract":"<div><div>Selective segmentation of inhomogeneous images is a challenging task in computer vision. Most existing distance-based selective segmentation models usually study homogeneous images and seldomly consider intensity inhomogeneity. On the other hand, in order to segment inhomogeneous images, the local intensity clustering (LIC) property of bias field has been considered as an important prior in various segmentation models. In this paper, we propose a new selective segmentation model based on the LIC property and spatial smoothness prior of bias field. To our knowledge, it is the first time that the LIC property is applied in selective segmentation of inhomogeneous images, which is different from the existing distance-based models. In addition, existence of the minimizers to the proposed model is established. By using the heat kernel convolution approximation, we design an effective and fast convergent numerical algorithm for solving the model, which significantly improves the operational speed. Furthermore, the stability of the proposed algorithm is proven. Extensive experiments on synthetic images, brain MR images, liver CT images and LiTS dataset demonstrate the effectiveness of the proposed method, and our method outperforms state-of-the-art methods in terms of selective segmentation accuracy and running efficiency.</div></div>","PeriodicalId":17283,"journal":{"name":"Journal of The Franklin Institute-engineering and Applied Mathematics","volume":"362 6","pages":"Article 107591"},"PeriodicalIF":3.7,"publicationDate":"2025-02-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143577060","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":"Fault detection for multirate systems with sensor saturation subject to stochastic delayed redundant channels","authors":"Zhihui Wu ,&nbsp;Tiantian Hu ,&nbsp;Siteng Ma ,&nbsp;Hui Yu","doi":"10.1016/j.jfranklin.2025.107588","DOIUrl":"10.1016/j.jfranklin.2025.107588","url":null,"abstract":"<div><div>In this paper, the fault detection (FD) problem is investigated for a class of multirate systems (MRSs) with sensor saturation subject to redundant channels. Lifting technology is utilized to convert MRSs into single rate systems. The redundant channel transmission strategy (RCTS) with communication delays is employed to improve quality and reliability of data transmission between the sensor and the remote fault detection filter (FDF), where the occurrence probability of delays is partially known. Specifically, an FDF is constructed to ensure that the augmented system maintains stochastic stability and meets the prescribed <span><math><msub><mrow><mi>H</mi></mrow><mrow><mi>∞</mi></mrow></msub></math></span> performance. Then, the FDF gains are obtained by linear matrix inequality (LMI) method. In addition, in order to verify the performance of the FDF subject to redundant channels, an FDF over single channel is also designed for comparison. Finally, a simulation case on continuous stirred tank reactor (CSTR) is utilized to illustrate the feasibility of the designed FD scheme and demonstrate the superiority of FDF subject to redundant channels.</div></div>","PeriodicalId":17283,"journal":{"name":"Journal of The Franklin Institute-engineering and Applied Mathematics","volume":"362 6","pages":"Article 107588"},"PeriodicalIF":3.7,"publicationDate":"2025-02-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143488496","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":"A generalized super-twisting algorithm based on adaptive dual layer mechanism","authors":"Jianxiong Li ,&nbsp;Qingqing Wang ,&nbsp;Miao Xu ,&nbsp;Yiming Fang","doi":"10.1016/j.jfranklin.2025.107587","DOIUrl":"10.1016/j.jfranklin.2025.107587","url":null,"abstract":"<div><div>This article proposes a generalized super-twisting algorithm based on adaptive dual-layer mechanism (GSTA-ADL), which can be regarded as an extension of the adaptive dual-layer super-twisting algorithm (ADLSTA). The GSTA-ADL not only inherits the excellent performance of ADLSTA in achieving finite time stability against Lipschitz disturbance without overestimation, but also counteracts effectively the state-dependent disturbance by means of the generalized super-twisting algorithm (GSTA) with an adaptive gain. It can be proved that the state of the resulting closed-loop system converges into the equilibrium in finite time. Simulation results are finally provided to demonstrate the effectiveness of the proposed control method.</div></div>","PeriodicalId":17283,"journal":{"name":"Journal of The Franklin Institute-engineering and Applied Mathematics","volume":"362 6","pages":"Article 107587"},"PeriodicalIF":3.7,"publicationDate":"2025-02-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143488492","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":"Periodic event-triggered predictive formation control of networked mobile robots under unknown disturbances","authors":"Chengyu Zhu ,&nbsp;Xiurui Lin ,&nbsp;Dongdong Qin ,&nbsp;Andong Liu ,&nbsp;Wen-An Zhang ,&nbsp;Jason J.R. Liu","doi":"10.1016/j.jfranklin.2025.107581","DOIUrl":"10.1016/j.jfranklin.2025.107581","url":null,"abstract":"<div><div>This paper proposes an Extended State Observer (ESO)-based periodic event-triggered predictive formation control algorithm for networked mobile robots under unknown disturbances with system constraints. The aim is to efficiently reduce the computational load and communication burden in the presence of unknown disturbances. First, our approach employs an improved virtual structure method, which divides the formation problem into two subtasks: path-following and formation coordination. Moreover, a periodic event-triggered distributed model predictive control (PETDMPC) strategy is proposed to enhance the implementation of discrete linear systems in computer control systems. This strategy incorporates cooperation constraints related to the parameterized variables in the cost function as coupling terms. Additionally, to reduce the adverse effects of disturbances, a disturbance compensation mechanism based on ESO is incorporated into the periodic event-triggered predictive formation control strategy. Finally, the feasibility of the algorithm and the stability of the closed-loop systems are derived using the discrete Gronwall–Bellman inequality for networked mobile robots under unknown disturbances. Simulation results show the effectiveness of the proposed strategy.</div></div>","PeriodicalId":17283,"journal":{"name":"Journal of The Franklin Institute-engineering and Applied Mathematics","volume":"362 6","pages":"Article 107581"},"PeriodicalIF":3.7,"publicationDate":"2025-02-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143488493","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":"L1-based virtual guidance and robust adaptive event-triggered control of large-scale USV for a narrow channel maneuver","authors":"Guoqing Zhang ,&nbsp;Zhu Sun ,&nbsp;Jiqiang Li ,&nbsp;Weidong Zhang","doi":"10.1016/j.jfranklin.2025.107586","DOIUrl":"10.1016/j.jfranklin.2025.107586","url":null,"abstract":"<div><div>This note proposes a robust adaptive control strategy for the narrow channel maneuvering mission of the large-scale underactuated surface vessel (USV). The proposed strategy consists of the guidance module and control module. For the former, a L1-based virtual guidance is developed to generate the reference signal and guide the large-scale USV to execute the narrow channel maneuver, which aims to overcome the overshoot problem near waypoints. For the latter, a robust adaptive control algorithm with a novel dynamic event-triggered mechanism is designed. In particular, the model uncertainties and external disturbances are addressed with a new approach called “robust bounded compensating technique”, leading to a lower design complexity while the robustness is increasing. Furthermore, the output-based dynamic event-triggered control (DETC) mechanism without preset parameters tuning is introduced to reduce the transmission frequency from controller to actuator. Besides, considerable efforts have done to prove the stability of the proposed algorithm via the Lyapunov theorem. Finally, the effectiveness and superiorities of the proposed method are demonstrated with two numerical examples, where the satisfied tracking accuracy and low transmission frequency are achieved in presence of the marine environment.</div></div>","PeriodicalId":17283,"journal":{"name":"Journal of The Franklin Institute-engineering and Applied Mathematics","volume":"362 5","pages":"Article 107586"},"PeriodicalIF":3.7,"publicationDate":"2025-02-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143474194","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 controllability conditions for multi-layer networked systems","authors":"Longkun Tang,&nbsp;Quan Shen,&nbsp;Lixin Jiang","doi":"10.1016/j.jfranklin.2025.107579","DOIUrl":"10.1016/j.jfranklin.2025.107579","url":null,"abstract":"<div><div>The controllability of networked system with high-dimensional nodes is far lack of understanding. From the perspective of the eigenvectors, based on the decoupled idea and dimensionality reduction technique, this paper investigates the controllability of multi-layer networks with high-dimensional nodes where the network topology is described by multiple connection structures with different coupling modes, and proposes some new necessary and sufficient conditions of the controllability for two intra-layer topology cases of simultaneously block diagonalization (SBD) and simultaneously diagonalization (SD), which are represented by the small-size units of intra-layer topologies and node dynamics. Furthermore, an easy-to-use algorithm is developed to check the controllability of multi-layer networked system, and two examples are used for illustration and verification, and then these conditions are specified for four cases of special intra-layer topologies. These findings provide a new and insight understandings for the controllability of multi-layer networks, and reveal the affect of multi-layer connections (outer topologies and inner couplings) on network controllability, particularly the impressive result that either one of two-layer networks being uncontrollable implies the two-layer networked system being uncontrollable when the two-layer network structures have the common left eigenvectors.</div></div>","PeriodicalId":17283,"journal":{"name":"Journal of The Franklin Institute-engineering and Applied Mathematics","volume":"362 6","pages":"Article 107579"},"PeriodicalIF":3.7,"publicationDate":"2025-02-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143488494","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":"Corrigendum to \"Dynamical analysis of a stochastic delayed epidemic model with Lévy jumps and regime switching\" [Journal of the Franklin Institute 360 (2023) 1252–1283]","authors":"Jasmina Đorđević,&nbsp;Bojana Jovanović","doi":"10.1016/j.jfranklin.2025.107582","DOIUrl":"10.1016/j.jfranklin.2025.107582","url":null,"abstract":"<div><div>The authors correct part of the proof of Theorem 1 in the above-titled paper <span><span>[1]</span></span>, in order to avoid using of the estimate <span><math><mrow><mi>I</mi><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow><mo>≥</mo><mn>1</mn><mo>⇔</mo><mfrac><mrow><mn>1</mn></mrow><mrow><mi>I</mi><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow></mrow></mfrac><mo>≤</mo><mn>1</mn></mrow></math></span>, which is not justified. For the same reason, the proofs of Theorems 2 and 3 were corrected, while the idea remained the same. The authors apologize for any inconvenience that may have been caused.</div></div>","PeriodicalId":17283,"journal":{"name":"Journal of The Franklin Institute-engineering and Applied Mathematics","volume":"362 6","pages":"Article 107582"},"PeriodicalIF":3.7,"publicationDate":"2025-02-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143521148","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}