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25 pages, 3075 KiB

Open AccessArticle

Robust Model Predictive Control for Two-DOF Flexible-Joint Manipulator System

by Rong Li, Hengli Wang, Gaowei Yan, Guoqiang Li and Long Jian

Mathematics 2023, 11(16), 3593; https://doi.org/10.3390/math11163593 - 19 Aug 2023

Cited by 1 | Viewed by 906

Abstract

This paper presents a practical study on how to improve the

ℋ_{\infty}

performance and meet the input–output constraints of the two-degrees-of-freedom (DOF) flexible-joint manipulator system (FJMS) with parameter uncertainties and external disturbances. For this reason, a robust constrained moving-horizon

ℋ_{\infty}

controller [...] Read more.

This paper presents a practical study on how to improve the

ℋ_{\infty}

performance and meet the input–output constraints of the two-degrees-of-freedom (DOF) flexible-joint manipulator system (FJMS) with parameter uncertainties and external disturbances. For this reason, a robust constrained moving-horizon

ℋ_{\infty}

controller is designed to improve the system

ℋ_{\infty}

performance while still satisfying the input–output constraints of the uncertain system. First, the uncertain controlled system model of the two-DOF FJMS is established via the Lagrange equation method, Spong’s assumption, and the linear fractional transformation (LFT) technique. Then, the control requirements and input–output constraints of the uncertain system are transformed into the linear matrix inequality (LMI) via the theory of

ℋ_{\infty}

control and the full-block multiplier technique. Next, the LMI optimization problem refreshed by the current state is addressed at each sample moment with the idea of the moving-horizon control of the model predictive control (MPC), and the calculated gain is implemented to the nonlinear closed-loop system under the state feedback structure. The validity and feasibility of the designed control scheme is finally verified via the results of simulation experiments. Full article

(This article belongs to the Special Issue Mathematical Methods Applied in Artificial Intelligence and Multi-Agent Systems)

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18 pages, 799 KiB

Open AccessArticle

Adaptive Consensus of the Stochastic Leader-Following Multi-Agent System with Time Delay

by Shoubo Jin and Guanghui Zhang

Mathematics 2023, 11(16), 3517; https://doi.org/10.3390/math11163517 - 14 Aug 2023

Cited by 1 | Viewed by 530

Abstract

For the multi-agent system with time delay and noise, the adaptive consensus of tracking control problems is discussed by the Lyapunov function. The main purpose of this study is to design an adaptive control protocol for the system, such that even if there [...] Read more.

For the multi-agent system with time delay and noise, the adaptive consensus of tracking control problems is discussed by the Lyapunov function. The main purpose of this study is to design an adaptive control protocol for the system, such that even if there exists time delay among agents, the protocol can still ensure the consensus of the stochastic system. The main contribution is to revise the protocols that were previously only applicable to system without time delay. Because the system is inevitably disrupted by time delay and noise during the interactive process, achieving coordination and consensus is difficult. To enable the followers to track the leader, a novel adaptive law depending on the Riccati equation is firstly proposed, and the adaptive law is different from previous mandatory control law completely depending on a known function. The ability to be altered online based on the state of system is a major feature of the adaptive law. When there are interactive noise and time delay between the followers and leader of the system, a special Lyapunov function is constructed to prove the adaptive consensus. And the upper bound of time delay is obtained by using the Itô integral theory. Finally, if the time delay of the system approaches zero, it is shown that the adaptive law still ensures that each follower tracks the leader under simpler conditions. Full article

(This article belongs to the Special Issue Mathematical Methods Applied in Artificial Intelligence and Multi-Agent Systems)

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12 pages, 641 KiB

Open AccessArticle

Distributed Disturbance Observer-Based Containment Control of Multi-Agent Systems via an Event-Triggered Approach

by Long Jian, Yongfeng Lv, Rong Li, Liwei Kou and Gengwu Zhang

Mathematics 2023, 11(10), 2363; https://doi.org/10.3390/math11102363 - 19 May 2023

Viewed by 956

Abstract

This paper studies the containment control problem of linear multi-agent systems (MASs) subject to external disturbances, where the communication graph is a directed graph with the followers being undirected connections. In order to save communication costs and energy consumption, a distributed disturbance observer-based [...] Read more.

This paper studies the containment control problem of linear multi-agent systems (MASs) subject to external disturbances, where the communication graph is a directed graph with the followers being undirected connections. In order to save communication costs and energy consumption, a distributed disturbance observer-based event-triggered controller is employed based on the relative outputs of neighboring followers. Compared with conventional controllers, our observer-based controller utilizes the relative outputs of neighboring followers at the same triggered instant. Furthermore, it is shown that Zeno behavior can be avoided. Finally, the validity of our proposed methodology is demonstrated by a simulation example. Full article

(This article belongs to the Special Issue Mathematical Methods Applied in Artificial Intelligence and Multi-Agent Systems)

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17 pages, 562 KiB

Open AccessArticle

Dynamics Analysis for the Random Homogeneous Biased Assimilation Model

by Jiangbo Zhang and Yiyi Zhao

Mathematics 2023, 11(7), 1661; https://doi.org/10.3390/math11071661 - 30 Mar 2023

Viewed by 760

Abstract

This paper studies the evolution of opinions over random social networks subject to individual biases. An agent reviews the opinion of a randomly selected one and then updates its opinion under homogeneous biased assimilation. This study investigates the impact of biased assimilation on [...] Read more.

This paper studies the evolution of opinions over random social networks subject to individual biases. An agent reviews the opinion of a randomly selected one and then updates its opinion under homogeneous biased assimilation. This study investigates the impact of biased assimilation on random opinion networks, which is different from the previous studies on fixed network structures. If the bias parameters are static, it is proven that the event in which all agents converge to extreme opinions happens almost surely. Next, the opinion polarization event is proved to be a probability one event. While if the bias parameters are dynamic, the opinion evolution is proven to depend on early finite time slots for the dynamical individual bias parameter functions independent of the biased parameter values after the time threshold. Numerical simulations further show that opinion evolution depends on early finite time slots for some nonlinear dynamical individual bias parameter functions. Full article

(This article belongs to the Special Issue Mathematical Methods Applied in Artificial Intelligence and Multi-Agent Systems)

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21 pages, 817 KiB

Open AccessArticle

Mixed-Delay-Dependent Augmented Functional for Synchronization of Uncertain Neutral-Type Neural Networks with Sampled-Data Control

by Shuoting Wang and Kaibo Shi

Mathematics 2023, 11(4), 872; https://doi.org/10.3390/math11040872 - 08 Feb 2023

Cited by 2 | Viewed by 938

Abstract

In this paper, the synchronization problem of uncertain neutral-type neural networks (NTNNs) with sampled-data control is investigated. First, a mixed-delay-dependent augmented Lyapunov–Krasovskii functional (LKF) is proposed, which not only considers the interaction between transmission delay and communication delay, but also takes the interconnected [...] Read more.

In this paper, the synchronization problem of uncertain neutral-type neural networks (NTNNs) with sampled-data control is investigated. First, a mixed-delay-dependent augmented Lyapunov–Krasovskii functional (LKF) is proposed, which not only considers the interaction between transmission delay and communication delay, but also takes the interconnected relationship between neutral delay and transmission delay into consideration. Then, a two-sided looped functional is also involved in the LKF, which effectively utilizes the information on the intervals

[t_{k}, t]

,

[t_{k} - τ, t - τ], [t, t_{k + 1}), [t - τ, t_{k + 1} - τ)

. Furthermore, based on the suitable LKF and a free-matrix-based integral inequality, two synchronization criteria via a sampled-data controller considering communication delay are derived in forms of linear matrix inequalities (LMIs). Finally, three numerical examples are carried out to confirm the validity of the proposed criteria. Full article

(This article belongs to the Special Issue Mathematical Methods Applied in Artificial Intelligence and Multi-Agent Systems)

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20 pages, 5700 KiB

Open AccessArticle

Learning to Utilize Curiosity: A New Approach of Automatic Curriculum Learning for Deep RL

by Zeyang Lin, Jun Lai, Xiliang Chen, Lei Cao and Jun Wang

Mathematics 2022, 10(14), 2523; https://doi.org/10.3390/math10142523 - 20 Jul 2022

Cited by 1 | Viewed by 1500

Abstract

In recent years, reinforcement learning algorithms based on automatic curriculum learning have been increasingly applied to multi-agent system problems. However, in the sparse reward environment, the reinforcement learning agents get almost no feedback from the environment during the whole training process, which leads [...] Read more.

In recent years, reinforcement learning algorithms based on automatic curriculum learning have been increasingly applied to multi-agent system problems. However, in the sparse reward environment, the reinforcement learning agents get almost no feedback from the environment during the whole training process, which leads to a decrease in the convergence speed and learning efficiency of the curriculum reinforcement learning algorithm. Based on the automatic curriculum learning algorithm, this paper proposes a curriculum reinforcement learning method based on the curiosity model (CMCL). The method divides the curriculum sorting criteria into temporal-difference error and curiosity reward, uses the K-fold cross validation method to evaluate the difficulty priority of task samples, uses the Intrinsic Curiosity Module (ICM) to evaluate the curiosity priority of the task samples, and uses the curriculum factor to adjust the learning probability of the task samples. This study compares the CMCL algorithm with other baseline algorithms in cooperative-competitive environments, and the experimental simulation results show that the CMCL method can improve the training performance and robustness of multi-agent deep reinforcement learning algorithms. Full article

(This article belongs to the Special Issue Mathematical Methods Applied in Artificial Intelligence and Multi-Agent Systems)

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38 pages, 2548 KiB

Open AccessArticle

On the Throughput of the Common Target Area for Robotic Swarm Strategies

by Yuri Tavares dos Passos, Xavier Duquesne and Leandro Soriano Marcolino

Mathematics 2022, 10(14), 2482; https://doi.org/10.3390/math10142482 - 16 Jul 2022

Cited by 2 | Viewed by 1370

Abstract

A robotic swarm may encounter traffic congestion when many robots simultaneously attempt to reach the same area. This work proposes two measures for evaluating the access efficiency of a common target area as the number of robots in the swarm rises: the maximum [...] Read more.

A robotic swarm may encounter traffic congestion when many robots simultaneously attempt to reach the same area. This work proposes two measures for evaluating the access efficiency of a common target area as the number of robots in the swarm rises: the maximum target area throughput and its maximum asymptotic throughput. Both are always finite as the number of robots grows, in contrast to the arrival time at the target per number of robots that tends to infinity. Using them, one can analytically compare the effectiveness of different algorithms. In particular, three different theoretical strategies proposed and formally evaluated for reaching a circular target area: (i) forming parallel queues towards the target area, (ii) forming a hexagonal packing through a corridor going to the target, and (iii) making multiple curved trajectories towards the boundary of the target area. The maximum throughput and the maximum asymptotic throughput (or bounds for it) for these strategies are calculated, and these results are corroborated by simulations. The key contribution is not the proposal of new algorithms to alleviate congestion but a fundamental theoretical study of the congestion problem in swarm robotics when the target area is shared. Full article

(This article belongs to the Special Issue Mathematical Methods Applied in Artificial Intelligence and Multi-Agent Systems)

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Review

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24 pages, 1615 KiB

Open AccessReview

Modeling and Control of Wide-Area Networks

by Qiuzhen Wang and Jiangping Hu

Mathematics 2023, 11(18), 3984; https://doi.org/10.3390/math11183984 - 19 Sep 2023

Viewed by 724

Abstract

This paper provides a survey of recent research progress in mathematical modeling and distributed control of wide-area networks. Firstly, the modeling is introduced for two types of wide-area networks, i.e., coopetitive networks and cooperative networks, with the help of algebraic graph theory. Particularly, [...] Read more.

This paper provides a survey of recent research progress in mathematical modeling and distributed control of wide-area networks. Firstly, the modeling is introduced for two types of wide-area networks, i.e., coopetitive networks and cooperative networks, with the help of algebraic graph theory. Particularly, bipartite network topologies and cluster network topologies are introduced for coopetitive networks. With respect to cooperative networks, an intermittent clustered network modeling is presented. Then, some classical distributed control strategies are reviewed for wide-area networks to ensure some desired collective behaviors, such as consensus (or synchronization), bipartite consensus (or polarization), and cluster consensus (or fragmentation). Finally, some conclusions and future directions are summarized. Full article

(This article belongs to the Special Issue Mathematical Methods Applied in Artificial Intelligence and Multi-Agent Systems)

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19 pages, 5778 KiB

Open AccessReview

On Model Identification Based Optimal Control and It’s Applications to Multi-Agent Learning and Control

by Rui Luo, Zhinan Peng and Jiangping Hu

Mathematics 2023, 11(4), 906; https://doi.org/10.3390/math11040906 - 10 Feb 2023

Cited by 29 | Viewed by 1809

Abstract

This paper reviews recent progress in model identification-based learning and optimal control and its applications to multi-agent systems (MASs). First, a class of learning-based optimal control method, namely adaptive dynamic programming (ADP), is introduced, and the existing results using ADP methods to solve [...] Read more.

This paper reviews recent progress in model identification-based learning and optimal control and its applications to multi-agent systems (MASs). First, a class of learning-based optimal control method, namely adaptive dynamic programming (ADP), is introduced, and the existing results using ADP methods to solve optimal control problems are reviewed. Then, this paper investigates various kinds of model identification methods and analyzes the feasibility of combining the model identification method with the ADP method to solve optimal control of unknown systems. In addition, this paper expounds the current applications of model identification-based ADP methods in the fields of single-agent systems (SASs) and MASs. Finally, some conclusions and some future directions are presented. Full article

(This article belongs to the Special Issue Mathematical Methods Applied in Artificial Intelligence and Multi-Agent Systems)

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