MDPI - Publisher of Open Access Journals

25 pages, 2543 KiB

Open AccessArticle

Granular Fuzzy Fractional Continuous-Time Linear Systems: Roesser and Fornasini–Marchesini Models

by Ghulam Muhammad, Muhammad Akram, Hamed Alsulami and Nawab Hussain

Fractal Fract. 2025, 9(7), 398; https://doi.org/10.3390/fractalfract9070398 - 20 Jun 2025

Viewed by 293

In this article, we introduce and investigate two classes of fuzzy fractional two-dimensional continuous-time (FFTDCT) linear systems to deal with uncertainty and fuzziness in system parameters. First, we analyze FFTDCT linear systems based on the Roesser model, incorporating fuzzy parameters into the state-space equations. The potential solution of the fuzzy fractional system is obtained using a two-dimensional granular Laplace transform approach. Second, we examine FFTDCT linear systems described by the second Fornasini–Marchesini (FM) model, where the state-space equations involve two-dimensional and one-dimensional partial fractional-order granular Caputo derivatives. We determine the fuzzy solution for this model by applying the two-dimensional granular Laplace transform. To enhance the validity of the proposed approaches, real-world applications, including signal processing systems and wireless sensor network data fusion, are solved to support the theoretical framework and demonstrate the impact of uncertainty on the system’s behavior. Full article

(This article belongs to the Special Issue Fractional Mathematical Modelling: Theory, Methods and Applications)

► Show Figures

Figure 1

14 pages, 297 KiB

Open AccessArticle

H_∞ Control for 2D Singular Continuous Systems

by Mariem Ghamgui, Marwa Elloumi, Moez Allouche and Mohamed Chaabane

Appl. Sci. 2024, 14(10), 4225; https://doi.org/10.3390/app14104225 - 16 May 2024

Viewed by 943

Abstract

This paper considers the problem of admissibility and admissibilization of 2D singular continuous systems described by the Roesser model. A necessary and sufficient admissibility condition is first proposed for 2D singular continuous systems in terms of a strict Linear Matrix Inequality (LMI). Then, a necessary and sufficient condition is established for the closed-loop system to be admissible (i.e., stable, regular, and impulse-free). Moreover, the stability condition is completed to give a sufficient condition to ensure a specified H_∞ disturbance attenuation level for the state feedback closed loop. To illustrate the effectiveness of the proposed methodology, a numerical example is given to illustrate an admissibilization of a state feedback closed-loop system. Full article

(This article belongs to the Special Issue Advanced Control Systems and Applications)

► Show Figures

Figure 1

13 pages, 1034 KiB

Open AccessArticle

Dynamic ILC for Linear Repetitive Processes Based on Different Relative Degrees

by Lei Wang, Liangxin Dong, Ruitian Yang and Yiyang Chen

Mathematics 2022, 10(24), 4824; https://doi.org/10.3390/math10244824 - 19 Dec 2022

Cited by 1 | Viewed by 1814

Abstract

The current research on iterative learning control focuses on the condition where the system relative degree is equal to 1, while the condition where the system relative degree is equal to 0 or greater than 1 is not considered. Therefore, this paper studies the monotonic convergence of the corresponding dynamic iterative learning controller systematically for discrete linear repetitive processes with different relative degrees. First, a 2D discrete Roesser model of the iterative learning control system is presented by means of 2D systems theory. Then, the monotonic convergence condition of the controlled system is analyzed according to the stability theory of linear repetitive process. Furthermore, the sufficient conditions of the controller existence are given in linear matrix inequality format under different relative degrees, which guarantees the system dynamic performance. Finally, through comparison with static controllers under different relative degrees, the simulation results show that the designed schemes are effective and feasible. Full article

► Show Figures

Figure 1

17 pages, 607 KiB

Open AccessArticle

Iterative Learning Control for Actuator Fault Uncertain Systems

by Lei Wang, Liangxin Dong, Yiyang Chen, Keqing Wang and Feng Gao

Symmetry 2022, 14(10), 1969; https://doi.org/10.3390/sym14101969 - 21 Sep 2022

Cited by 6 | Viewed by 1625

Abstract

An iterative learning fault-tolerant control method is designed for an actuator fault intermittent process with simultaneous uncertainties for the system parameters. First, an intermittent fault tolerance controller is designed using 2D system theory, and the iterative learning control (ILC) intermittent process is transformed into a 2D Roesser model. Secondly, sufficient conditions for the controller’s existence are analyzed using the linear matrix inequality (LMI) technique, and the control gain matrices are obtained by convex optimization with LMI constraints. Under these conditions for all additive uncertainties for the system parameters and admissible failures, the controller can ensure closed-loop fault-tolerant performance in both the time and batch directions, and it can also meet the H∞ robust performance level against outside disturbances. Eventually, the algorithm’s computational complexity is analyzed, and the effectiveness of the algorithm is verified by simulation with respect to an injection molding machine model. Compared with traditional ILC laws, which do not consider actuator faults, the proposed algorithm has a better convergence speed and stability when the time-invariant and time-variant actuator faults occur during implementation. Full article

(This article belongs to the Section Engineering and Materials)

► Show Figures

Figure 1

12 pages, 344 KiB

Open AccessArticle

General Response Formula for CFD Pseudo-Fractional 2D Continuous Linear Systems Described by the Roesser Model

by Krzysztof Rogowski

Symmetry 2020, 12(12), 1934; https://doi.org/10.3390/sym12121934 - 24 Nov 2020

Cited by 8 | Viewed by 2122

Abstract

In many engineering problems associated with various physical phenomena, there occurs a necessity of analysis of signals that are described by multidimensional functions of more than one variable such as time t or space coordinates x, y, z. Therefore, in such cases, we should consider dynamical models of two or more dimensions. In this paper, a new two-dimensional (2D) model described by the Roesser type of state-space equations will be considered. In the introduced model, partial differential operators described by the Conformable Fractional Derivative (CFD) definition with respect to the first (horizontal) and second (vertical) variables will be applied. For the model under consideration, the general response formula is derived using the inverse fractional Laplace method. Next, the properties of the solution will be considered. Usefulness of the general response formula will be discussed and illustrated by a numerical example. Full article

(This article belongs to the Special Issue Ordinary and Partial Differential Equations: Theory and Applications)

► Show Figures

Figure 1

12 pages, 4370 KiB

Open AccessArticle

Line and V-Shape Formation Based Distributed Processing for Robotic Swarms

by Jian Yang, Xin Wang and Peter Bauer

Sensors 2018, 18(8), 2543; https://doi.org/10.3390/s18082543 - 3 Aug 2018

Cited by 19 | Viewed by 3862

Abstract

Efficient distributed processing is vital for collaborative searching tasks of robotic swarm systems. Typically, those systems are decentralized, and the members have only limited communication and processing capacities. What is illustrated in this paper is a distributed processing paradigm for robotic swarms moving in a line or v-shape formation. The introduced concept is capable of exploits the line and v-shape formations for 2-D filtering and processing algorithms based on a modified multi-dimensional Roesser model. The communication is only between nearest adjacent members with a simple state variable. As an example, we applied a salient region detection algorithm to the proposed framework. The simulation results indicate the designed paradigm can detect salient regions by using a moving line or v-shape formation in a scanning way. The requirement of communication and processing capability in this framework is minimal, making it a good candidate for collaborative exploration of formatted robotic swarms. Full article

(This article belongs to the Special Issue Bio-Inspiring Sensing)

► Show Figures

Figure 1

Search Results (6)

Further Information

Guidelines

MDPI Initiatives

Follow MDPI

Saved Queries

Search Filter Reset All

Years

Feature Papers

Subjects

Journals

Article Types

Countries / Regions

Search Results (6)

Further Information

Guidelines

MDPI Initiatives

Follow MDPI