Article
Engineering, Mechanical
Oscar Martinez-Fuentes, Aldo Jonathan Munoz-Vazquez, Guillermo Fernandez-Anaya, Esteban Tlelo-Cuautle
Summary: In this paper, a class of dynamic observers for nonlinear fractional-order systems is studied, and the Mittag-Leffler stability is analyzed. The Riemann-Liouville integral is utilized to provide robustness against noisy measurements, and a family of high gain proportional rho-integral observers is designed for estimating unmeasured state variables.
NONLINEAR DYNAMICS
(2023)
Article
Mathematics, Applied
Oscar Martinez-Fuentes, Guillermo Fernandez-Anaya, Aldo Jonathan Munoz-Vazquez
Summary: Stability analysis is crucial in control systems design. This paper focuses on fractional systems modeled by the Atangana-Baleanu derivative, introducing novel inequalities and considering quadratic and convex Lyapunov functions for stability analysis using the Direct Lyapunov Method.
MATHEMATICAL METHODS IN THE APPLIED SCIENCES
(2021)
Article
Engineering, Mechanical
Rui-Yang Cai, Hua-Cheng Zhou, Chun-Hai Kou
Summary: In this paper, the sliding mode control (SMC) design for unstable fractional heat and wave equations involving unknown external disturbances is studied. A backstepping transform is constructed to stabilize the system in the sense of Mittag-Leffler (M-L) when the disturbance vanishes. Sliding mode controllers and reaching conditions are provided for fractional heat and wave systems when the disturbance flows into the boundary. Based on the Riesz basis approach, well-posedness and closed-loop algebraic stability conclusions are established for fractional partial differential inclusion systems with discontinuous boundary conditions. Furthermore, a longtime unsolved problem regarding the boundary feedback stabilization control for fractional partial differential equations (PDEs) is completely solved.
NONLINEAR DYNAMICS
(2023)
Review
Mathematics
Oana Brandibur, Roberto Garrappa, Eva Kaslik
Summary: This paper provides a detailed analysis of the stability of linear systems of fractional differential equations with Caputo derivative, including investigations into single-order systems, multi-order systems, and the role of the Mittag-Leffler function. Numerical experiments are presented to illustrate the main results.
Article
Computer Science, Information Systems
Truong Vinh An, Ngo Van Hoa
Summary: This article discusses the stability theory of fuzzy fractional dynamic systems with the random-order Caputo fractional derivative. New inequalities on the random-order Caputo fractional derivative are established, which are essential tools in investigating the stability theory of RO-FFDSs. Based on the extension of the Lyapunov direct method, the asymptotical stability and the Mittag-Leffler stability of the controlled problem of RO-FFDSs are investigated using a linear feedback controller. Numerical examples are given to demonstrate the effectiveness of the theoretical results.
INFORMATION SCIENCES
(2022)
Article
Automation & Control Systems
Zhang Zhe, Wang Yaonan, Zhang Jing, Zhaoyang Ai, FanYong Cheng, Feng Liu
Summary: A novel decentralized non-integer order controller is proposed for nonlinear fractional-order composite systems (NFOCS), and some novel results for asymptotic stabilization are shown. The controller provides a solution for the asymptotic stabilization problem of NFOCS and has a wider control gain range with weaker requirements.
Article
Mathematics
Xinggui Li, Ruofeng Rao, Shouming Zhong, Xinsong Yang, Hu Li, Yulin Zhang
Summary: This paper presents a new global Mittag-Leffler synchronization criterion for fractional-order hyper-chaotic financial systems by designing impulsive control and state feedback controller. The significance lies in achieving synchronization between backward and advanced economic systems under effective impulse macroeconomic management means. The effectiveness of the proposed methods is demonstrated in a numerical example, overcoming the mathematical difficulty of non-Lipschitz continuous activation function.
Article
Mathematics, Interdisciplinary Applications
Tran Minh Duc, Ngo Van Hoa
Summary: This paper investigates the stability and stabilization problem of variable-order fractional nonlinear dynamic systems with impulsive effects using a linear feedback controller. New inequalities on the VO Caputo fractional derivatives are established, and several criteria on Mittag-Leffler stability and asymptotical stability are presented. Numerical examples are provided to demonstrate the efficiency of the proposed method.
CHAOS SOLITONS & FRACTALS
(2021)
Article
Computer Science, Artificial Intelligence
Shenglong Chen, Hong-Li Li, Haibo Bao, Long Zhang, Haijun Jiang, Zhiming Li
Summary: This paper investigates discrete-time fractional-order delayed quaternion-valued neural networks (DFDQNNs) using the direct quaternion approach. A novel lemma and its corresponding corollaries are proposed for estimating the nabla fractional difference of the quaternion-valued Lyapunov function. The existence and uniqueness of equilibrium point for DFDQNNs are proved by constructing a new quaternion-valued contraction mapping. Sufficient criteria for global Mittag-Leffler stability and Mittag-Leffler synchronization of DFDQNNs are obtained using designed Lyapunov functions, effective feedback controller, and neoteric nabla difference inequalities. Numerical examples are provided to verify the results.
Article
Mathematics, Applied
Thi Thu Huong Nguyen, Nhu Thang Nguyen, Minh Nguyet Tran
Summary: In this paper, the robust finite time stability of fractional order systems with time varying delay and nonlinear perturbation is investigated. The sufficient condition for general fractional delay systems is improved by utilizing the special structure of a singular Gronwall inequality. For stable fractional delay systems, the approach is based on a global Halanay type inequality in differential and integral forms. A sharper delay dependent sufficient condition for robust finite time stability of such systems is formulated in terms of the Mittag-Leffler functions and the delayed size. The connection between the new sufficient condition and the previous results is compared and discussed thoroughly.
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
(2023)
Article
Mathematics, Interdisciplinary Applications
Peng Xu, Fei Long, Qixiang Wang, Ji Tian, Xiaowu Yang, Lipo Mo
Summary: This paper addresses the finite-time stability problem of Caputo nabla fractional-order switched linear systems with α∈(0,1). It proposes the monotonicity of the discrete Mittag-Leffler function and obtains the form of the solution for Caputo nabla fractional-order switched linear systems under pre-designed switching rules using the discrete unit step function. Based on these, it proposes some sufficient conditions of finite-time stability for Caputo nabla fractional-order switched linear systems according to the discrete Gronwall inequality and the monotonicity of the discrete Mittag-Leffler function. Simulation verification is carried out through three numerical examples.
FRACTAL AND FRACTIONAL
(2022)
Article
Automation & Control Systems
Lorenz Josue Oliva-Gonzalez, Rafael Martinez-Guerra, Juan Pablo Flores-Flores
Summary: This paper proposes a novel fractional observer based on observability for incommensurate fractional order systems with parametric uncertainties. The observer design only considers the available output and its fractional derivatives, and it does not require a system copy, which provides robustness and reduced order. The effectiveness of the proposed observer is demonstrated with numerical and real-world examples.
Article
Mathematics, Applied
G. Arthi, K. Suganya
Summary: This article focuses on the controllability of linear and nonlinear higher order stochastic fractional control delay systems with Caputo fractional derivative, utilizing the MLF and BDG inequality. By applying the Banach fixed point theorem, an exact method to design stochastic perturbations for control is established for the considered nonlinear higher order fractional differential systems. The derived design is illustrated with two numerical examples.
APPLIED MATHEMATICS AND COMPUTATION
(2021)
Article
Automation & Control Systems
Le Anh Tuan
Summary: This article presents a control system for rubber-tired gantry (RTG) cranes using three actuators to track three actuated outputs and stabilize two unactuated outputs. Advanced techniques such as fast-terminal sliding mode, fractional calculus, backstepping, and neural networks are incorporated to endow the control system with adaptive and robust features. Simulation and experimentation are conducted to evaluate the quality and effectiveness of the control system.
IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS
(2021)
Article
Materials Science, Multidisciplinary
Tianwei Zhang, Yongkun Li, Jianwen Zhou
Summary: This paper establishes the basic structure of Mittag-Leffler implicit Euler scheme for fractional differential equations by using the constant variation methods in fractional calculus. The paper proposes the fractional PECE algorithms to solve these implicit differences effectively. Additionally, a novel nonlocal difference operator is proposed and the existence and boundedness of a unique globally exponentially stable solution of some nonlocal difference system with short-term memory are investigated.
RESULTS IN PHYSICS
(2022)
Article
Mathematics, Applied
Aldo Jonathan Munoz-Vazquez, Guillermo Fernandez-Anaya, Juan Diego Sanchez-Torres
Summary: This paper proposes a robust sliding mode controller for distributed-order systems, utilizing a dynamic extension to induce an integer-order reaching phase and a continuous fractional sliding mode controller to compensate disturbances. Theoretical results demonstrate exact compensation of disturbances and asymptotic convergence of the pseudo-state, with numerical simulation confirming the reliability and efficacy of the method, outperforming conventional sliding mode schemes.
JOURNAL OF APPLIED MATHEMATICS AND COMPUTING
(2022)
Article
Computer Science, Interdisciplinary Applications
Aldo Jonathan Munoz-Vazquez, Oscar Martinez-Fuentes, Guillermo Fernandez-Anaya
Summary: This paper presents a generalization of existing control methods to robustly stabilize a large class of physical and engineering systems. The proposed control structure includes state feedback and a generalized PI controller to compensate for uncertainties and disturbances. The contribution lies in the extension of conventional PI structures to handle more diverse closed-loop responses.
MATHEMATICS AND COMPUTERS IN SIMULATION
(2022)
Article
Engineering, Mechanical
Guillermo Fernandez-Anaya, Oscar Martinez-Fuentes, Aldo Jonathan Munoz-Vazquez, Juan Diego Sanchez-Torres, Luis Alberto Quezada-Tellez, Fidel Melendez-Vazquez
Summary: Vector field decomposition is used in physics and engineering to analyze dynamical systems. This paper suggests novel stabilization methods using gradient control and Presnov decomposition to achieve stability in nonlinear systems. Numerical simulations demonstrate the feasibility of these schemes.
NONLINEAR DYNAMICS
(2022)
Article
Mathematics, Applied
Aldo Jonathan Munoz-Vazquez, Guillermo Fernandez-Anaya, Juan Diego Sanchez-Torres, Salah Boulaaras
Summary: This paper presents a new methodology for robust stabilisation of distributed-order systems, which can handle both matched and mismatched disturbances using a nonlinear controller and a pseudo-state feedback. The gain of the pseudo-state feedback is adjusted by solving a linear matrix inequality. Numerical simulations demonstrate the reliability of the proposed scheme.
MATHEMATICAL METHODS IN THE APPLIED SCIENCES
(2022)
Article
Automation & Control Systems
Oscar A. Angeles-Ramirez, Guillermo Fernandez-Anaya, Aldo J. Munoz-Vazquez, Juan D. Sanchez-Torres, Fidel Melendez-Vazquez
Summary: This paper derives the sufficient and necessary conditions for a distributed-order linear time invariant system to be positive real in terms of linear matrix inequalities. The positive realness conditions are derived for three common cases in the literature. The strictly positive realness condition is also obtained as an additional result. Moreover, the concept of learnability of fractional-order multi-input multi-output systems is extended to distributed-order systems using an iterative learning scheme based on output-dissipativity.
ASIAN JOURNAL OF CONTROL
(2023)
Article
Computer Science, Artificial Intelligence
Chidentree Treesatayapun, Aldo Jonathan Munoz-Vazquez
Summary: In this article, a nonlinear mathematical model is used to analyze the biological phenomena in chemotherapy cancer treatment. The model considers unknown discrete-time systems with limited input and output data. The actor-critic architecture is utilized to develop a control strategy without a full-state observer. Fuzzy rules emulated networks are constructed based on human knowledge, and the learning laws are derived from an incoherent reward function. The proposed scheme is shown to have convergence and robustness through theoretical and numerical analysis, and comparative results demonstrate its effectiveness.
NEURAL COMPUTING & APPLICATIONS
(2023)
Article
Automation & Control Systems
Jorge E. Ayala-Carrillo, Vicente Parra-Vega, Ernesto Olguin-Diaz, Christian A. Trejo-Ramos
Summary: This article studies the Lagrangian dynamics of a highly coupled nonlinear cPSR system equipped with three embedded pneumatic chambers and proposes a robust feedback cascade tracking controller for controlling the pneumatic dynamics.
IEEE CONTROL SYSTEMS LETTERS
(2023)
Article
Automation & Control Systems
Chidentree Treesatayapun, Aldo Jonathan Munoz-Vazquez
Summary: In this paper, a reinforcement learning-based optimal control strategy is developed for the drug administration in chemotherapy cancer treatment. The controller is designed based on a class of unknown discrete-time systems, utilizing only drug administration as input and tumor cells population as output, without the full-state observer. The proposed controller employs an actor-critic architecture with two fuzzy-rule emulated networks, where IF-THEN rules are imposed based on human knowledge of pharmacokinetics and pharmacodynamics. A discontinuous reward function is also proposed to derive online learning laws guaranteeing robustness and convergence of adjustable parameters. Numerical simulations are performed to validate the robustness of the patient group and the closed-loop performance with comparative results.
ENGINEERING APPLICATIONS OF ARTIFICIAL INTELLIGENCE
(2023)
Article
Automation & Control Systems
Rodolfo Garcia-Rodriguez, Vicente Parra-Vega, Luis Pantoja-Garcia, Ernesto Olguin-Diaz
Summary: This study investigates the problem of simultaneous holonomic and nonholonomic constraints in robot control. A controller is proposed to ensure the convergence of both constraint forces, and a simulation study demonstrates its advantages in complex dexterity tasks.
INTERNATIONAL JOURNAL OF CONTROL AUTOMATION AND SYSTEMS
(2023)
Article
Computer Science, Artificial Intelligence
Chidentree Treesatayapun, Aldo Jonathan Munoz-Vazquez, Naret Suyaroj
Summary: In this article, the dynamics of cell populations for cancer patients under chemotherapy drug administration are reformulated using pseudopartial derivative of input-output data. A model-free adaptive controller is established with two fuzzy-rules emulated networks based on a reinforcement learning scheme with convergence analysis of internal signals, using only the tumor cells population as the output and the drug administration as the output data. The optimal drug administration is derived according to the robustness of individual patients and delaying treatments, and the effectiveness of the proposed scheme is validated using a rigorous numerical system.
Article
Engineering, Electrical & Electronic
Pablo De Villeros, Juan Diego Sanchez-Torres, Aldo Jonathan Munoz-Vazquez, Michael Defoort, Guillermo Fernandez-Anaya, Alexander Loukianov
Summary: This paper investigates the problem of distributed predefined-time optimization for leaderless consensus of second-order multi-agent systems under a class of weighted digraphs. It proposes a framework with two main steps. In the first step, the agents perform a consensus-based distributed predefined-time optimization and generate a constant optimal output reference for each agent. In the second step, each agent tracks its corresponding optimal output reference using a sliding-mode controller to achieve the global optimum within a predefined time, even in the presence of matched disturbances. The proposed algorithm explicitly relies on user-defined constant parameters. Numerical simulations are conducted to validate the effectiveness of the algorithm.
Article
Engineering, Electrical & Electronic
Alejandro Tevera-Ruiz, Rodolfo Garcia-Rodriguez, Vicente Parra-Vega, Luis Enrique Ramos-Velasco
Summary: Some critical tasks require refined actions near the target to increase maneuvering precision. Novel approaches, such as Q-learning, have been proposed to learn from scratch and make action decisions that lead to an increase in reward. However, reducing the resolution box needed for critical tasks may increase computational load.
Article
Mathematics, Interdisciplinary Applications
Aldo Jonathan Munoz-Vazquez, Oscar Martinez-Fuentes, Guillermo Fernandez-Anaya
Summary: This report studies conditions for the nonexistence of finite-time stable equilibria in a class of systems described by nonlinear integral equations with Sonine kernel pairs. It firstly proves that a real-valued function, which converges in finite-time to a constant value different from the initial condition and remains there afterwards, cannot have a Sonine derivative that also remains at zero after some finite time, under certain criteria. Then, the concept of equilibrium is generalized to equivalent equilibrium, and it is demonstrated that a nonlinear integral equation with Sonine kernel pairs cannot have equivalent finite-time stable equilibria. Finally, illustrative examples are presented.
FRACTAL AND FRACTIONAL
(2023)
Article
Engineering, Mechanical
Oscar Martinez-Fuentes, Aldo Jonathan Munoz-Vazquez, Guillermo Fernandez-Anaya, Esteban Tlelo-Cuautle
Summary: In this paper, a class of dynamic observers for nonlinear fractional-order systems is studied, and the Mittag-Leffler stability is analyzed. The Riemann-Liouville integral is utilized to provide robustness against noisy measurements, and a family of high gain proportional rho-integral observers is designed for estimating unmeasured state variables.
NONLINEAR DYNAMICS
(2023)
Article
Robotics
Iram Munoz-Pepi, Nadia Garcia-Hernandez, Vicente Parra-Vega
Summary: This letter introduces an explicit biomechanical framework for solving forward neuromusculoskeletal models (NMSMs) and proposes a novel muscle-wrapping method. The simulation results show that the proposed method yields improved results compared to OpenSim and demonstrates the reliability of the proposed modular NMSM framework for simulating human-robot interaction dynamics. Overall, this research contributes as a baseline for modeling and studying more representative forward NMSMs to assess human movement and interaction with robots.
IEEE ROBOTICS AND AUTOMATION LETTERS
(2023)
Article
Computer Science, Interdisciplinary Applications
Vitaly Chernik, Pavel Buklemishev
Summary: The paper introduces a simple 2D model for describing the cell motility on a homogeneous isotropic surface. The model incorporates the dynamics of complex actomyosin liquid, which affects the boundary dynamics and cell motility. It consists of a system of equations with a free boundary domain and includes a non-local term. The numerical solution of this model is presented in this work.
MATHEMATICS AND COMPUTERS IN SIMULATION
(2024)
Article
Computer Science, Interdisciplinary Applications
Hasan Karjoun, Abdelaziz Beljadid
Summary: In this study, we developed a numerical model based on the depth-averaged shallow water equations to simulate flows through vegetation field. The model takes into account the drag and inertia forces induced by vegetation, using different formulations for the stem drag coefficient. Turbulence induced by vegetation is also considered through the addition of diffusion terms in the momentum equations. The proposed numerical model is validated through numerical simulations and shows good accuracy in simulating overland flows under vegetation effects.
MATHEMATICS AND COMPUTERS IN SIMULATION
(2024)
Article
Computer Science, Interdisciplinary Applications
Bechir Naffeti, Hamadi Ammar, Walid Ben Aribi
Summary: This paper proposes a branch and bound multidimensional Holder optimization method, which converts a multivariate objective function into a single variable function and minimizes it using an iterative optimization method. The method is applied to solve a parameters identification problem resulting from the increase in infections, providing information about the prevalence and infection force.
MATHEMATICS AND COMPUTERS IN SIMULATION
(2024)
Article
Computer Science, Interdisciplinary Applications
Heba F. Eid, Erik Cuevas, Romany F. Mansour
Summary: The proposed modified Bonobo optimizer algorithm dynamically adjusts the trajectory of each search agent to overcome the flaw of the original algorithm and improve the performance and solution quality by exploring and exploiting different regions of the solution space.
MATHEMATICS AND COMPUTERS IN SIMULATION
(2024)
Article
Computer Science, Interdisciplinary Applications
Farshid Mehrdoust, Idin Noorani, Juho Kanniainen
Summary: This paper proposes a Markov-switching model to evaluate the dynamics of commodity futures and spot prices, and introduces a hidden Markov chain to model the sudden jumps in commodity prices. The model is calibrated using the crude oil spot price and estimation-maximization algorithm. The study also evaluates European call options written on crude oil futures under the regime-switching model and derives Greek formulas for risk assessment. The importance of this paper is rated at 8 out of 10.
MATHEMATICS AND COMPUTERS IN SIMULATION
(2024)
Article
Computer Science, Interdisciplinary Applications
Rupa Mishra, Tapas Kumar Saha
Summary: This paper presents a control scheme for distributed generation units to operate in stand-alone and grid-connected modes, with a smooth transition between the two. The control strategy includes predictive control for voltage and frequency regulation in stand-alone mode, and power control for symmetrical and unbalanced grid voltage conditions in grid-connected mode. The proposed control method improves power factor, reduces grid current harmonics, and eliminates grid frequency ripple.
MATHEMATICS AND COMPUTERS IN SIMULATION
(2024)
Article
Computer Science, Interdisciplinary Applications
Yu Wang, Yang Tian, Yida Guo, Haoping Wang
Summary: This paper proposes a multi-level control strategy for lower limb patient-exoskeleton coupling system (LLPECS) in rehabilitation training based on active torque. The controller consists of three sub-controllers: gait adjustment layer, interaction torque design layer, and trajectory tracking layer. The effectiveness of the proposed control strategy is demonstrated through co-simulations in the SimMechanics environment using an exoskeleton virtual prototype developed in SolidWorks.
MATHEMATICS AND COMPUTERS IN SIMULATION
(2024)
Article
Computer Science, Interdisciplinary Applications
Takuji Arai, Yuto Imai
Summary: The Barndorff-Nielsen and Shephard model is a jump-type stochastic volatility model, and this paper proposes two simulation methods for computing option prices under a representative martingale measure. The performance of these methods is evaluated through numerical experiments.
MATHEMATICS AND COMPUTERS IN SIMULATION
(2024)
Article
Computer Science, Interdisciplinary Applications
Wanai Li
Summary: This paper proposes a new framework that combines quadrature-based and quadrature-free discontinuous Galerkin methods and applies them to triangular and tetrahedral grids. Four different DG schemes are derived by choosing specific test functions and collocation points, improving computational efficiency and ease of code implementation.
MATHEMATICS AND COMPUTERS IN SIMULATION
(2024)
Article
Computer Science, Interdisciplinary Applications
Xiyuan Chen, Qiubao Wang
Summary: This paper introduces a technique that combines dynamical mechanisms and machine learning to reduce dimensionality in high-dimensional complex systems. The method utilizes Hopf bifurcation theory to establish a model paradigm and utilizes machine learning to train location parameters. The effectiveness and robustness of the proposed method are tested and validated through experiments and simulations.
MATHEMATICS AND COMPUTERS IN SIMULATION
(2024)
Article
Computer Science, Interdisciplinary Applications
Muhammad Farman, Aqeel Ahmad, Anum Zehra, Kottakkaran Sooppy Nisar, Evren Hincal, Ali Akgul
Summary: Diabetes is a significant public health issue that affects millions of people worldwide. This study proposes a mathematical model to understand the mechanisms of glucose homeostasis, providing valuable insights for diabetes management. The model incorporates fractional operators and analyzes the impact of a new wave of dynamical transmission on equilibrium points, offering a comprehensive understanding of glucose homeostasis.
MATHEMATICS AND COMPUTERS IN SIMULATION
(2024)
Article
Computer Science, Interdisciplinary Applications
Gholamreza Shobeyri
Summary: This study introduces two improved Laplacian models for more accurate simulation of free surface flows in the context of the MPS method. The higher accuracy of these models compared to the traditional methods is verified through solving 2D Poisson equations and solving three benchmark free surface flow problems. These models can also resolve the issue of wave damping in the original MPS computations.
MATHEMATICS AND COMPUTERS IN SIMULATION
(2024)
Article
Computer Science, Interdisciplinary Applications
Qiang Li, Jinling Liang, Weiqiang Gong, Kai Wang, Jinling Wang
Summary: This paper addresses the problem of nonfragile state estimation for semi-Markovian switching complex-valued networks with time-varying delay. By constructing an event-triggered generator and solving matrix inequalities, less conservative criteria are obtained, and the gains of the nonfragile estimator are explicitly designed. A numerical example is provided to demonstrate the effectiveness of the proposed estimation scheme.
MATHEMATICS AND COMPUTERS IN SIMULATION
(2024)
Article
Computer Science, Interdisciplinary Applications
Gengen Zhang, Jingyu Li, Qiong-Ao Huang
Summary: In this paper, a novel class of unconditionally energy stable schemes are constructed for solving gradient flow models by combining the relaxed scalar auxiliary variable (SAV) approach with the linear multistep technique. The proposed schemes achieve second-order temporal accuracy and strictly unconditional energy stability.
MATHEMATICS AND COMPUTERS IN SIMULATION
(2024)
Article
Computer Science, Interdisciplinary Applications
S. Clain, J. Figueiredo
Summary: This study proposes a detailed construction of a very high-order polynomial representation and introduces a functional to assess the quality of the reconstruction. Several optimization techniques are implemented and their advantages in terms of accuracy and stability are demonstrated.
MATHEMATICS AND COMPUTERS IN SIMULATION
(2024)
