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In this paper, a novel uncertain fractional-orders and parameters' inversion mechanism via the differential evolution algorithms (DE) with a general mathematical model is proposed for non-commensurate and hyper fractional chaotic systems.…

Chaotic Dynamics · Physics 2012-09-10 Fei Gao , Feng-xia Fei , Qian Xu , Yan-fang Deng , Yi-bo Qi

Highly non-linear vehicle dynamics plays an important role in autonomous driving systems, especially in congested traffic situations at very low speeds. Due to this fact, accurate controllers are needed in order to ensure safety during…

Adaptation and Self-Organizing Systems · Physics 2012-06-05 S. Hassan HosseinNia , Ines Tejado , Blas M. Vinagre , Vicente Milanes , Jorge Villagra

It is well known that using high-order numerical algorithms to solve fractional differential equations leads to almost the same computational cost with low-order ones but the accuracy (or convergence order) is greatly improved, due to the…

Numerical Analysis · Mathematics 2017-05-25 Hengfei Ding , Changpin Li

Considering the large number of fractional operators that exist, and since it does not seem that their number will stop increasing soon at the time of writing this paper, it is presented for the first time, as far as the authors know, a…

Numerical Analysis · Mathematics 2024-03-27 A. Torres-Hernandez , F. Brambila-Paz

This paper contributes to the design of a fractional order (FO) internal model controller (IMC) for a first order plus time delay (FOPTD) process model to satisfy a given set of desired robustness specifications in terms of gain margin (Am)…

Systems and Control · Electrical Eng. & Systems 2020-02-19 Pushkar Prakash Arya , Sohom Chakrabarty

A parallel numerical simulation algorithm is presented for fractional-order systems involving Caputo-type derivatives, based on the Adams-Bashforth-Moulton (ABM) predictor-corrector scheme. The parallel algorithm is implemented using…

Mathematical Software · Computer Science 2017-10-04 Cosmin Bonchis , Eva Kaslik , Florin Rosu

System identification refers to estimation of process parameters and is a necessity in control theory. Physical systems usually have varying parameters. For such processes, accurate identification is particularly important. Online…

Other Computer Science · Computer Science 2008-11-04 Deepyaman Maiti , Ayan Acharya , Amit Konar

In this paper, we consider the problem of computing robust controlled invariants for discrete-time monotone dynamical systems. We consider different classes of monotone systems depending on whether the sets of states, control inputs and…

Systems and Control · Electrical Eng. & Systems 2023-06-27 Adnane Saoud , Murat Arcak

The paper deals with an optimal control problem in a dynamical system described by a linear differential equation with the Caputo fractional derivative. The goal of control is to minimize a Bolza-type cost functional, which consists of two…

Optimization and Control · Mathematics 2019-09-25 Mikhail Gomoyunov

Fractional calculus is a generalization of classical theories of integration and differentiation to arbitrary order (i.e., real or complex numbers). In the last two decades, this new mathematical modeling approach has been widely used to…

Logic in Computer Science · Computer Science 2016-08-10 Umair Siddique , Osman Hasan , Sofiène Tahar

Modeling of phenomena such as anomalous transport via fractional-order differential equations has been established as an effective alternative to partial differential equations, due to the inherent ability to describe large-scale behavior…

Analysis of PDEs · Mathematics 2021-10-25 Jorge Suzuki , Mamikon Gulian , Mohsen Zayernouri , Marta D'Elia

In this paper, we present a new numerical method to solve fractional differential equations. Given a fractional derivative of arbitrary real order, we present an approximation formula for the fractional operator that involves integer-order…

Numerical Analysis · Mathematics 2015-12-16 Ricardo Almeida , Nuno R. O. Bastos

Number-conserving cellular automata are discrete dynamical systems that simulate interacting particles like e.g. grains of sand. In an earlier paper, I had already derived a uniform construction for all transition rules of one-dimensional…

Cellular Automata and Lattice Gases · Physics 2025-06-02 Markus Redeker

The notion of fractional dynamics is related to equations of motion with one or a few terms with derivatives of a fractional order. This type of equation appears in the description of chaotic dynamics, wave propagation in fractal media, and…

Classical Physics · Physics 2015-03-19 Vasily E. Tarasov , George M. Zaslavsky

This study reexamines diffusive representations for fractional integrals with the goal of pioneering new variants of such representations. These variants aim to offer highly efficient numerical algorithms for the approximate computation of…

Numerical Analysis · Mathematics 2025-07-08 Renu Chaudhary , Kai Diethelm

In this paper an offset-free model predictive control scheme is presented for fractional-order systems using the Gr\"unwald-Letnikov derivative. The infinite-history fractional-order system is approximated by a finite-dimensional…

Dynamical Systems · Mathematics 2019-04-26 Sotiris Ntouskas , Haralambos Sarimveis , Pantelis Sopasakis

Particle Swarm Optimization technique offers optimal or suboptimal solution to multidimensional rough objective functions. In this paper, this optimization technique is used for designing fractional order PID controllers that give better…

Other Computer Science · Computer Science 2008-10-22 Deepyaman Maiti , Sagnik Biswas , Amit Konar

This paper proposes an simple but yet effective approach to structured parametric controller design in a linear fractional form. The main contribution consists in using structured $\mathcal{H}_\infty$ oriented optimization tools in an…

Systems and Control · Computer Science 2017-04-12 C. Poussot-Vassal

This paper considers the problem of robust stability and stabilization for linear fractional-order system with nonlinear uncertain parameters, with fractional order 0<a<2. A dynamic output feedback controller, with predetermined order, for…

Optimization and Control · Mathematics 2021-06-25 Pouya Badri , Mahdi Sojoodi , Elyar Zavvari

We consider general convolutional derivatives and related fractional statistical dynamics of continuous interacting particle systems. We apply the subordination principle to construct kinetic fractional statistical dynamics in the continuum…

Mathematical Physics · Physics 2016-10-11 Anatoly N. Kochubei , Yuri Kondratiev