Application of Mathematical Method in Robust and Nonlinear Control

A special issue of Mathematics (ISSN 2227-7390). This special issue belongs to the section "E2: Control Theory and Mechanics".

Deadline for manuscript submissions: closed (31 January 2025) | Viewed by 2694

Special Issue Editor

College of Artificial Intelligence and Automation, Hohai University, Nanjing 210098, China
Interests: intelligent information processing and intelligent control; advanced control theory and application
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Special Issue Information

Dear Colleagues,

Recently, the significance of dealing with uncertainties in the field of control design has been realized from both academic and industrial perspectives. In general, uncertainties derive from the modeling of nonlinear systems, namely plant uncertainties, and the operation of nonlinear systems, namely external disturbances. As a challenging task, a number of robust and nonlinear control approaches using mathematical methods have been presented to further improve control performance against uncertainties, such as sliding mode control, fuzzy control, adaptive control, and H infinite control.

This Special Issue, titled “Application of Mathematical Method in Robust and Nonlinear Control”, presents the latest research and developments in mathematic-based robust and nonlinear control techniques for various engineering, science, and management applications. This Special Issue aims to serve as a forum for exchanging ideas and knowledge among researchers and practitioners worldwide, inspiring new research directions and applications in this field. Both original research and review papers are welcome to be submitted to this Special Issue. Topics of interest include, but are not limited to, the following:

  • Nonlinear control;
  • Robust control;
  • Adaptive control;
  • Fuzzy neural networks;
  • Sliding mode control;
  • Backstepping control;
  • Reinforcement learning;
  • Deep learning;
  • Artificial intelligence.

Dr. Shixi Hou
Guest Editor

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Keywords

  • nonlinear control
  • robust control
  • adaptive control
  • fuzzy neural networks
  • sliding mode control
  • backstepping control
  • reinforcement learning
  • deep learning
  • artificial intelligence

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Published Papers (2 papers)

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Research

21 pages, 1775 KiB  
Article
Adaptive Visual Control for Robotic Manipulators with Consideration of Rigid-Body Dynamics and Joint-Motor Dynamics
by Zhitian Chen, Weijian Wen and Weijun Yang
Mathematics 2024, 12(15), 2413; https://doi.org/10.3390/math12152413 - 2 Aug 2024
Cited by 1 | Viewed by 1118
Abstract
A novel cascade visual control scheme is proposed to tailor for electrically driven robotic manipulators that operate under kinematic and dynamic uncertainties, utilizing an uncalibrated stationary camera. The proposed control approach incorporates adaptive weight radial basis function neural networks (RBFNNs) to learn the [...] Read more.
A novel cascade visual control scheme is proposed to tailor for electrically driven robotic manipulators that operate under kinematic and dynamic uncertainties, utilizing an uncalibrated stationary camera. The proposed control approach incorporates adaptive weight radial basis function neural networks (RBFNNs) to learn the behaviors of the uncertain dynamics of the robot and the joint actuators. The controllers are designed to nullify the approximation error and mitigate unknown disturbances through an integrated robust adaptive mechanism. A major advantage of the proposed approach is that prior knowledge of the dynamics of the robotic manipulator and its actuator is no longer required. The controller autonomously assimilates the robot and actuator dynamics online, thereby obviating the need for fussy regression matrix derivation and advance dynamic measurement to establish the adaptive dynamic parameter update algorithm. The proposed scheme ensures closed-loop system stability, bounded system states, and the convergence of tracking errors to zero. Simulation results, employing a PUMA manipulator as a testbed, substantiate the viability of the proposed control policy. Full article
(This article belongs to the Special Issue Application of Mathematical Method in Robust and Nonlinear Control)
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18 pages, 2250 KiB  
Article
Adaptive Iterative Learning Constrained Control for Linear Motor-Driven Gantry Stage with Fault-Tolerant Non-Repetitive Trajectory Tracking
by Chaohai Yu
Mathematics 2024, 12(11), 1673; https://doi.org/10.3390/math12111673 - 27 May 2024
Cited by 2 | Viewed by 1059
Abstract
This article introduces an adaptive fault-tolerant control method for non-repetitive trajectory tracking of linear motor-driven gantry platforms under state constraints. It provides a comprehensive solution to real-world issues involving state constraints and actuator failures in gantry platforms, alleviating the challenges associated with precise [...] Read more.
This article introduces an adaptive fault-tolerant control method for non-repetitive trajectory tracking of linear motor-driven gantry platforms under state constraints. It provides a comprehensive solution to real-world issues involving state constraints and actuator failures in gantry platforms, alleviating the challenges associated with precise modeling. Through the integration of iterative learning and backstepping cooperative design, this method achieves system stability without requiring a priori knowledge of system dynamic models or parameters. Leveraging a barrier composite energy function, the proposed controller can effectively regulate the stability of the controlled system, even when operating under state constraints. Instability issues caused by actuator failures are properly addressed, thereby enhancing controller robustness. The design of a trajectory correction function further extends applicability. Experimental validation on a linear motor-driven gantry platform serves as empirical evidence of the effectiveness of the proposed method. Full article
(This article belongs to the Special Issue Application of Mathematical Method in Robust and Nonlinear Control)
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