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Advanced Nonlinear and Learning-Based Control Techniques for Complex Dynamical Systems

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A special issue of Electronics (ISSN 2079-9292). This special issue belongs to the section "Systems & Control Engineering".

Deadline for manuscript submissions: closed (15 September 2023) | Viewed by 18312

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Special Issue Editors

Prof. Dr. Mahmut Reyhanoglu

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Guest Editor

Robotics Engineering Department, Columbus State University, Columbus, GA 31907, USA
Interests: thermoacustics; synthetic jet actuators; flow-induced-noise control; marine vehicle control; flow control
Special Issues, Collections and Topics in MDPI journals

Dr. Erkan Kayacan

E-Mail Website
Guest Editor

School of Aerospace and Mechanical Engineering, University of Oklahoma, Norman, OK 73019, USA
Interests: real-time optimization-based control and estimation methods, nonlinear control, and machine learning, with special emphasis on foundational theory and experimental realization on robotic and autonomous systems
Special Issues, Collections and Topics in MDPI journals

Dr. Mohammad Jafari

E-Mail Website
Guest Editor

Robotics Engineering Program, Columbus State University, Columbus, GA 31907, USA
Interests: real-time learning-based control; machine learning; multi-agent systems; control & systems theory; robotics
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

There has been a great deal of excitement during the recent past over the emergence of new mathematical techniques for the modeling and analysis of complex dynamical systems. For example, recent years have witnessed an explosion of work on the development of both learning-based and nonlinear control system models in a geometric form that are globally defined without singularities or ambiguities. These models are applied to the motion planning and feedback control of constrained robotic systems. These fascinating topics require the use of diverse parts of mathematics. Nonlinear and learning-based control system theory and various design techniques are used widely in the robotics arena, especially in developing nonlinear robust control algorithms. The design of these systems involves advanced techniques including nonlinear optimization, machine learning, adaptive estimation, and nonlinear observer and control design methodologies. In this context, this Special Issue welcomes the submission of papers from a wide range of researchers in applied mathematics and various engineering disciplines.

Potential topics include, but are not limited to:

Nonlinear optimization techniques;
Nonlinear observer design;
Nonlinear adaptive estimation;
Nonlinear robust control;
Reduced-order modeling and control;
Learning-based/intelligent control;
Neuro-adaptive control;
Gaussian-process-based control methods;
Real-time learning-based control;
Multi-agent systems control;
Formation/flocking control;
Geometric control theory and applications.

Prof. Dr. Mahmut Reyhanoglu
Dr. Erkan Kayacan
Dr. Mohammad Jafari
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. Electronics 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 2400 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

optimization
observer design
adaptive control
learning control
intelligent control
robust control
formation control
geometric control

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Related Special Issue

Advanced Nonlinear and Learning-Based Control Techniques for Complex Dynamical Systems, 2nd Edition in Electronics (2 articles)

Published Papers (11 papers)

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Research

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17 pages, 5061 KiB

Open AccessArticle

Research on the Current Control Strategy of a Brushless DC Motor Utilizing Infinite Mixed Sensitivity Norm

by Tianqing Yuan, Jiu Chang and Yupeng Zhang

Electronics 2023, 12(21), 4525; https://doi.org/10.3390/electronics12214525 - 3 Nov 2023

Cited by 2 | Viewed by 2296

Abstract

During the brushless DC (BLDC) motor working process, the system encounters inevitable uncertainties. These ambiguities stem from potential fluctuations, random occurrences, measurement inaccuracies, varying operational conditions, environmental shifts such as temperature alterations, among other factors. Uncertainties, an inherent aspect of any real control system, can be broadly classified into two categories: sensor signal uncertainties and discrepancies between the mathematical and actual models due to parameter perturbations. To mitigate the impact of sensor noise and parameter perturbations on the BLDC motor, a robust control strategy utilizing infinite norm mixed sensitivity based on PI control strategy (PI-H∞-MIX) is proposed in this paper. Firstly, the closed-loop control structure and transfer function model of the BLDC motor control system current loop are analyzed based on the current loop circuit topology, and then, the model parameters perturbation is analyzed, and the multiplicative uncertainty bound is given. In addition, the appropriate weighting function is selected to ensure the robustness of the system. In this case, the controller design problem is transformed into the H∞ standard control problem, and then, the system augmentation matrix is established, and the controller is solved by Matlab/Simulink. Finally, the performances of the traditional PI control strategy and the PI-H∞-MIX are compared and analyzed. The results show that (1) the proposed PI-H∞-MIX strategy can improve the control system robustness under the parameter perturbation condition effectively, and (2) the proposed PI-H∞-MIX strategy can suppress the noise signal of the sensor. Full article

(This article belongs to the Special Issue Advanced Nonlinear and Learning-Based Control Techniques for Complex Dynamical Systems)

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12 pages, 2323 KiB

Open AccessArticle

Design and Analysis of the Model Based Control System for an MRE Axisymmetric Actuator

by Paweł Czopek and Jakub Bernat

Electronics 2023, 12(21), 4386; https://doi.org/10.3390/electronics12214386 - 24 Oct 2023

Viewed by 1107

Abstract

The magnetorheological elastomer membrane is an interesting kind of smart material that is gaining new innovative applications. This work is focused on the design of the control system for magnetorheological elastomer actuators. In general, the plant is characterized by fast oscillations and slow drift. Therefore, controllers utilize the described features to obtain the solution aimed at, which makes them unique. We analyze two approaches based on output feedback with state estimation. The control algorithms have different observers to estimate the state. The first is a Linear Extended State Observer, which is applied to reject the disturbances in a case with a simple model. The second is a Linear State Observer, which is used to estimate a state based on the plant model. Furthermore, in both cases, we have the same proportional-derivative controller after decoupling the dynamics. The main goal of the paper is to examine both controllers for the magnetorheological actuator. Therefore, the designed control systems are verified in a series of experiments. Full article

(This article belongs to the Special Issue Advanced Nonlinear and Learning-Based Control Techniques for Complex Dynamical Systems)

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18 pages, 10203 KiB

Open AccessArticle

Nonlinear Multi-Object Differential Game Simulation Model in LabVIEW

by Józef Lisowski

Electronics 2023, 12(18), 3848; https://doi.org/10.3390/electronics12183848 - 11 Sep 2023

Cited by 1 | Viewed by 1343

Abstract

This article presents the synthesis of a nonlinear multi-object differential game model in relation to the process of safe ship control in collision situations at sea. Nonlinear dynamic equations of a target ship and linear kinematic equations of passing ships were used to formulate the game state equations. The model of such a differential game was developed using LabVIEW 2022 version software. This was then subjected to simulation tests using the example of a navigational situation in which the target ship passed three encountered ships at a safe distance under the conditions of non-cooperation of ships, their cooperation, and optimal non-game control. The results of the computer simulation are presented in the form of ship trajectories and time courses of individual game control variables. The distinguishing feature of the model built in LabVIEW software is the ability to conduct research in online mode, where the user has the opportunity to track the impact of changes in the model parameters on the course of the differential game simulation on an ongoing basis. Further refinements of the simulation model should concern the larger number of ships and test the sensitivity of the game control quality to inaccuracies in the measured state variables and to changes in the parameters of the ship’s dynamics. Full article

(This article belongs to the Special Issue Advanced Nonlinear and Learning-Based Control Techniques for Complex Dynamical Systems)

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16 pages, 15223 KiB

Open AccessArticle

Optimality of Safe Game and Non-Game Control of Marine Objects

by Józef Lisowski

Electronics 2023, 12(17), 3637; https://doi.org/10.3390/electronics12173637 - 28 Aug 2023

Cited by 1 | Viewed by 871

Abstract

The article presents a model of the process of safe and optimal control of an autonomous surface object in a group of encountered objects. An algorithm for determining the optimal and safe trajectory based on a multi-object game model was proposed, and an algorithm for determining the optimal trajectory was proposed for comparative analysis, not taking into account the maneuverability of other objects. Simulation studies of the algorithms made it possible to assess the optimality of the trajectories for various acceptable object strategies. An analysis of the characteristics of the sensitivity of the safe control—assessed with the risk of collision, both on the inaccuracy of navigation data and on the number of possible strategies of objects, was carried out. Full article

(This article belongs to the Special Issue Advanced Nonlinear and Learning-Based Control Techniques for Complex Dynamical Systems)

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18 pages, 391 KiB

Open AccessArticle

Global Prescribed-Time Stabilization of Input-Quantized Nonlinear Systems via State-Scale Transformation

by Xin Guo, Wenhui Zhang and Fangzheng Gao

Electronics 2023, 12(15), 3357; https://doi.org/10.3390/electronics12153357 - 5 Aug 2023

Cited by 3 | Viewed by 1170

Abstract

The problem of global prescribed-time stabilization is reported in this paper for a kind of uncertain nonlinear system in power normal form. Compared with related work, the distinct characteristics of this study are that the system under consideration has an input-quantized actuator, and the prescribed time convergence of the system states is wanted. To meet these special requirements, a novel state-scaling transformation (SST) is firstly given to convert the prescribed-time stabilization of original systems to the asymptotic stabilization of the transformed one. Then, under the new framework of equivalent transformation, a quantized state feedback controller that ensures the achievement of the performance requirements is developed by using a power integrator (API) technique. Finally, the simulation results of a liquid-level system are provided to confirm the efficacy of the proposed approach. Full article

(This article belongs to the Special Issue Advanced Nonlinear and Learning-Based Control Techniques for Complex Dynamical Systems)

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16 pages, 1190 KiB

Open AccessArticle

A Simple Learning Approach for Robust Tracking Control of a Class of Dynamical Systems

by Mahmut Reyhanoglu and Mohammad Jafari

Electronics 2023, 12(9), 2026; https://doi.org/10.3390/electronics12092026 - 27 Apr 2023

Cited by 2 | Viewed by 1628

Abstract

This paper studies the robust tracking control problem for a class of uncertain nonlinear dynamical systems subject to unknown disturbances. A robust trajectory tracking control law is designed via a simple learning-based control strategy. In the developed design, the cost function based on the desired closed-loop error dynamics is minimized by means of gradient descent technique. A stability proof for the closed-loop nonlinear system is provided based on the pseudo-linear system theory. The learning capability of the developed robust trajectory tracking control law allows the system to mitigate the adverse effects of the uncertainties and disturbances. The numerical simulation results for a planar PPR robot are included to illustrate the effectiveness of the developed control law. Full article

(This article belongs to the Special Issue Advanced Nonlinear and Learning-Based Control Techniques for Complex Dynamical Systems)

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18 pages, 2230 KiB

Open AccessArticle

Nonlinear Simulation and Performance Characterisation of an Adaptive Model Predictive Control Method for Booster Separation and Re-Entry

by Joseph Chai and Erkan Kayacan

Electronics 2023, 12(6), 1488; https://doi.org/10.3390/electronics12061488 - 21 Mar 2023

Viewed by 1421

Abstract

This paper evaluates the

L_{1}

adaptive model predictive control (AMPC-

L_{1}

This paper evaluates the

L_{1}

adaptive model predictive control (AMPC-

L_{1}

) method in terms of its control performance and computational load. The control performance is assessed on the basis of the nonlinear simulation of a fly-back booster conducting stage separation and re-entry, and compared to baseline nonadaptive MPC and as a pole placement controller in both longitudinal and lateral control tasks. Simulation results show that AMPC-

L_{1}

exhibits superior control performance under nominal conditions, and aerodynamic and guidance law uncertainties. The computational load of AMPC-

L_{1}

is also evaluated on an embedded platform to demonstrate that AMPC-

L_{1}

preserves the efficiency properties of AMPC while improving its performance. Full article

(This article belongs to the Special Issue Advanced Nonlinear and Learning-Based Control Techniques for Complex Dynamical Systems)

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23 pages, 6002 KiB

Open AccessArticle

Passification-Based Robust Phase-Shift Control for Two-Rotor Vibration Machine

by Boris Andrievsky, Iuliia Zaitceva and Itzhak Barkana

Electronics 2023, 12(4), 1006; https://doi.org/10.3390/electronics12041006 - 17 Feb 2023

Cited by 6 | Viewed by 1898

Abstract

In this paper, the solution to the problem of robust control of the phase shift during rotation at a given speed of the unbalanced rotors for a two-rotor vibratory machine is presented. The solution to this problem is relevant for the development of vibration technologies (for example, a vibro-transportation of bulk materials). The proposed controller includes two proportional-integral (PI) rotor speed controllers with a cross-coupling, which receive signals with opposite signs from the phase shift controller. Unlike previous works, where a PI controller for phase shift control was also taken, including the adaptive controller with an implicit reference model (IRM), in the present paper, a relay-type signal controller with an integral component without a parametric adaptation is used. This approach allows, while maintaining robustness, to increase the operation speed and accuracy of the control process, avoiding at the same time the possible divergence of the tunable parameters due to the influence of noises and disturbances caused, among other things, by vibrations of the setup’s structural elements and measurement errors. For the control law design, the speed-gradient method was employed. For various types of reference phase-shift signals (constant, harmonic, chaotic), the results of extensive experimental studies performed on the mechatronic vibration setup and the simulations accomplished based on the results of identifying the parameters of the stand drive model are presented in the paper. The obtained results confirm the efficiency and robustness of the proposed algorithm and allow one to reveal the system performance properties. Full article

(This article belongs to the Special Issue Advanced Nonlinear and Learning-Based Control Techniques for Complex Dynamical Systems)

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30 pages, 2329 KiB

Open AccessArticle

Intelligent Distributed Swarm Control for Large-Scale Multi-UAV Systems: A Hierarchical Learning Approach

by Shawon Dey and Hao Xu

Electronics 2023, 12(1), 89; https://doi.org/10.3390/electronics12010089 - 26 Dec 2022

Cited by 7 | Viewed by 2015

Abstract

In this paper, a distributed swarm control problem is studied for large-scale multi-agent systems (LS-MASs). Different than classical multi-agent systems, an LS-MAS brings new challenges to control design due to its large number of agents. It might be more difficult for developing the appropriate control to achieve complicated missions such as collective swarming. To address these challenges, a novel mixed game theory is developed with a hierarchical learning algorithm. In the mixed game, the LS-MAS is represented as a multi-group, large-scale leader–follower system. Then, a cooperative game is used to formulate the distributed swarm control for multi-group leaders, and a Stackelberg game is utilized to couple the leaders and their large-scale followers effectively. Using the interaction between leaders and followers, the mean field game is used to continue the collective swarm behavior from leaders to followers smoothly without raising the computational complexity or communication traffic. Moreover, a hierarchical learning algorithm is designed to learn the intelligent optimal distributed swarm control for multi-group leader–follower systems. Specifically, a multi-agent actor–critic algorithm is developed for obtaining the distributed optimal swarm control for multi-group leaders first. Furthermore, an actor–critic–mass method is designed to find the decentralized swarm control for large-scale followers. Eventually, a series of numerical simulations and a Lyapunov stability proof of the closed-loop system are conducted to demonstrate the performance of the developed scheme. Full article

(This article belongs to the Special Issue Advanced Nonlinear and Learning-Based Control Techniques for Complex Dynamical Systems)

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18 pages, 1809 KiB

Open AccessArticle

Adaptive Discontinuous Control for Fixed-Time Consensus of Nonlinear Multi-Agent Systems

by Lu Wang, Min Zou, Wanli Guo, Hajid Alsubaie, Ahmed Alotaibi, Rasha Osman Ahmed Taie and Hadi Jahanshahi

Electronics 2022, 11(21), 3545; https://doi.org/10.3390/electronics11213545 - 30 Oct 2022

Cited by 6 | Viewed by 1648

Abstract

This paper mainly focuses on the fixed-time consensus (FXC) control problem for nonlinear multi-agent systems (MASs). For the cases of leader-following and leaderless, two adaptive discontinuous protocols are designed, respectively, to realize our control goals. Common adaptive control protocols always significantly increase the dimension of the considered system model, while the protocols presented here only require two adaptive update laws and are therefore simpler to apply in the engineering control. Moreover, no additional conditions are required to ensure that the system can achieve FXC successfully, except for some necessary assumptions. Simulation examples also illustrate that these two protocols are effective. Full article

(This article belongs to the Special Issue Advanced Nonlinear and Learning-Based Control Techniques for Complex Dynamical Systems)

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Review

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34 pages, 13943 KiB

Open AccessReview

Research on Synthesis of Multi-Layer Intelligent System for Optimal and Safe Control of Marine Autonomous Object

by Wojciech Koznowski, Krzysztof Kula, Agnieszka Lazarowska, Józef Lisowski, Anna Miller, Andrzej Rak, Monika Rybczak, Mostefa Mohamed-Seghir and Mirosław Tomera

Electronics 2023, 12(15), 3299; https://doi.org/10.3390/electronics12153299 - 31 Jul 2023

Cited by 5 | Viewed by 1581

Abstract

The article presents the synthesis of a multi-layer group control system for a marine autonomous surface vessel with the use of modern control theory methods. First, an evolutionary programming algorithm for determining the optimal route path was presented. Then the algorithms—dynamic programming with neural state constraints, ant colony, and neuro-phase safe control algorithms—were presented. LMI and predictive line-of-sight methods were used for optimal control. The direct control layer is implemented in multi-operations on the principle of switching. The results of the computer simulation of the algorithms were used to assess the quality control. Full article

(This article belongs to the Special Issue Advanced Nonlinear and Learning-Based Control Techniques for Complex Dynamical Systems)

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