Article
Automation & Control Systems
Xiang Ren, Fei Hao
Summary: This paper investigates the application of observer-based event-triggered control in the stabilization of singularly perturbed systems. By designing two event-triggering conditions, ultimately bounded stability of the closed-loop system is achieved and Zeno behavior is eliminated.
Article
Automation & Control Systems
Jixing Lv, Changhong Wang, Yonggui Kao, Yushi Jiang
Summary: This paper investigates the fixed-time distributed estimation problem for a class of second-order nonlinear systems with uncertain input, unknown nonlinearity, and matched perturbation. A fixed-time distributed extended state observer is proposed, which can reconstruct both the full state and unknown dynamics of the system. The proposed observer reduces the communication load by requiring only the output of the leader and 1-dimensional output estimates from the neighboring nodes.
Article
Automation & Control Systems
Yuezu Lv, Zhongkui Li, Zhisheng Duan
Summary: This paper presents a framework on minimal-order specified-time unknown input observers for linear systems based on a pairwise observer structure. It first proposes a minimal-order specified-time observer for the linear system without the unknown input that can exactly estimate the state at the preset time. Another form of the specified-time observer is designed to further reduce the computational burden. In the presence of the unknown input, a minimal-order specified-time unknown input observer is presented by introducing a singular transformation to decouple the effect of the unknown input, with strong observability as the sufficient and necessary condition. The robustness of the proposed observers is also discussed.
Article
Automation & Control Systems
Zhe Zhang, Yunxia Song, Huaiyuan Jiang, Xuefei Yang
Summary: A family of observer-based periodic delayed feedback (PDF) controllers are proposed in this paper for the fixed-time stabilization of the linear input-delay system with immeasurable states. The relationship between the control gain and the system matrix is established by periodically switching the controller gain. Two different observer-predictor-based PDF controllers are proposed to address the open-loop problem faced by the standard PDF controller. Both controllers ensure that the closed-loop system converges asymptotically throughout the control period. Furthermore, a modified PDF is proposed for multi-input-multi-output systems utilizing the characteristic of controllability index set and observability index set.
INTERNATIONAL JOURNAL OF ROBUST AND NONLINEAR CONTROL
(2023)
Article
Engineering, Mechanical
Ming Yang, Zheng Wang, Dengxiu Yu, Zhen Wang, Yan -Jun Liu
Summary: This article discusses the practical fixed-time control algorithm for multi-agent systems (MASs) with unmeasurable states and disturbances. Neural networks are used to fit the nonlinear functions of MASs. The extended state observer (ESO) is applied to estimate the unmeasured states and unknown disturbances in MASs. The combination of adding power integration method and backstepping approach is employed to avoid singular phenomenon in the fixed time controller. The command filter is also used to reduce computational complexity in the controller design. Based on the practical fixed-time stability theory, it is guaranteed that the tracking error of MASs converges within a fixed time, independent of the initial states of MASs. Simulation results validate the effectiveness of the proposed MASs consensus algorithm.
NONLINEAR DYNAMICS
(2023)
Article
Mathematics, Applied
Shahzad Khattak, Ijaz Hussain, Jose Francisco Gomez-Aguilar, Rashid Jan
Summary: This article investigates the convergence characteristic of the PD-type iterative learning control scheme for linear discrete-time singular systems, and shows that the second-order PD-type algorithm has better tracking performance than the first-order throughout the entire time interval. Numerical analysis is conducted to validate the results.
MATHEMATICAL METHODS IN THE APPLIED SCIENCES
(2021)
Article
Automation & Control Systems
Agostino Martinelli
Summary: This article extends the observability rank condition to time-varying nonlinear systems and provides a general analytic condition. The proposed condition is applied to aerospace robotics to study the observability of a lunar-module-type system equipped with monocular vision and inertial sensors.
IEEE TRANSACTIONS ON AUTOMATIC CONTROL
(2022)
Article
Engineering, Mechanical
Bo Li, Haichao Zhang, Bing Xiao, Chenghu Wang, Yongsheng Yang
Summary: This paper introduces a novel control approach for fixed-time tracking of high-order nonlinear systems, using IHOSM surface and fixed-time sliding mode disturbance observer to achieve stability and accuracy. Experimental results demonstrate the effectiveness and superiority of the proposed method.
NONLINEAR DYNAMICS
(2022)
Article
Engineering, Electrical & Electronic
Wei Liu, Mou Chen, Peng Shi
Summary: This paper proposes an adaptive hierarchical sliding mode control scheme for anti-disturbance tracking control of under-actuated quadcopter suspension transportation system (UQSTS). The under-actuated characteristics of UQSTS are handled by HSMC, and the external disturbance is estimated using the fixed-time sliding mode disturbance observer (FTSMDO). The stability of the closed-loop system is verified through Lyapunov-based stability analysis. Physical experiment results demonstrate the effectiveness and potential of the proposed control techniques.
IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS I-REGULAR PAPERS
(2022)
Article
Engineering, Marine
Shun An, Longjin Wang, Yan He
Summary: This paper investigates the problem of fixed-time trajectory tracking control of underactuated autonomous underwater vehicles subject to external disturbances. The backstepping control technique and fixed-time control method are integrated to ensure the convergence of the vehicle's trajectory to a reference trajectory within a fixed time. A continuous fixed-time disturbance observer is developed to estimate the unknown external disturbances, and a nonlinear first-order filter is applied to avoid the adverse effects of complexity inherent in conventional backstepping. Theoretical analyses show that the proposed fixed-time backstepping controller can drive the tracking errors of the vehicle to a residual set in fixed time. Simulation results demonstrate the effectiveness and superiority of the proposed control method.
Article
Automation & Control Systems
Konstantin Zimenko, Andrey Polyakov, Denis Efimov, Artem Kremlev
Summary: This article focuses on the problem of finite-time and fixed-time observation of linear multiple input multiple output control systems. The proposed dynamic observers do not require system transformation to a canonical form and ensure convergence of the observation error to zero within a finite or fixed time. It is demonstrated that the observers are robust (in input-to-state sense) against input disturbances and measurement noises. Simulation examples are provided to support the results.
INTERNATIONAL JOURNAL OF ROBUST AND NONLINEAR CONTROL
(2023)
Article
Engineering, Marine
Meng Joo Er, Zhongkun Li
Summary: This paper proposes a fixed-time control strategy for the formation control of unmanned surface vehicles (USVs) under complex external disturbances and system uncertainties. The strategy includes a leader-follower formation control and the design of an observer for uncertainty items, ensuring fast and stable formation.
JOURNAL OF MARINE SCIENCE AND ENGINEERING
(2022)
Article
Automation & Control Systems
Lei Cui, Qi Zhou, Di Huang
Summary: This article proposes a fixed-time backstepping distributed cooperative containment control scheme for multiple unmanned aerial vehicles (UAVs). It solves the actuator saturation problem of fixed-wing UAVs with a fixed-time compensator. An improved fixed-time disturbance observer is proposed to address the excessive initial peak problem. The fixed-time differential filter solves the complexity explosion problem. For the distributed containment control of multiple UAVs, a cooperative control architecture based on a fixed-time anti-saturation compensation system is proposed. Simulation results demonstrate the effectiveness of the proposed control scheme.
INTERNATIONAL JOURNAL OF ROBUST AND NONLINEAR CONTROL
(2023)
Article
Engineering, Multidisciplinary
Yunfeng Hu, Chong Zhang, Xun Gong, Jinwu Gao, Lin Zhang, Hong Chen
Summary: This research focuses on developing a nonlinear dynamic output feedback controller to address the multivariable, nonlinear and unmeasurable state of the air supply system. Two fixed-time radial basis function neural network disturbance observers are used to estimate and compensate modeling uncertainties. Observer-based nonlinear cathode pressure tracking controller and supply manifold pressure tracking controller are designed using backstepping method. Simulation results demonstrate the effectiveness of the designed controller compared to PID and MPC.
Article
Automation & Control Systems
Guojie Li, Lei Liu, Jinguo Liu, Yanming Wu, Juanping Zhao
Summary: This paper investigates the three-dimensional integrated guidance and control (IGC) method for skid-to-turn (STT) missile with strap-down seeker under the constraints of field-of-view (FOV) and roll angle. A new low-order IGC model is constructed based on strap-down decoupling theory and roll angle equation. A low-order fixed-time IGC scheme is developed using the integral barrier Lyapunov function (iBLF) to limit the FOV and roll angles. The effectiveness and robustness of the proposed IGC scheme are verified through numerical simulations.
JOURNAL OF THE FRANKLIN INSTITUTE-ENGINEERING AND APPLIED MATHEMATICS
(2023)
Article
Computer Science, Artificial Intelligence
Xiang-Peng Xie, Qian Wang, Mohammed Chadli, Kaibo Shi
Summary: In this paper, a relaxed observer-based state estimation method for discrete-time Takagi-Sugeno fuzzy systems is proposed via a new augmented matrix approach. The method introduces additional matrices without redundant constraints under the framework of homogeneous polynomials, resulting in less conservative results compared to recent methods. Numerical simulations validate the superiority and generality of the developed method.
IEEE TRANSACTIONS ON FUZZY SYSTEMS
(2022)
Article
Automation & Control Systems
Saliha Marir, Mohammed Chadli, Michael V. Basin
Summary: This paper studies the stabilization problem for linear continuous-time singular fractional-order systems and obtains new formulations of the admissibility for the closed-loop system by dynamic output feedback controller using LMI conditions, to generalize existing results for integer-order systems. The presented approach is validated by numerical examples demonstrating its applicability and efficacy.
ASIAN JOURNAL OF CONTROL
(2023)
Article
Energy & Fuels
Sofiane Bououden, Fouad Allouani, Abdelaziz Abboudi, Mohammed Chadli, Ilyes Boulkaibet, Zaher Al Barakeh, Bilel Neji, Raymond Ghandour
Summary: This paper presents a novel observer-based robust fault predictive control (OBRFPC) approach for wind turbines with time-delay system subject to constraints, faults, and disturbances. The approach includes an augmented state-space representation, a robust predictive controller synthesis, and an observer for state and fault estimation. The proposed method utilizes disturbance estimates and formulates the control process as an optimization problem subject to linear matrix inequalities (LMIs) to ensure disturbance rejection and fault tolerance. A simulation example on a nonlinear wind turbine model demonstrates the effectiveness of the proposed method in dealing with nonlinear systems subject to disturbances and faults.
Article
Computer Science, Artificial Intelligence
Yueyang Li, Ming Yuan, Mohammed Chadli, Zi-Peng Wang, Dong Zhao
Summary: This article proposes a novel unknown input functional observer design approach for discrete-time interval type-2 Takagi-Sugeno fuzzy system models. By constructing a new state vector and solving a linear matrix equation, the existence conditions of observers are obtained. The solution of the simplified matrix equation is used to derive observer gains.
IEEE TRANSACTIONS ON FUZZY SYSTEMS
(2022)
Article
Automation & Control Systems
Li Ma, Fanglai Zhu, Jiancheng Zhang, Xudong Zhao
Summary: This article proposes a leader-follower asymptotic consensus control strategy for linear multiagent systems with unknown external disturbances and measurement noises. The article discusses the preconditions, minimum phase condition (MPC) and observer matching condition (OMC), and presents an equivalent result under these two preconditions. A reduced-order observer and a novel unknown disturbance reconstruction method are designed to estimate the system states and noises of each agent. The article also demonstrates the effectiveness and advantages of the proposed methods through simulation examples.
IEEE TRANSACTIONS ON CYBERNETICS
(2023)
Article
Automation & Control Systems
Kamil Hassan, Fatima Tahir, Muhammad Rehan, Choon Ki Ahn, Mohammed Chadli
Summary: This article addresses the group consensus problem in a network of multiagent systems by proposing a relative-output-based distributed control law. By utilizing Lyapunov stability theory and a linear matrix inequality, the sufficient and necessary conditions for achieving group consensus are formulated and validated.
IEEE TRANSACTIONS ON CYBERNETICS
(2023)
Article
Automation & Control Systems
B. Visakamoorthi, Samson Shenglong Yu, K. Subramanian, P. Muthukumar, Mohammed Chadli, Hieu Trinh
Summary: This study proposes a practical consensus control method for heterogeneous multiagent systems with gain fluctuations using sampled-data-based approach. A more general retarded sampled-data control approach is designed to achieve practical consensus by considering gain fluctuations, actual sampling pattern, and constant time delay. The stability condition of the closed-loop system is derived using a Wirtinger's inequality-based discontinuous Lyapunov-Krasovskii functional and linear matrix inequality. Numerical simulation validates the theoretical results obtained.
EUROPEAN JOURNAL OF CONTROL
(2023)
Article
Automation & Control Systems
Wenhai Qi, Guangdeng Zong, Yakun Hou, Mohammed Chadli
Summary: This article focuses on the discrete-time sliding mode control (DSMC) for nonlinear semi-Markovian switching systems (S-MSSs). Due to the difficulty in obtaining complete information of the semi-Markov Kernel in practical applications, it is commonly considered to be partly unknown. By utilizing the prior information of the sojourn-time upper bound for each switching mode, this article proposes sufficient conditions under the equivalent DSMC law for mean square stability. Moreover, the designed DSMC law achieves finite-time reachability of the sliding region and finite-time convergence of the sliding dynamics to the predesignated sliding region. A numerical example and an electronic throttle model are provided to validate the proposed control strategy.
IEEE TRANSACTIONS ON AUTOMATIC CONTROL
(2023)
Article
Computer Science, Artificial Intelligence
Zi-Peng Wang, Xu Zhang, Huai-Ning Wu, Mohammed Chadli, Tingwen Huang, Junfei Qiao
Summary: This article introduces a dynamic fuzzy boundary output feedback control for nonlinear space-varying parabolic partial differential equation systems with random time-varying delay under noncollocated boundary measurement. The nonlinear delayed PPDESs are represented by Takagi-Sugeno (T-S) fuzzy models and a fuzzy observer under NCBM is presented to overcome the design difficulty of boundary control. An observer-based fuzzy boundary controller is proposed and conditions for mean-square exponential stability are obtained by utilizing the Lyapunov direct method and Wirtinger inequality. Feasibility conditions for the DFBOF controller design are expressed in LMIs to solve the SLMIs. Two examples are provided to demonstrate the validity of the proposed approach.
IEEE TRANSACTIONS ON FUZZY SYSTEMS
(2023)
Article
Computer Science, Artificial Intelligence
Yang Wu, Xixiang Yang, Huaicheng Yan, Mohammed Chadli, Yueying Wang
Summary: This article presents a design of an event-triggered finite-time singularity-free terminal sliding-mode control algorithm for tracking Euler-Lagrange systems. The proposed algorithm can handle state/error constraints, unstructured dynamics, and external disturbances. It introduces a novel sliding-mode manifold that ensures finite-time convergence of tracking errors and strict constraint requirements. A fuzzy logic system is used to compensate for uncertainties, and an event-triggered mechanism is integrated to reduce signal transmission frequency.
IEEE TRANSACTIONS ON FUZZY SYSTEMS
(2023)
Article
Computer Science, Artificial Intelligence
Yajing Yu, Jian Guo, Mohammed Chadli, Zhengrong Xiang
Summary: This article investigates a distributed fuzzy adaptive formation control strategy for quadrotor multiple unmanned aerial vehicles (UAVs) under unmodeled dynamics and switching topologies. The strategy includes generating attitude commands, solving the position controller, constructing a communication mechanism, and designing a fuzzy adaptive sliding mode controller. The simulation results confirm the effectiveness of the proposed control strategy.
IEEE TRANSACTIONS ON FUZZY SYSTEMS
(2023)
Article
Automation & Control Systems
Panming Zhu, Guangdeng Chen, Guohuai Lin, Mohammed Chadli
Summary: This study investigates the leader-following consensus issue for multiagent systems under external disturbances and denial-of-service (DoS) attacks. A novel triggering mechanism is designed to save communication resources during normal communication periods and detect the end of attack periods. Estimators are constructed to predict the states of the agent and its neighbors during attacks. A distributed switching controller is designed that includes event-triggered and predicted states. The proposed secure control protocol ensures eventual consensus and avoids Zeno behavior. A simulation example demonstrates the effectiveness of the strategy.
TRANSACTIONS OF THE INSTITUTE OF MEASUREMENT AND CONTROL
(2023)
Article
Green & Sustainable Science & Technology
Omar Hazil, Fouad Allouani, Sofiane Bououden, Mohammed Chadli, Mohamed Chemachema, Ilyes Boulkaibet, Bilel Neji
Summary: In this paper, a new robust model predictive control (RMPC) algorithm is designed to regulate the terminal voltage of a photovoltaic generator (PVG) supplying power to a DC motor-pump via a buck DC-DC converter. The control task is complex due to the nonlinear behavior of the system and its dependency on climate conditions. Based on the dead-zone property, a new RMPC technique is introduced to ensure the robust stability of the closed-loop system in the presence of actuator nonlinearity.
Article
Computer Science, Artificial Intelligence
Yan Zhang, Mohammed Chadli, Zhengrong Xiang
Summary: In this article, the adaptive fuzzy predefined-time tracking control problem for a class of nonlinear systems with output hysteresis is investigated. An inverse model is utilized to capture the output hysteresis phenomenon, and the Nussbaum-type function technique is utilized to overcome the difficulty of unknown time-varying control gain caused by output hysteresis. An adaptive fuzzy control scheme under the backstepping framework is developed using the predefined-time stability criterion. The feasibility of the developed scheme is verified by an example of an electromechanical system.
IEEE TRANSACTIONS ON FUZZY SYSTEMS
(2023)
Article
Automation & Control Systems
Hao Shen, Yu-An Liu, Jing Wang, Huaicheng Yan, Mohammed Chadli
Summary: This work proposes an Hop sliding-mode control for nonlinear singularly perturbed system under the framework of network control. The system's nonlinearities with parameter uncertainties are described using the interval type-2 (IT2) fuzzy method for system modeling. A disturbance observer is developed to estimate and neutralize the unknown disturbance. An event-triggered communication protocol with a dynamic threshold parameter is adopted to reduce network resource occupation. A fuzzy integral sliding motion is constructed based on the system model and disturbance estimation. The proposed approach is demonstrated with IT2 fuzzy extensions of two classical examples.
IEEE TRANSACTIONS ON SYSTEMS MAN CYBERNETICS-SYSTEMS
(2023)
Article
Mathematics, Applied
Peter Frolkovic, Nikola Gajdosova
Summary: This paper presents compact semi-implicit finite difference schemes for solving advection problems using level set methods. Through numerical tests and stability analysis, the accuracy and stability of the proposed schemes are verified.
APPLIED MATHEMATICS AND COMPUTATION
(2024)
Article
Mathematics, Applied
Md. Rajib Arefin, Jun Tanimoto
Summary: Human behaviors are strongly influenced by social norms, and this study shows that injunctive social norms can lead to bi-stability in evolutionary games. Different games exhibit different outcomes, with some showing the possibility of coexistence or a stable equilibrium.
APPLIED MATHEMATICS AND COMPUTATION
(2024)
Article
Mathematics, Applied
Dingyi Du, Chunhong Fu, Qingxiang Xu
Summary: A correction and improvement are made on a recent joint work by the second and third authors. An optimal perturbation bound is also clarified for certain 2 x 2 Hermitian matrices.
APPLIED MATHEMATICS AND COMPUTATION
(2024)
Article
Mathematics, Applied
Pingrui Zhang, Xiaoyun Jiang, Junqing Jia
Summary: In this study, improved uniform error bounds are developed for the long-time dynamics of the nonlinear space fractional Dirac equation in two dimensions. The equation is discretized in time using the Strang splitting method and in space using the Fourier pseudospectral method. The major local truncation error of the numerical methods is established, and improved uniform error estimates are rigorously demonstrated for the semi-discrete scheme and full-discretization. Numerical investigations are presented to verify the error bounds and illustrate the long-time dynamical behaviors of the equation with honeycomb lattice potentials.
APPLIED MATHEMATICS AND COMPUTATION
(2024)
Article
Mathematics, Applied
Kuan Zou, Wenchen Han, Lan Zhang, Changwei Huang
Summary: This research extends the spatial PGG on hypergraphs and allows cooperators to allocate investments unevenly. The results show that allocating more resources to profitable groups can effectively promote cooperation. Additionally, a moderate negative value of investment preference leads to the lowest level of cooperation.
APPLIED MATHEMATICS AND COMPUTATION
(2024)
Article
Mathematics, Applied
Kui Du
Summary: This article introduces two new regularized randomized iterative algorithms for finding solutions with certain structures of a linear system ABx = b. Compared to other randomized iterative algorithms, these new algorithms can find sparse solutions and have better performance.
APPLIED MATHEMATICS AND COMPUTATION
(2024)
Article
Mathematics, Applied
Shadi Malek Bagomghaleh, Saeed Pishbin, Gholamhossein Gholami
Summary: This study combines the concept of vanishing delay arguments with a linear system of integral-algebraic equations (IAEs) for the first time. The piecewise collocation scheme is used to numerically solve the Hessenberg type IAEs system with vanishing delays. Well-established results regarding regularity, existence, uniqueness, and convergence of the solution are presented. Two test problems are studied to verify the theoretical achievements in practice.
APPLIED MATHEMATICS AND COMPUTATION
(2024)
Article
Mathematics, Applied
Qi Hu, Tao Jin, Yulian Jiang, Xingwen Liu
Summary: Public supervision plays an important role in guiding and influencing individual behavior. This study proposes a reputation incentives mechanism with public supervision, where each player has the authority to evaluate others. Numerical simulations show that reputation provides positive incentives for cooperation.
APPLIED MATHEMATICS AND COMPUTATION
(2024)
Article
Mathematics, Applied
Werner M. Seiler, Matthias Seiss
Summary: This article proposes a geometric approach for the numerical integration of (systems of) quasi-linear differential equations with singular initial and boundary value problems. It transforms the original problem into computing the unstable manifold at a stationary point of an associated vector field, allowing efficient and robust solutions. Additionally, the shooting method is employed for boundary value problems. Examples of (generalized) Lane-Emden equations and the Thomas-Fermi equation are discussed.
APPLIED MATHEMATICS AND COMPUTATION
(2024)
Article
Mathematics, Applied
Lisandro A. Raviola, Mariano F. De Leo
Summary: We evaluated the performance of novel numerical methods for solving one-dimensional nonlinear fractional dispersive and dissipative evolution equations and showed that the proposed methods are effective in terms of accuracy and computational cost. They can be applied to both irreversible models and dissipative solitons, offering a promising alternative for solving a wide range of evolutionary partial differential equations.
APPLIED MATHEMATICS AND COMPUTATION
(2024)
Article
Mathematics, Applied
Yong Wang, Jie Zhong, Qinyao Pan, Ning Li
Summary: This paper studies the set stability of Boolean networks using the semi-tensor product of matrices. It introduces an index-vector and an algorithm to verify and achieve set stability, and proposes a hybrid pinning control technique to reduce computational complexity. The issue of synchronization is also discussed, and simulations are presented to demonstrate the effectiveness of the results obtained.
APPLIED MATHEMATICS AND COMPUTATION
(2024)
Article
Mathematics, Applied
Ling Cheng, Sirui Zhang, Yingchun Wang
Summary: This paper considers the optimal capacity allocation problem of integrated energy systems (IESs) with power-gas systems for clean energy consumption. It establishes power-gas network models with equality and inequality constraints, and designs a novel full distributed cooperative optimal regulation scheme to tackle this problem. A distributed projection operator is developed to handle the inequality constraints in IESs. The simulation demonstrates the effectiveness of the distributed optimization approach.
APPLIED MATHEMATICS AND COMPUTATION
(2024)
Article
Mathematics, Applied
Abdurrahim Toktas, Ugur Erkan, Suo Gao, Chanil Pak
Summary: This study proposes a novel image encryption scheme based on the Bessel map, which ensures the security and randomness of the ciphered images through the chaotic characteristics and complexity of the Bessel map.
APPLIED MATHEMATICS AND COMPUTATION
(2024)
Article
Mathematics, Applied
Xinjie Fu, Jinrong Wang
Summary: In this paper, we establish an SAIQR epidemic network model and explore the global stability of the disease in both disease-free and endemic equilibria. We also consider the control of epidemic transmission through non-instantaneous impulsive vaccination and demonstrate the sustainability of the model. Finally, we validate the results through numerical simulations using a scale-free network.
APPLIED MATHEMATICS AND COMPUTATION
(2024)
Article
Mathematics, Applied
Maria Han Veiga, Lorenzo Micalizzi, Davide Torlo
Summary: The paper focuses on the iterative discretization of weak formulations in the context of ODE problems. Several strategies to improve the accuracy of the method are proposed, and the method is combined with a Deferred Correction framework to introduce efficient p-adaptive modifications. Analytical and numerical results demonstrate the stability and computational efficiency of the modified methods.
APPLIED MATHEMATICS AND COMPUTATION
(2024)
