Yiming Cui , Tianjiao An , Bo Dong , Bing Ma , Zhenguo Zhang
{"title":"Bilayer nonzero-sum differential game-based optimal control of modular robot manipulator for human–robot collaboration","authors":"Yiming Cui , Tianjiao An , Bo Dong , Bing Ma , Zhenguo Zhang","doi":"10.1016/j.ejcon.2025.101225","DOIUrl":"10.1016/j.ejcon.2025.101225","url":null,"abstract":"<div><div>This paper introduces a bilayer nonzero-sum differential game-based optimal control framework for a Modular Robot Manipulator (MRM) in Human–Robot Collaboration (HRC) tasks. The dynamic model of the MRM is obtained with the Joint Torque Feedback (JTF) technique. Consider the <span><math><mi>N</mi></math></span>-player nonzero-sum differential game within the MRM subsystems and the 2-player nonzero-sum differential game involving both the MRM and human collaborators in HRC tasks as the inner and outer layers of the bilayer nonzero-sum differential game. The Nash equilibrium solutions for the inner and outer layers of the nonzero-sum differential games are independently determined using the Adaptive Dynamic Programming (ADP) algorithm, which is based on a fuzzy logic system. As a result, optimal control policies for MRM subsystems and the optimal interaction force in HRC tasks are derived. The trajectory tracking error of the MRM system and the outer layer physical Human–Robot Interaction (pHRI) system have both been proven to be Ultimately Uniformly Bounded (UUB) under the bilayer nonzero-sum differential game-based optimal control of MRM for HRC with the application of Lyapunov theory. Finally, experiment results are presented to validate the superiority and effectiveness of the proposed method.</div></div>","PeriodicalId":50489,"journal":{"name":"European Journal of Control","volume":"83 ","pages":"Article 101225"},"PeriodicalIF":2.5,"publicationDate":"2025-04-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143848637","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Observer-based adaptive consensus of intelligent vehicle convoys with directed and undirected networks subject to input saturation","authors":"Hossein Chehardoli , Ehsan Shafie","doi":"10.1016/j.ejcon.2025.101233","DOIUrl":"10.1016/j.ejcon.2025.101233","url":null,"abstract":"<div><div>In this research work, the consensus control design of intelligent vehicle convoys with directed and undirected networks and third-order dynamic equation is studied. The engine saturation as an input saturation is involved in the dynamical model which will make the longitudinal dynamics of each following intelligent vehicle to be nonlinear. All followers track an actual leading intelligent vehicle that has no input. For some reasons such as reducing the communication burden, external attacks and sensor failure, it is assumed that some of the states of followers and the leader are not available. Three common network structures are considered in consensus design and analysis: some predecessors following, bi-directional and uni-directional. To estimate the inaccessible states of followers and the leader, two different observers combined with an output feedback controller are designed so that each follower can estimate its own and the leader's unknown states. Afterward, a linear output feedback law is introduced to attain the global asymptotic consensus. The Lyapunov theory is applied to prove that the output control protocol leads the proposed intended convoy to asymptotic stability in the linear and nonlinear input saturation regions. For all three structures, several examples are provided to evaluate the method of this article.</div></div>","PeriodicalId":50489,"journal":{"name":"European Journal of Control","volume":"84 ","pages":"Article 101233"},"PeriodicalIF":2.5,"publicationDate":"2025-04-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143873330","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Xun Li , Guangchen Wang , Yu Wang , Jie Xiong , Heng Zhang
{"title":"Two system transformation data-driven algorithms for linear quadratic mean-field games","authors":"Xun Li , Guangchen Wang , Yu Wang , Jie Xiong , Heng Zhang","doi":"10.1016/j.ejcon.2025.101226","DOIUrl":"10.1016/j.ejcon.2025.101226","url":null,"abstract":"<div><div>This paper studies a class of continuous-time linear quadratic (LQ) mean-field game problems. We develop two system transformation data-driven algorithms to approximate the decentralized strategies of the LQ mean-field games. The main feature of the obtained data-driven algorithms is that they eliminate the requirement on all system matrices. First, we transform the original stochastic system into an ordinary differential equation (ODE). Subsequently, we construct some Kronecker product-based matrices by the input/state data of the ODE. By virtue of these matrices, we implement a model-based policy iteration (PI) algorithm and a model-based value iteration (VI) algorithm in data-driven fashions. In addition, we also demonstrate the convergence of these two data-driven algorithms under some mild conditions. Finally, we illustrate the practicality of our algorithms via two numerical examples.</div></div>","PeriodicalId":50489,"journal":{"name":"European Journal of Control","volume":"83 ","pages":"Article 101226"},"PeriodicalIF":2.5,"publicationDate":"2025-04-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143833608","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"High-order consensus: Optimal controller design","authors":"Pedro Trindade, Pedro Batista, Rita Cunha","doi":"10.1016/j.ejcon.2025.101227","DOIUrl":"10.1016/j.ejcon.2025.101227","url":null,"abstract":"<div><div>This paper considers the optimal design of a high-order consensus protocol applied to agents modeled with multiple integrators. The problem addressed amounts to determining the optimal values for the coupling gains and for the edge weights of the directed graph that models the network. With that goal in mind, an LQR-like cost function is proposed, which is obtained from the typical LQR cost function by taking the expectation over the initial state of the system. To enable the implementation of optimization algorithms, and ultimately solve the considered problem, it is first necessary to tackle the evaluation of the cost and its derivatives, taking into account the particularities of the consensus problem. Then, to determine the optimal parameters of the high-order consensus protocol, a truncated Newton method is considered. Furthermore, a suboptimal design approach is proposed, which consists in splitting the problem into two simpler ones that are solved sequentially, in a reduced amount of time. It is also shown that if one considers symmetric Laplacian matrices, these simpler problems are convex for second- and third-order consensus under a mild assumption on the initial conditions. Finally, the proposed algorithms are illustrated with examples that demonstrate their efficacy as well as the benefits to the controller synthesis.</div></div>","PeriodicalId":50489,"journal":{"name":"European Journal of Control","volume":"83 ","pages":"Article 101227"},"PeriodicalIF":2.5,"publicationDate":"2025-04-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143845007","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Uniform approximation of exponential stability for 1-D wave equation with potential","authors":"Jiankang Liu , Bao-Zhu Guo","doi":"10.1016/j.ejcon.2025.101221","DOIUrl":"10.1016/j.ejcon.2025.101221","url":null,"abstract":"<div><div>In this paper, we investigate uniform exponential stability approximation for a one-dimensional wave equation with potential. Given the challenges in identifying the time-domain multiplier for the exponentially stable continuous system, we opt for a frequency domain approach. Through the application of the order-reduction method, we devise a novel spatially semi-discretized finite difference scheme for the continuous system. We then establish the uniform exponential stability of the semi-discretized system using the discrete version of the frequency domain method, with the discrete proof mirroring the continuous case.</div></div>","PeriodicalId":50489,"journal":{"name":"European Journal of Control","volume":"83 ","pages":"Article 101221"},"PeriodicalIF":2.5,"publicationDate":"2025-04-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143823317","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Event-triggered optimal fault-tolerant control for a class of uncertain strict-feedback nonlinear systems","authors":"Jing-Yu Guo , Li-Bing Wu","doi":"10.1016/j.ejcon.2025.101228","DOIUrl":"10.1016/j.ejcon.2025.101228","url":null,"abstract":"<div><div>This paper investigates the event-triggered optimal control for a class of strict-feedback nonlinear systems with actuator faults. With the help of identifier–critic–actor structure based on neural network, the difficulties posed by inherent nonlinearity of the Hamilton–Jacobi–Bellman (HJB) equation and unknown nonlinear dynamics are solved, a novel optimal control method is designed without using persistence excitation (PE) condition. By using the backstepping technique, the adaptive fault-tolerant control (FTC) and event-triggered control (ETC) schemes are co-designed. It is proved that all signals of the closed-loop system are semiglobally uniformly ultimately bounded (SGUUB) and the Zeno-behavior is avoided. Simulation results verify the effectiveness of the method.</div></div>","PeriodicalId":50489,"journal":{"name":"European Journal of Control","volume":"83 ","pages":"Article 101228"},"PeriodicalIF":2.5,"publicationDate":"2025-04-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143816042","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Expression of analytical solution and almost sure exponential stability for linear regime-switching jump diffusion systems","authors":"Gui-Hua Zhao, Ran Ni","doi":"10.1016/j.ejcon.2025.101206","DOIUrl":"10.1016/j.ejcon.2025.101206","url":null,"abstract":"<div><div>In this paper, we consider linear regime-switching jump diffusion systems. First, for the homogeneous and nonhomogeneous linear regime-switching jump diffusion systems, we respectively present the expressions of the analytical solutions, which depend on the fundamental matrix of the homogeneous systems. Then, for several classes of the linear homogeneous regime-switching jump diffusion systems, the expression of solutions are given explicitly by showing the expression of the fundamental matrices. For multi-dimensional linear homogeneous regime-switching jump diffusion systems, we obtain that system is exponentially stable almost surely if and only if the sample Lyapunov exponent of the fundamental matrix is less than zero. Furthermore, through the expressions of the explicit solutions, the sufficient conditions dependent directly on coefficients are developed for the almost sure exponential stability of multi-dimensional linear homogeneous regime-switching jump diffusion systems. Especially, for a class of multi-dimensional linear homogeneous regime-switching jump diffusion systems, the sufficient and necessary condition of almost sure exponential stability is obtained. Finally, two examples, whose almost sure exponential stability cannot be analyzed by the existing related work, are given and their numerical simulations are presented to illustrate the obtained results about almost sure exponential stability.</div></div>","PeriodicalId":50489,"journal":{"name":"European Journal of Control","volume":"83 ","pages":"Article 101206"},"PeriodicalIF":2.5,"publicationDate":"2025-03-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143628969","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"A multiple connected recurrent neural network based super-twisting terminal sliding mode control for quad-rotor UAV","authors":"Jixun Li, Likai Wu","doi":"10.1016/j.ejcon.2025.101220","DOIUrl":"10.1016/j.ejcon.2025.101220","url":null,"abstract":"<div><div>Considering the complex environment in which quad-rotor unmanned aerial vehicle (UAV) perform their tasks, it is difficult to establish an accurate UAV model and obtain information about external disturbances. Aiming at the above problems, a multiple connected recurrent neural network (MCRNN) based on super-twisting algorithm (STA) terminal sliding mode control (TSMC) strategy is proposed. Due to the unknown dynamics, the equivalent control law of sliding mode control cannot be directly applied to UAVs. Therefore, the MCRNN controller is used to approximate the equivalent control rather than to estimate the dynamics of the quad-rotor UAV. All hidden layer neurons in MCRNN receive self-feedback as well as signals from other hidden layer neurons, thereby augmenting their capacity to capture intricate dynamic features. In addition, the robustness of the sliding mode is used to suppress the mismatched disturbance instead of the traditional disturbance observer. This solution is more flexible, and reduces computing costs. Lyapunov stability theory is used to ensure the finite-time stability of the whole system, and the real-time update law of MCRNN weights is derived. Finally, the proposed method is applied to a path-following task, obtaining a maximum overshoot of 4.58e−02 and the settling time of 0.935s. By comparing the results obtained by different methods, it is concluded that the proposed controller is insensitive to model parameter variations, is able to suppress mismatched disturbances, and has significant stability and robustness.</div></div>","PeriodicalId":50489,"journal":{"name":"European Journal of Control","volume":"83 ","pages":"Article 101220"},"PeriodicalIF":2.5,"publicationDate":"2025-03-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143621150","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Fixed-time stability for parabolic PDE","authors":"Anna Michalak","doi":"10.1016/j.ejcon.2025.101218","DOIUrl":"10.1016/j.ejcon.2025.101218","url":null,"abstract":"<div><div>In this paper, we introduce a novel methodology for investigating the fixed-time stability properties of the zero solution to a semilinear parabolic equation. In pursuit of this, we introduce a novel dual approach to the Lyapunov concept of stability. The dual Lyapunov function adheres to a dual Hamilton–Jacobi inequality, forming the foundation for investigating fixed-time stability (fixed extinction time) in the original problem.</div></div>","PeriodicalId":50489,"journal":{"name":"European Journal of Control","volume":"83 ","pages":"Article 101218"},"PeriodicalIF":2.5,"publicationDate":"2025-03-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143619461","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Raffaele Giuseppe Cestari, Andrea Castelletti, Simone Formentin
{"title":"Non-linear multi-objective Bayesian MPC of water reservoir systems","authors":"Raffaele Giuseppe Cestari, Andrea Castelletti, Simone Formentin","doi":"10.1016/j.ejcon.2025.101205","DOIUrl":"10.1016/j.ejcon.2025.101205","url":null,"abstract":"<div><div>Addressing multiple conflicting objectives in online control problems is a challenge. Traditional causal approaches optimize cost functions defined as a weighted sum of cost contributions, each representing a control objective. However, the way cost weights are chosen is traditionally heuristic, based at most on sensitivity analyses. In the literature, some solutions optimize weights based on multi-objective genetic algorithms (NSGA-II). Still, these strategies inherit the well-known deterioration phenomenon in which NSGA-II occurs. Here, we introduce a novel Non-Linear Model Predictive Control (NLMPC) formulation that automatically selects the optimal weight combination, i.e., the one resulting in the best-aggregated performance. We run <span><math><mi>N</mi></math></span> NLMPC controllers simultaneously at each time step, calibrating their cost function weights using a Bayesian Optimization that optimizes the Pareto frontier’s Hypervolume and Additive Epsilon Indicator. We then select the controller, minimizing the trade-off between objectives. We apply our approach to the Red River system, a highly non-linear and multipurpose water resource system in Vietnam. The proposed tuning algorithm overcomes the literature deterioration issue and validation over six years of observational data shows that our method minimizes the aggregated normalized cost, with and without disturbance knowledge assumption. The back-test of experimental data finally validates our control strategy, demonstrating a dominating solution against historical control.</div></div>","PeriodicalId":50489,"journal":{"name":"European Journal of Control","volume":"83 ","pages":"Article 101205"},"PeriodicalIF":2.5,"publicationDate":"2025-03-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143601632","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}