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Nonlinear Control: Theory and Applications
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Nonlinear Control: Theory and Applications

A special issue of Applied Sciences (ISSN 2076-3417). This special issue belongs to the section "Mechanical Engineering".

Deadline for manuscript submissions: closed (31 March 2021) | Viewed by 38403

Special Issue Editor

Dr. Chih-Chiang Chen

E-Mail Website
Guest Editor
Department of Systems and Naval Mechatronic Engineering, National Cheng Kung University, Tainan 70101, Taiwan
Interests: nonlinear systems; non-smooth control; homogeneous system theory
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

I am very pleased to introduce the Special Issue on “Nonlinear Control: Theory and Applications” to be published in the open access journal Applied Sciences.

Nonlinear control problems such as robust stabilization and adaptive tracking naturally arise when coping with controlled systems which are inherently nonlinear and potentially suffer from various unknown uncertainties and/or time-varying disturbances. Over the past decades, with the aid of different mathematical tools, tremendous progress has been made toward the development of design methodologies for the control of nonlinear systems and their applications. Although a considerable number of interesting and valuable results can be found in the literature, the synthesis of control strategies for a wider class of nonlinear systems along with broader applications remains challenging and open, especially for the diversely complicated control tasks arising from the growing integration with emerging technologies in communication and computation areas. The main intention of the proposed Special Issue is to present a state-of-the-art collection of articles presenting the novel developments of nonlinear control approaches in both theoretical background and applications. The principal topics to be covered include, but are not limited to, the following:

  • New tools and developments for nonlinear control
  • Nonlinear control for complex systems
  • Nonlinear observer design and output feedback
  • Applications of novel nonlinear control approaches

Prof. Dr. Chih-Chiang Chen
Guest Editor

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Applied Sciences is an international peer-reviewed open access semimonthly journal published by MDPI.

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Keywords

  • Nonlinear system
  • State/output feedback
  • Robust control
  • Non-smooth/finite-time/fixed-time control
  • Observer design

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Published Papers (12 papers)

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Research

24 pages, 3699 KiB  
Article
On Invertibility of an Interconnected System Composed of Two Dynamic Subsystems
by Mei Zhang, Boutaïeb Dahhou and Ze-Tao Li
Appl. Sci. 2021, 11(2), 596; https://doi.org/10.3390/app11020596 - 9 Jan 2021
Cited by 3 | Viewed by 1778
Abstract
In this paper, the invertibility of an interconnected system that consists of two dynamic subsystems was studied. It can be viewed as the distinguishability of the impacts of local input on the final global output, that is to say, whether the input at [...] Read more.
In this paper, the invertibility of an interconnected system that consists of two dynamic subsystems was studied. It can be viewed as the distinguishability of the impacts of local input on the final global output, that is to say, whether the input at the local level can be recovered uniquely under a given output at the global level and initial state. The interconnected system constitutes two dynamic subsystems connected in a cascade manner. In order to guarantee the invertibility of the studied system, a necessary and sufficient condition was established. On the condition that both individual subsystems are invertible, the invertibility of the global system can be guaranteed. In order to recover the local input which generates a given global output, an algorithm was proposed for the studied interconnected system. Numerical examples were considered to confirm the effectiveness and robustness of the proposed algorithm. Full article
(This article belongs to the Special Issue Nonlinear Control: Theory and Applications)
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13 pages, 563 KiB  
Article
Trajectory/Path-Following Controller Based on Nonlinear Jerk-Level Error Dynamics
by Patrick Piprek, Michael M. Marb, Pranav Bhardwaj and Florian Holzapfel
Appl. Sci. 2020, 10(23), 8760; https://doi.org/10.3390/app10238760 - 7 Dec 2020
Cited by 10 | Viewed by 3512
Abstract
This study proposes a novel, nonlinear trajectory/path-following controller based on jerk-level error dynamics. Therefore, at first the nonlinear acceleration-based kinematic equations of motion of a dynamic system are differentiated with respect to time to obtain a representation connecting the translation jerk with the [...] Read more.
This study proposes a novel, nonlinear trajectory/path-following controller based on jerk-level error dynamics. Therefore, at first the nonlinear acceleration-based kinematic equations of motion of a dynamic system are differentiated with respect to time to obtain a representation connecting the translation jerk with the (specific) force derivative. Furthermore, the path deviation, i.e., the difference between the planned and the actual path, is formulated as nonlinear error dynamics based on the jerk error. Combining the derived equations of motion with the nonlinear error dynamics as well as employing nonlinear dynamic inversion, a control law can be derived that provides force derivative commands, which may be commanded to an inner loop for trajectory control. This command ensures an increased smoothness and faster reaction time compared to traditional approaches based on a force directly. Furthermore, the nonlinear parts in the error dynamic are feedforward components that improve the general performance due to their physical connection with the real dynamics. The validity and performance of the proposed trajectory/path-following controller are shown in an aircraft-related application example. Full article
(This article belongs to the Special Issue Nonlinear Control: Theory and Applications)
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23 pages, 2303 KiB  
Article
Observer Design for Nonlinear Invertible System from the View of Both Local and Global Levels
by Mei Zhang, Qinmu Wu, Xiangping Chen, Boutaïeb Dahhou and Zetao Li
Appl. Sci. 2020, 10(22), 7966; https://doi.org/10.3390/app10227966 - 10 Nov 2020
Cited by 1 | Viewed by 1643
Abstract
This paper emphasizes the importance of the influences of local dynamics on the global dynamics of a control system. By considering an actuator as an individual, nonlinear subsystem connected with a nonlinear process subsystem in cascade, a structure of interconnected nonlinear systems is [...] Read more.
This paper emphasizes the importance of the influences of local dynamics on the global dynamics of a control system. By considering an actuator as an individual, nonlinear subsystem connected with a nonlinear process subsystem in cascade, a structure of interconnected nonlinear systems is proposed which allows for global and local supervision properties of the interconnected systems. To achieve this purpose, a kind of interconnected observer design method is investigated, and the convergence is studied. One major difficulty is that a state observation can only rely on the global system output at the terminal boundary. This is because the connection point between the two subsystems is considered unable to be measured, due to physical or economic reasons. Therefore, the aim of the interconnected observer is to estimate the state vector of each subsystem and the unmeasurable connection point. Specifically, the output used in the observer of the actuator subsystem is replaced by the estimation of the process subsystem observer, while the estimation of this interconnection is treated like an additional state in the observer design of the process subsystem. Expression for this new state is achieved by calculating the derivatives of the output equation of the actuator subsystem. Numerical simulations confirm the effectiveness and robustness of the proposed observer, which highlight the significance of the work compared with state-of-the-art methods. Full article
(This article belongs to the Special Issue Nonlinear Control: Theory and Applications)
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23 pages, 1302 KiB  
Article
Particle Swarm Optimization of a Passivity-Based Controller for Dynamic Positioning of Ships
by Mutaz Ryalat, Hazem Salim Damiri and Hisham ElMoaqet
Appl. Sci. 2020, 10(20), 7314; https://doi.org/10.3390/app10207314 - 19 Oct 2020
Cited by 6 | Viewed by 2488
Abstract
Dynamic positioning (DP) control system is an essential module used in offshore ships for accurate maneuvering and maintaining of ship’s position and heading (fixed location or pre-determined track) by means of thruster forces being generated by controllers. In this paper, an interconnection and [...] Read more.
Dynamic positioning (DP) control system is an essential module used in offshore ships for accurate maneuvering and maintaining of ship’s position and heading (fixed location or pre-determined track) by means of thruster forces being generated by controllers. In this paper, an interconnection and damping assignment-passivity based control (IDA-PBC) controller is developed for DP of surface ships. The design of the IDA-PBC controller involves a dynamic extension utilizing the coordinate transformation which adds damping to some coordinates to ensure asymptotic stability and adds integral action to enhance the robustness of the system against disturbances. The particle swarm optimization (PSO) technique is one of the the population-based optimization methods that has gained the attention of the control research communities and used to solve various engineering problems. The PSO algorithm is proposed for the optimization of the IDA-PBC controller. Numerical simulations results with comparisons illustrate the effectiveness of the new PSO-tuned dynamic IDA-PBC controller. Full article
(This article belongs to the Special Issue Nonlinear Control: Theory and Applications)
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14 pages, 8972 KiB  
Article
Development and Application of a Human–Machine Interface Using Head Control and Flexible Numeric Tables for the Severely Disabled
by Che-Ming Chang, Chern-Sheng Lin, Wei-Cheng Chen, Chung-Ting Chen and Yu-Liang Hsu
Appl. Sci. 2020, 10(19), 7005; https://doi.org/10.3390/app10197005 - 8 Oct 2020
Cited by 6 | Viewed by 2733
Abstract
The human–machine interface with head control can be applied in many domains. This technology has the valuable application of helping people who cannot use their hands, enabling them to use a computer or speak. This study combines several image processing and computer vision [...] Read more.
The human–machine interface with head control can be applied in many domains. This technology has the valuable application of helping people who cannot use their hands, enabling them to use a computer or speak. This study combines several image processing and computer vision technologies, a digital camera, and software to develop the following system: image processing technologies are adopted to capture the features of head motion; the recognized head gestures include forward, upward, downward, leftward, rightward, right-upper, right-lower, left-upper, and left-lower; corresponding sound modules are used so that patients can communicate with others through a phonetic system and numeric tables. Innovative skin color recognition technology can obtain head features in images. The barycenter of pixels in the feature area is then quickly calculated, and the offset of the barycenter is observed to judge the direction of head motion. This architecture can substantially reduce the distraction of non-targeted objects and enhance the accuracy of systematic judgment. Full article
(This article belongs to the Special Issue Nonlinear Control: Theory and Applications)
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16 pages, 1351 KiB  
Article
Nonlinear Adaptive Robust Control of the Electro-Hydraulic Servo System
by Lijun Feng and Hao Yan
Appl. Sci. 2020, 10(13), 4494; https://doi.org/10.3390/app10134494 - 29 Jun 2020
Cited by 32 | Viewed by 3773
Abstract
This paper focuses on high performance adaptive robust position control of electro-hydraulic servo system. The main feature of the paper is the combination of adaptive robust algorithm with discrete disturbance estimation to cope with the parametric uncertainties, uncertain nonlinearities, and external disturbance in [...] Read more.
This paper focuses on high performance adaptive robust position control of electro-hydraulic servo system. The main feature of the paper is the combination of adaptive robust algorithm with discrete disturbance estimation to cope with the parametric uncertainties, uncertain nonlinearities, and external disturbance in the hydraulic servo system. First of all, a mathematical model of the single-rod position control system is developed and a nonlinear adaptive robust controller is proposed using the backstepping design technique. Adaptive robust control is used to encompass the parametric uncertainties and uncertain nonlinearities. Subsequently, a discrete disturbance estimator is employed to compensate for the effect of strong external disturbance. Furthermore, a special Lyapunov function is formulated to handle unknown nonlinear parameters in the system state equations. Simulations are carried out, and the results validate the superior performance and robustness of the proposed method. Full article
(This article belongs to the Special Issue Nonlinear Control: Theory and Applications)
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27 pages, 4122 KiB  
Article
Novel Active Disturbance Rejection Control Based on Nested Linear Extended State Observers
by Wameedh Riyadh Abdul-Adheem, Ahmad Taher Azar, Ibraheem Kasim Ibraheem and Amjad J. Humaidi
Appl. Sci. 2020, 10(12), 4069; https://doi.org/10.3390/app10124069 - 12 Jun 2020
Cited by 39 | Viewed by 3196
Abstract
In this paper, a Novel Active Disturbance Rejection Control (N-ADRC) strategy is proposed that replaces the Linear Extended State Observer (LESO) used in Conventional ADRC (C-ADRC) with a nested LESO. In the nested LESO, the inner-loop LESO actively estimates and eliminates the generalized [...] Read more.
In this paper, a Novel Active Disturbance Rejection Control (N-ADRC) strategy is proposed that replaces the Linear Extended State Observer (LESO) used in Conventional ADRC (C-ADRC) with a nested LESO. In the nested LESO, the inner-loop LESO actively estimates and eliminates the generalized disturbance. Increasing the bandwidth improves the estimation accuracy which may tolerate noise and conflict with H/W limitations and the sampling frequency of the system. Therefore, an alternative scenario is offered without increasing the bandwidth of the inner-loop LESO provided that the rate of change of the generalized disturbance estimation error is upper bounded. This was achieved by the placing of an outer-loop LESO in parallel with the inner one that estimates and eliminates the remaining generalized disturbance originating from the inner-loop LESO due to bandwidth limitations. The stability of LESO and nested LESO was investigated using Lyapunov stability analysis. Simulations on uncertain nonlinear single-input-single-output (SISO) system with time-varying exogenous disturbance revealed that the proposed nested LESO could successfully deal with a generalized disturbance in both noisy and noise-free environments, where the Integral Time Absolute Error (ITAE) of the tracking error for the nested LESO was reduced by 69.87% from that of the LESO. Full article
(This article belongs to the Special Issue Nonlinear Control: Theory and Applications)
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Graphical abstract

14 pages, 1873 KiB  
Article
Adaptive Model-Free Coupling Controller Design for Multi-Axis Motion Systems
by Bo-Sheng Chen and Ching-Hung Lee
Appl. Sci. 2020, 10(10), 3592; https://doi.org/10.3390/app10103592 - 22 May 2020
Cited by 4 | Viewed by 2237
Abstract
In this study, we introduce an adaptive model-free coupling controller while using recurrent fuzzy neural network (RFNN) for multi-axis system to minimize the contour error. The proposed method can be applied to linear or nonlinear multi-axis motion control systems following desired paths. By [...] Read more.
In this study, we introduce an adaptive model-free coupling controller while using recurrent fuzzy neural network (RFNN) for multi-axis system to minimize the contour error. The proposed method can be applied to linear or nonlinear multi-axis motion control systems following desired paths. By the concept of cross-coupling control (CCC), multi-axis system is transferred into a nonlinear time-varying system due to the time-dependent coordinate transformation; tangential, normal, and bi-normal components of desired contour. Herein, we propose a model-free adaptive coupling controller design approach for multi-axis linear motor system with uncertainty and nonlinear phenomena. RFNN establishes the corresponding adaptive coupling controller to treat the uncertain system with nonlinear phenomenon. The stability of closed-loop system is guaranteed by the Lyapunov method and the adaptation of RFNN is also obtained. Simulation results are introduced in order to illustrate the effectiveness. Full article
(This article belongs to the Special Issue Nonlinear Control: Theory and Applications)
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19 pages, 5101 KiB  
Article
Adaptive Observer-Based Fault Detection and Fault-Tolerant Control of Quadrotors under Rotor Failure Conditions
by Yu-Hsuan Lien, Chao-Chung Peng and Yi-Hsuan Chen
Appl. Sci. 2020, 10(10), 3503; https://doi.org/10.3390/app10103503 - 19 May 2020
Cited by 17 | Viewed by 4072
Abstract
This paper aims to propose a strategy for the flight control of quad-rotors under single rotor failure conditions. The proposed control strategy consists of two stages—fault detection (FD) and fault tolerant control (FTC). A dual observer-based strategy for FD and fault estimation is [...] Read more.
This paper aims to propose a strategy for the flight control of quad-rotors under single rotor failure conditions. The proposed control strategy consists of two stages—fault detection (FD) and fault tolerant control (FTC). A dual observer-based strategy for FD and fault estimation is developed. With the combination of the results from both observers, the decision making in whether a fault actually happened or the observed anomaly was caused by an external disturbance could be distinguished. Following the FD result, a control strategy for normal flight, as well as the abnormal one, is presented. The FTC considers a real-time coordinate transformation scheme to manipulate the target angles for the quad-rotor to follow a prescribed trajectory. When a rotor fault happens, it is going to be detected by the dual observers and then the FTC is activated to stabilize the system such that the trajectory following task can still be fulfilled. Furthermore, in order to achieve robust flight in the presence of external wind perturbation, the sliding mode control (SMC) theory is further integrated. Simulations illustrate the effectiveness and feasibility of the proposed method. Full article
(This article belongs to the Special Issue Nonlinear Control: Theory and Applications)
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17 pages, 1023 KiB  
Article
Nonlinear Control Design of a Half-Car Model Using Feedback Linearization and an LQR Controller
by Muhammad Aseer Khan, Muhammad Abid, Nisar Ahmed, Abdul Wadood and Herie Park
Appl. Sci. 2020, 10(9), 3075; https://doi.org/10.3390/app10093075 - 28 Apr 2020
Cited by 22 | Viewed by 5717
Abstract
Effective control of ride quality and handling performance are challenges for active vehicle suspension systems, particularly for off-road applications. The nonlinearities tend to degrade the performance of active suspension systems; these introduce harshness to the ride quality and reduce off-road mobility. Typical control [...] Read more.
Effective control of ride quality and handling performance are challenges for active vehicle suspension systems, particularly for off-road applications. The nonlinearities tend to degrade the performance of active suspension systems; these introduce harshness to the ride quality and reduce off-road mobility. Typical control strategies rely on linear models of the suspension dynamics. While these models are convenient, nominally accurate, and controllable due to the abundance of linear control techniques, they neglect the nonlinearities present in real suspension systems. The techniques already implemented and methods used to cope with problem of Half-Car model were studied. Every method and technique had some drawbacks in terms of complexity, cost-effectiveness, and ease of real time implementation. In this paper, an improved control method for Half-Car model was proposed. First, input/output feedback linearization was performed to convert the nonlinear system of Half-Car model into an equivalent linear system. This was followed by a Linear Quadratic Regulator (LQR) controller. This controller had minimized the effects of road disturbances by designing a gain matrix with optimal robustness properties. The proposed control technique was applied in the presence of the deterministic road disturbance. The results were verified using the Matlab/Simulink toolbox. Full article
(This article belongs to the Special Issue Nonlinear Control: Theory and Applications)
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29 pages, 4535 KiB  
Article
Improved Active Disturbance Rejection-Based Decentralized Control for MIMO Nonlinear Systems: Comparison with The Decoupled Control Scheme
by Wameedh Riyadh Abdul-Adheem, Ibraheem Kasim Ibraheem, Ahmad Taher Azar and Amjad J. Humaidi
Appl. Sci. 2020, 10(7), 2515; https://doi.org/10.3390/app10072515 - 6 Apr 2020
Cited by 23 | Viewed by 3322
Abstract
A decentralized control scheme is developed in this paper based on an improved active disturbance rejection control (IADRC) for output tracking of square Multi-Input-Multi-Output (MIMO) nonlinear systems and compared with the decoupled control scheme. These nonlinear MIMO systems were subjected to exogenous disturbances [...] Read more.
A decentralized control scheme is developed in this paper based on an improved active disturbance rejection control (IADRC) for output tracking of square Multi-Input-Multi-Output (MIMO) nonlinear systems and compared with the decoupled control scheme. These nonlinear MIMO systems were subjected to exogenous disturbances and composed of high couplings between subsystems, input couplings, and uncertain elements. In the decentralized control scheme, it was assumed that the input couplings and subsystem couplings were both parts of the generalized disturbance. Moreover, the generalized disturbance included other components, such as exogenous disturbances and system uncertainties, and it was estimated within the context of Active Disturbance rejection Control (ADRC) via a novel nonlinear higher order extended state observer (NHOESO) from the measured output and canceled from the input channel in a real-time fashion. Then, based on the designed NHOESO, a separate feedback control law was developed for each subsystem to achieve accurate output tracking for given reference input. With the proposed decentralized control scheme, the square MIMO nonlinear system was converted into approximately separate linear time invariant Single-Input-Single-Output (SISO) subsystems. Numerical simulations in a MATLAB environment showed the effectiveness of the proposed technique, where it was applied on a hypothetical MIMO nonlinear system with strong couplings and vast uncertainties. The proposed decentralized control scheme reduced the total control signal energy by 20.8% as compared to the decoupled control scheme using Conventional ADRC (CADRC), while the reduction was 27.18% using the IADRC. Full article
(This article belongs to the Special Issue Nonlinear Control: Theory and Applications)
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12 pages, 1125 KiB  
Article
Passivity-Based Control Design for Magnetic Levitation System
by Wang Yang, Fanwei Meng, Man Sun and Kai Liu
Appl. Sci. 2020, 10(7), 2392; https://doi.org/10.3390/app10072392 - 1 Apr 2020
Cited by 11 | Viewed by 2373
Abstract
The passivity-based control (PBC) is a new direction of nonlinear control, but the method is basically a qualitative method. A quantifiable design method in combination with PBC is provided in this paper. To solve the partial differential equation (PDE) for PBC, the nonlinear [...] Read more.
The passivity-based control (PBC) is a new direction of nonlinear control, but the method is basically a qualitative method. A quantifiable design method in combination with PBC is provided in this paper. To solve the partial differential equation (PDE) for PBC, the nonlinear system must first be transformed into a Hamiltonian model. The PDE for the Hamiltonian system is then quantifiably solved with an electromagnetic levitation example. The resulting control law is presented and discussed. The proposed method provides a practical design tool for nonlinear control. Full article
(This article belongs to the Special Issue Nonlinear Control: Theory and Applications)
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