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Analysis and Control of Dynamical Systems
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Analysis and Control of Dynamical Systems

A special issue of Mathematics (ISSN 2227-7390). This special issue belongs to the section "Computational and Applied Mathematics".

Deadline for manuscript submissions: 30 June 2024 | Viewed by 17173

Special Issue Editors

Prof. Dr. Fangzheng Gao

E-Mail Website
Guest Editor
1. School of Automation, Nanjing Institute of Technology, Nanjing 211167, China
2. School of Automation, Southeast University, Nanjing 210096, China
Interests: nonlinear control; control theory; dynamical systems
Prof. Dr. Zhongcai Zhang

E-Mail Website
Guest Editor
College of Engineering, Qufu Normal University, Rizhao 276827, China
Interests: nonlinear control; constrained control; control theory; dynamical systems

Special Issue Information

Dear Colleagues,

Dynamical systems are encountered everywhere in modern life, including engineering, economics, and ecology. As a result, in recent decades the study and control of dynamical systems have become the focus of research in the field of system control. However, as science and technology develop, control systems become more complicated, and controllers’ performance standards grow increasingly stringent. The control of dynamical systems faces significant problems, necessitating the development of novel theories for system analysis and control. This Special Issue is dedicated to the study of dynamical system analysis and control, which includes but is not limited to:
1) Stability analysis and control design of dynamical systems.

2) Intelligent control of uncertain dynamical systems.

3) Applications of dynamical systems in robotics, aerospace, electrical systems and other fields.

4) Overview of the latest control theory of dynamical systems.

Prof. Dr. Fangzheng Gao
Prof. Dr. Zhongcai Zhang
Guest Editors

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. Mathematics is an international peer-reviewed open access semimonthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2600 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

  • stability analysis
  • control design
  • intelligent control
  • networked control
  • fuzzy control
  • robust control
  • security control
  • dynamical systems
  • nonlinear systems
  • hybrid systems
  • networked control systems

Published Papers (17 papers)

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Research

25 pages, 418 KiB  
Article
Finite-Time Fuzzy Fault-Tolerant Control for Nonlinear Flexible Spacecraft System with Stochastic Actuator Faults
by Jiao Xu, Tao Song and Jiaxin Wang
Mathematics 2024, 12(4), 503; https://doi.org/10.3390/math12040503 - 06 Feb 2024
Viewed by 457
Abstract
In the quest for unparalleled reliability and robustness within control systems, significant attention has been directed toward mitigating actuator faults in diverse applications, from space vehicles to sophisticated industrial systems. Despite these advances, the prevalent assumption of homogeneous actuator faults remains a stark [...] Read more.
In the quest for unparalleled reliability and robustness within control systems, significant attention has been directed toward mitigating actuator faults in diverse applications, from space vehicles to sophisticated industrial systems. Despite these advances, the prevalent assumption of homogeneous actuator faults remains a stark simplification, failing to encapsulate the stochastic and unpredictable nature of real-world operational environments. The problem of finite-time fault-tolerant control for nonlinear flexible spacecraft systems with actuator faults is addressed in this paper, utilizing the T-S fuzzy framework. In a departure from conventional approaches, actuator failures are modeled as random signals following a nonhomogeneous Markov process, thus comprehensively addressing the issue of timeliness, which has previously been overlooked in the literature. To effectively manage the intricacies introduced by these factors, the nonhomogeneous Markov process is represented as a polytope set. The proposed solution involves the development of a nonhomogeneous matrix transformation, accompanied by the introduction of adaptable parameters. This innovative controller design methodology yields a stability criterion that ensures H∞ performance in a mean-square sense. To empirically substantiate the effectiveness and advantages of the proposed approaches, a numerical example featuring a nonlinear spacecraft system is presented. Full article
(This article belongs to the Special Issue Analysis and Control of Dynamical Systems)
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19 pages, 456 KiB  
Article
Robust and Adaptive Stabilization Controllers of State-Constrained Nonholonomic Chained Systems: A Discontinuous Approach
by Zhongcai Zhang, Xueli Hu, Yang Gao and Xiaodan Hou
Mathematics 2024, 12(1), 59; https://doi.org/10.3390/math12010059 - 24 Dec 2023
Viewed by 510
Abstract
In this paper, two systematic control design strategies are proposed for strict-feedback nonholonomic systems with full-state constraints to solve stabilization and adaptive stabilization problems. The stabilization schemes involve the introduction of state scaling, the barrier Lyapunov function (BLF), the integrator backstepping method, and [...] Read more.
In this paper, two systematic control design strategies are proposed for strict-feedback nonholonomic systems with full-state constraints to solve stabilization and adaptive stabilization problems. The stabilization schemes involve the introduction of state scaling, the barrier Lyapunov function (BLF), the integrator backstepping method, and the tuning function approach. In addition, a discontinuous switching control strategy is proposed to achieve the control goal if the first system state’s initial state is confined to zero. In both stabilization and adaptive stabilization control, the system states can be regulated at the origin, and meanwhile, the full-state constraints are realized. Finally, it is shown that the simulation results are consistent with the theory analysis results, which further demonstrates the effectiveness of the proposed control schemes. Full article
(This article belongs to the Special Issue Analysis and Control of Dynamical Systems)
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14 pages, 2188 KiB  
Article
A Model-Free Control Scheme for Rehabilitation Robots: Integrating Real-Time Observations with a Deep Neural Network for Enhanced Control and Reliability
by Hajid Alsubaie and Ahmed Alotaibi
Mathematics 2023, 11(23), 4791; https://doi.org/10.3390/math11234791 - 27 Nov 2023
Viewed by 775
Abstract
Effective control of rehabilitation robots is of paramount importance and requires increased attention to achieve a fully reliable, automated system for practical applications. As the domain of robotic rehabilitation progresses rapidly, the imperative for precise and dependable control mechanisms grows. In this study, [...] Read more.
Effective control of rehabilitation robots is of paramount importance and requires increased attention to achieve a fully reliable, automated system for practical applications. As the domain of robotic rehabilitation progresses rapidly, the imperative for precise and dependable control mechanisms grows. In this study, we present an innovative control scheme integrating state-of-the-art machine learning algorithms with traditional control techniques. Our approach offers enhanced adaptability to patient-specific needs while ensuring safety and effectiveness. We introduce a model-free feedback linearization control method underpinned by deep neural networks and online observation. While our controller is model-free, and system dynamics are learned during training phases, we employ an online observer to robustly estimate uncertainties that the systems may face in real-time, beyond their training. The proposed technique was tested through different simulations with varying initial conditions and step references, demonstrating the controller’s robustness and adaptability. These simulations, combined with Lyapunov’s stability verification, validate the efficacy of our proposed scheme in effectively controlling the system under diverse conditions. Full article
(This article belongs to the Special Issue Analysis and Control of Dynamical Systems)
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13 pages, 522 KiB  
Article
Stability of Stochastic Networks with Proportional Delays and the Unsupervised Hebbian-Type Learning Algorithm
by Famei Zheng, Xiaojing Wang and Xiwang Cheng
Mathematics 2023, 11(23), 4755; https://doi.org/10.3390/math11234755 - 24 Nov 2023
Viewed by 528
Abstract
The stability problem of stochastic networks with proportional delays and unsupervised Hebbian-type learning algorithms is studied. Applying the Lyapunov functional method, a stochastic analysis technique and the Ito^ formula, we obtain some sufficient conditions for global asymptotic stability. We also discuss [...] Read more.
The stability problem of stochastic networks with proportional delays and unsupervised Hebbian-type learning algorithms is studied. Applying the Lyapunov functional method, a stochastic analysis technique and the Ito^ formula, we obtain some sufficient conditions for global asymptotic stability. We also discuss the estimation of the second moment. The correctness of the main results is verified by two numerical examples. Full article
(This article belongs to the Special Issue Analysis and Control of Dynamical Systems)
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17 pages, 4288 KiB  
Article
Novel Composite Speed Control of Permanent Magnet Synchronous Motor Using Integral Sliding Mode Approach
by Xiaodong Miao, Wenzheng Yao, Huimin Ouyang and Zichong Zhu
Mathematics 2023, 11(22), 4666; https://doi.org/10.3390/math11224666 - 16 Nov 2023
Viewed by 613
Abstract
Permanent magnet synchronous motors (PMSMs) are widely applied in industry, and proportional integral (PI) controllers are often used to control PMSMs. Aiming at the characteristics of the poor anti-disturbance ability and speed ripple of traditional PI controllers, a novel composite speed controller for [...] Read more.
Permanent magnet synchronous motors (PMSMs) are widely applied in industry, and proportional integral (PI) controllers are often used to control PMSMs. Aiming at the characteristics of the poor anti-disturbance ability and speed ripple of traditional PI controllers, a novel composite speed controller for PMSMs is proposed in this paper that uses a novel sliding mode control (SMC). To improve the chattering problem of traditional SMC, a high-order approaching law super-twisting algorithm (STA) is applied. Considering the internal and external disturbance of motor driver systems, such as motor parameter drifts and load torque changes, a disturbance estimator based on an extended state observer (ESO) is proposed, and it is used for the feed-forward compensation of the current. The composite super-twisting integral sliding mode controller (ST-ISMC) with a nonlinear ESO is tested by simulations and experiments, and the comparative results verify that the proposed controller has the higher control accuracy, smaller speed ripple and stronger robustness. Full article
(This article belongs to the Special Issue Analysis and Control of Dynamical Systems)
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19 pages, 1801 KiB  
Article
Peak-to-Peak Stabilization of Sampled-Data Systems Subject to Actuator Saturation and Its Practical Application to an Inverted Pendulum
by Khanh Hieu Nguyen and Sung Hyun Kim
Mathematics 2023, 11(22), 4592; https://doi.org/10.3390/math11224592 - 09 Nov 2023
Viewed by 655
Abstract
This paper investigates the local stability and stabilization criteria of sampled-data control systems, taking into account actuator saturation and peak-bounded exogenous disturbances. Specifically, this study introduces two innovations to extend the maximum upper bound of the sampling interval: two novel time integrals of [...] Read more.
This paper investigates the local stability and stabilization criteria of sampled-data control systems, taking into account actuator saturation and peak-bounded exogenous disturbances. Specifically, this study introduces two innovations to extend the maximum upper bound of the sampling interval: two novel time integrals of the weighted state derivative are introduced to formulate an improved looped-functional; second, the introduction of two supplementary zero-equalities to improve the relationship among the components of the augmented state. Building on this, a set of linear matrix inequality-based stabilization conditions is derived. These conditions ensure that a closed-loop sampled-data system can become exponentially stable and achieve a guaranteed peak-to-peak performance in the domain of attraction. Finally, the efficacy of the proposed methodology is substantiated through both simulation and experimental results, focusing on the sampled-data control of an inverted pendulum system. Full article
(This article belongs to the Special Issue Analysis and Control of Dynamical Systems)
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12 pages, 548 KiB  
Article
An Application of Rouché’s Theorem to Delimit the Zeros of a Certain Class of Robustly Stable Polynomials
by Noé Martínez, Luis E. Garza and Gerardo Romero
Mathematics 2023, 11(20), 4244; https://doi.org/10.3390/math11204244 - 11 Oct 2023
Viewed by 505
Abstract
An important problem related to the study of the robust stability of a linear system that presents variation in terms of an uncertain parameter consists of understanding the variation in the roots of a system’s characteristic polynomial in terms of the uncertain parameter. [...] Read more.
An important problem related to the study of the robust stability of a linear system that presents variation in terms of an uncertain parameter consists of understanding the variation in the roots of a system’s characteristic polynomial in terms of the uncertain parameter. In this contribution, we propose an algorithm to provide sufficient conditions on the uncertain parameter in such a way that a robustly stable family of polynomials has all of its zeros inside a specific subset of its stability region. Our method is based on the Rouché’s theorem and uses robustly stable polynomials constructed by using basic properties of orthogonal polynomials. Full article
(This article belongs to the Special Issue Analysis and Control of Dynamical Systems)
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15 pages, 1823 KiB  
Article
Analytical Design of Optimal Model Predictive Control and Its Application in Small-Scale Helicopters
by Weijun Hu, Jiale Quan, Xianlong Ma, Mostafa M. Salah and Ahmed Shaker
Mathematics 2023, 11(8), 1845; https://doi.org/10.3390/math11081845 - 13 Apr 2023
Viewed by 1191
Abstract
A new method for controlling the position and speed of a small-scale helicopter based on optimal model predictive control is presented in this paper. In the proposed method, the homotopy perturbation technique is used to analytically solve the optimization problem and, as a [...] Read more.
A new method for controlling the position and speed of a small-scale helicopter based on optimal model predictive control is presented in this paper. In the proposed method, the homotopy perturbation technique is used to analytically solve the optimization problem and, as a result, to find the control signal. To assess the proposed method, a small-scale helicopter system is modeled and controlled using the proposed method. The proposed method has been investigated under different conditions and its results have been compared with the conventional predictive control method. The simulation results show that the proposed technique is highly proficient in the face of various uncertainties and disturbances, and can quickly return the helicopter to its path. Full article
(This article belongs to the Special Issue Analysis and Control of Dynamical Systems)
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17 pages, 992 KiB  
Article
A Mathematical Tool to Investigate the Stability Analysis of Structured Uncertain Dynamical Systems with M-Matrices
by Mutti-Ur Rehman, Jehad Alzabut, Nahid Fatima and Sajid Khan
Mathematics 2023, 11(7), 1622; https://doi.org/10.3390/math11071622 - 27 Mar 2023
Cited by 1 | Viewed by 994
Abstract
The μ-value or structured singular value is a prominent mathematical tool to analyze and synthesize both the robustness and performance of time-invariant systems. We establish and analyze new results concerning structured singular values for the Hadamard product of real square M-matrices. [...] Read more.
The μ-value or structured singular value is a prominent mathematical tool to analyze and synthesize both the robustness and performance of time-invariant systems. We establish and analyze new results concerning structured singular values for the Hadamard product of real square M-matrices. The new results are obtained for structured singular values while considering a set of block diagonal uncertainties. The targeted uncertainties are of two types, that is, pure real scalar block uncertainties and real full-block uncertainties. The eigenvalue perturbation result is utilized in order to determine the behavior of the spectrum of perturbed matrices (A∘B)Δ(t) and ((A∘B)TΔ(t)+Δ(t)(A∘B)). Full article
(This article belongs to the Special Issue Analysis and Control of Dynamical Systems)
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18 pages, 3565 KiB  
Article
A New Self-Tuning Deep Neuro-Sliding Mode Control for Multi-Machine Power System Stabilizer
by Chan Gu, Encheng Chi, Chujia Guo, Mostafa M. Salah and Ahmed Shaker
Mathematics 2023, 11(7), 1616; https://doi.org/10.3390/math11071616 - 27 Mar 2023
Cited by 2 | Viewed by 914
Abstract
In order to increase the accuracy and improve the performance of the power system stabilizer (PSS) controller compared to the methods presented in other studies, this paper presents a new method for tuning sliding mode control (SMC) parameters for a PSS using a [...] Read more.
In order to increase the accuracy and improve the performance of the power system stabilizer (PSS) controller compared to the methods presented in other studies, this paper presents a new method for tuning sliding mode control (SMC) parameters for a PSS using a deep neural network. This controller requires fast switching which can create unwanted signals. To solve this problem, a boundary layer is used. First, the equations of a multi-machine power system are converted into the standard form of sliding mode control, and then the sliding surfaces are determined with three unknown parameters. Calculating and determining the optimal values (at any moment) for these parameters are fundamental challenges. A deep neural network can overcome this challenge and adjust the control system regularly. In the simulation, a power system with 4 machines and 11 buses is implemented and both phase-to-ground and three-phase errors are applied. The simulation results clearly show the good performance of the proposed method and especially the importance of the deep neural network in the SMC structure compared to other methods. Full article
(This article belongs to the Special Issue Analysis and Control of Dynamical Systems)
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20 pages, 711 KiB  
Article
Non-Fragile Fuzzy Tracking Control for Nonlinear Networked Systems with Dynamic Quantization and Randomly Occurring Gain Variations
by Zhimin Li, Chengming Lu and Hongyu Wang
Mathematics 2023, 11(5), 1116; https://doi.org/10.3390/math11051116 - 23 Feb 2023
Viewed by 702
Abstract
This paper investigates the observer-based non-fragile output feedback tracking control problem for nonlinear networked systems with randomly occurring gain variations. The considered nonlinear networked systems are represented by a Takagi–Sugeno (T–S) fuzzy model. The dynamical quantization methodology is employed to achieve the reasonable [...] Read more.
This paper investigates the observer-based non-fragile output feedback tracking control problem for nonlinear networked systems with randomly occurring gain variations. The considered nonlinear networked systems are represented by a Takagi–Sugeno (T–S) fuzzy model. The dynamical quantization methodology is employed to achieve the reasonable and efficacious utilization of the limited communication resources. The objective is to design the observer-based non-fragile output feedback tracking controller, such that the resulting system is mean-square asymptotically stable with the given H∞ tracking performance. Based on the descriptor representation strategy combined with the S-procedure, sufficient conditions for the existence of the desired dynamic quantizers and observer-based non-fragile tracking controller are proposed in the form of linear matrix inequalities. Finally, simulation results are provided to show the effectiveness of the proposed design method Full article
(This article belongs to the Special Issue Analysis and Control of Dynamical Systems)
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30 pages, 3977 KiB  
Article
Adaptive Controller for Bus Voltage Regulation on a DC Microgrid Using a Sepic/Zeta Battery Charger/Discharger
by Jhoan Alejandro Montenegro-Oviedo, Carlos Andres Ramos-Paja, Martha Lucia Orozco-Gutierrez, Edinson Franco-Mejía and Sergio Ignacio Serna-Garcés
Mathematics 2023, 11(4), 793; https://doi.org/10.3390/math11040793 - 04 Feb 2023
Cited by 2 | Viewed by 1500
Abstract
In a DC microgrid that involves a battery storage system, the primary energy management is performed by a battery charger/discharger based on a dc/dc power converter. Moreover, the battery charger/discharger is also used to regulate the voltage of the dc bus. One of [...] Read more.
In a DC microgrid that involves a battery storage system, the primary energy management is performed by a battery charger/discharger based on a dc/dc power converter. Moreover, the battery charger/discharger is also used to regulate the voltage of the dc bus. One of the challenges at the control level is to regulate the DC bus voltage under battery charge and discharge conditions but also under different relations between the battery and bus voltages. For this reason, this paper proposes a battery charger/discharger based on the Sepic/Zeta converter and an adaptive controller, which provides bidirectional current flow, stable bus voltage, and satisfactory electrical characteristics. The main advantage of the proposed control system is the capability to adapt the controller parameters to any operation condition, which provides a general solution to interface any battery to any bus voltage. This study is focused on the design procedure of both the power converter and the controller, where a detailed mathematical analysis is performed to ensure the system performance and stability. Finally, the proposed solution is validated using an experimental prototype and a practical application case. Full article
(This article belongs to the Special Issue Analysis and Control of Dynamical Systems)
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15 pages, 9273 KiB  
Article
A Novel Double-Layered Central Pattern Generator-Based Motion Controller for the Hexapod Robot
by Ying Zhang, Guifang Qiao, Qi Wan, Lei Tian and Di Liu
Mathematics 2023, 11(3), 617; https://doi.org/10.3390/math11030617 - 26 Jan 2023
Cited by 1 | Viewed by 1545
Abstract
To implement the various movement control of the hexapod robot, a motion controller based on the double-layered central pattern generator (CPG) is proposed in this paper. The novel CPG network is composed of a rhythm layer and a pattern layer. The CPG neurons [...] Read more.
To implement the various movement control of the hexapod robot, a motion controller based on the double-layered central pattern generator (CPG) is proposed in this paper. The novel CPG network is composed of a rhythm layer and a pattern layer. The CPG neurons are constructed based on Kuramoto nonlinear oscillator. The parameters including the frequency, coupling strength, and phase difference matrix of the CPG network for four typical gaits are planned. The mapping relationship between the signals of the CPG network and the joint trajectories of the hexapod robot is designed. The co-simulations and experiments have been conducted to verify the feasibility of the proposed CPG-based controller. The actual average velocities of the wave gait, the tetrapod gait, the tripod gait, and the self-turning gait are 10.8 mm/s, 25.5 mm/s, 37.8 mm/s and 26°/s, respectively. The results verify that the hexapod robot with the proposed double-layered CPG-based controller can perform stable and various movements. Full article
(This article belongs to the Special Issue Analysis and Control of Dynamical Systems)
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20 pages, 8586 KiB  
Article
Adaptive Interval Type-2 Fuzzy Neural Network Sliding Mode Control of Nonlinear Systems Using Improved Extended State Observer
by Lunhaojie Liu, Juntao Fei and Xianghua Yang
Mathematics 2023, 11(3), 605; https://doi.org/10.3390/math11030605 - 25 Jan 2023
Cited by 3 | Viewed by 1250
Abstract
An adaptive sliding mode control (ASMC) based on improved linear extended state observer (LESO) is proposed for nonlinear systems with unknown and uncertain dynamics. An improved LESO is designed to estimate total disturbance of the uncertain nonlinear system, and an interval type-2 fuzzy [...] Read more.
An adaptive sliding mode control (ASMC) based on improved linear extended state observer (LESO) is proposed for nonlinear systems with unknown and uncertain dynamics. An improved LESO is designed to estimate total disturbance of the uncertain nonlinear system, and an interval type-2 fuzzy neural network (IT2FNN) is used to optimize and approximate the observe bandwidth of LESO, and the adaptive parameter tuning is realized based on the gradient descent (GD) method. Based on the total disturbance estimated by LESO, an ASMC strategy is designed to ensure the system stability. By adapting the sliding mode gain, the observation performance of LESO compared to the total disturbance can be better utilized, and system chattering is reduced. Finally, some simulation results are given which show that the proposed control strategy has a good control effect, strong practicability, and wide versatility. Full article
(This article belongs to the Special Issue Analysis and Control of Dynamical Systems)
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13 pages, 1900 KiB  
Article
Design of Observer and Dynamic Output Feedback Control for Fuzzy Networked Systems
by Hejun Yao and Fangzheng Gao
Mathematics 2023, 11(1), 148; https://doi.org/10.3390/math11010148 - 28 Dec 2022
Cited by 3 | Viewed by 1245
Abstract
The observer design and dynamic output feedback control for a class of nonlinear networked systems are studied in this paper. The model of the networked systems is established by using T-S fuzzy method, and the state observer of the systems is designed when [...] Read more.
The observer design and dynamic output feedback control for a class of nonlinear networked systems are studied in this paper. The model of the networked systems is established by using T-S fuzzy method, and the state observer of the systems is designed when the states of the systems are unknown. On this basis, the sufficient conditions for the exponential stability of the system are explored by using the linear matrix inequality (LMI) method and Lyapunov stability theory. Then, the dynamic output feedback control of the systems is designed by using the observer states, which ensures that the states of the closed-loop systems and the error systems exponentially converge to the origin at the same time. Finally, a simulation example is given to illustrate the feasibility and effectiveness of the design method. Full article
(This article belongs to the Special Issue Analysis and Control of Dynamical Systems)
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19 pages, 1010 KiB  
Article
Robust Tracking Control of Dual-Active-Bridge DC–DC Converters with Parameter Uncertainties and Input Saturation
by Nguyen Ngoc Nam and Sung Hyun Kim
Mathematics 2022, 10(24), 4719; https://doi.org/10.3390/math10244719 - 12 Dec 2022
Cited by 4 | Viewed by 1344
Abstract
This paper proposes a method for robust tracking control synthesis of dual-active-bridge (DAB) DC–DC converters with parameter uncertainties and input saturation. In the proposed method, the nonlinear function of the phase shift ratio is expressed as a control input, and the phase shift [...] Read more.
This paper proposes a method for robust tracking control synthesis of dual-active-bridge (DAB) DC–DC converters with parameter uncertainties and input saturation. In the proposed method, the nonlinear function of the phase shift ratio is expressed as a control input, and the phase shift ratio is determined by the one-to-one relationship with the control input. Especially, the proposed method is developed with consideration of the input saturation phenomenon that occurs physically in the phase shift ratio of DAB DC–DC converters. Furthermore, based on the proposed method, a set of exponential constrained stabilization conditions for DAB DC–DC converter systems with parameter uncertainties is provided to ensure a fast convergence rate. Finally, to verify the effectiveness of the proposed control method, various simulation results are provided and compared with the well-known improved model phase shift control (IMPSC) and load current feedforward (LCFF) control methods. Full article
(This article belongs to the Special Issue Analysis and Control of Dynamical Systems)
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15 pages, 355 KiB  
Article
Global Prescribed-Time Stabilization of High-Order Nonlinear Systems with Asymmetric Actuator Dead-Zone
by Xin Guo, Hejun Yao and Fangzheng Gao
Mathematics 2022, 10(12), 2147; https://doi.org/10.3390/math10122147 - 20 Jun 2022
Viewed by 1204
Abstract
This paper is concerned with the global prescribed-time stabilization problem for a class of uncertain high-order nonlinear systems (HONSs) with an asymmetric actuator dead-zone. Firstly, a new state-scaling transformation (SST) is developed for high-order nonlinear systems to change the original prescribed-time stabilization into [...] Read more.
This paper is concerned with the global prescribed-time stabilization problem for a class of uncertain high-order nonlinear systems (HONSs) with an asymmetric actuator dead-zone. Firstly, a new state-scaling transformation (SST) is developed for high-order nonlinear systems to change the original prescribed-time stabilization into the finite-time stabilization of the transformed one. The defects of the conventional one introduced in Song et al. (2017), which is unable to ensure the closed-loop stability behind a prespecified convergence time and a closed-loop system, which is only driven to the neighborhood of destination, is successfully overcome by introducing a switching mechanism in our proposed SST. Then, by using the adding a power integrator (API) technique, a state feedback controller is explicitly constructed to achieve the requirements of the closed-loop prescribed time convergence. Lastly, a liquid-level system is utilized to validate the theoretical results. Full article
(This article belongs to the Special Issue Analysis and Control of Dynamical Systems)
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