AutomaticaPub Date : 2025-09-19DOI: 10.1016/j.automatica.2025.112598
Yuxuan Liu , Maojiao Ye , Lei Ding , Lihua Xie , Qing-Long Han
{"title":"Distributed Nash equilibrium seeking with a dynamic set of players","authors":"Yuxuan Liu , Maojiao Ye , Lei Ding , Lihua Xie , Qing-Long Han","doi":"10.1016/j.automatica.2025.112598","DOIUrl":"10.1016/j.automatica.2025.112598","url":null,"abstract":"<div><div>This paper formulates a new distributed Nash equilibrium seeking problem with a dynamic set of players in which players are allowed to join and leave the network in a free manner during the decision-making process. To accommodate the dynamic joining and leaving behaviors of the players, a status estimation mechanism, which is capable of estimating in a finite time whether the players are active or inactive, is introduced. Based on the status estimation mechanism, a gradient play based algorithm is developed for distributed Nash equilibrium seeking in the dynamic environment. It is shown that under strongly connected communication graphs, players’ actions are convergent to a small neighborhood of the new Nash equilibrium linearly every time the player set changes. Moreover, the convergence accuracy and convergence rate can be adjusted by suitably tuning the step-size. To cover more general communication scenarios, strongly connected graphs are further relaxed to be B-jointly connected graphs, under which the convergence properties of the proposed algorithm are analytically studied. Furthermore, the upper bound of the average tracking error is quantified to evaluate the dynamic performance of the proposed algorithm. In the last, a simulation study on energy consumption games is given to verify the effectiveness of the proposed algorithm.</div></div>","PeriodicalId":55413,"journal":{"name":"Automatica","volume":"183 ","pages":"Article 112598"},"PeriodicalIF":5.9,"publicationDate":"2025-09-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145106129","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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":"Adversarial dynamic games for Markov jump systems: A policy iteration Q-learning method","authors":"Hao Shen , Jiacheng Wu , Jing Wang , Zhengguang Wu","doi":"10.1016/j.automatica.2025.112591","DOIUrl":"10.1016/j.automatica.2025.112591","url":null,"abstract":"<div><div>This paper presents a reinforcement Q-learning approach for solving adversarial dynamic games in Markov jump systems. The <span><math><msub><mrow><mi>H</mi></mrow><mrow><mi>∞</mi></mrow></msub></math></span> control problem is first formulated as a two-player zero-sum dynamic game, where the control policy and the disturbance policy act as adversarial players. To derive the Nash equilibrium control strategies for such games, a set of coupled algebraic Riccati equations is established, with the disturbance attenuation level properly prescribed. On this basis, two novel data-driven parallel Q-learning algorithms are proposed. The advantages of the proposed method are threefold: (i) it does not require precise knowledge of the system dynamics; (ii) it learns the optimal disturbance attenuation level; (iii) it yields Nash equilibrium control strategies. Finally, two simulation examples validate the effectiveness of the proposed method.</div></div>","PeriodicalId":55413,"journal":{"name":"Automatica","volume":"183 ","pages":"Article 112591"},"PeriodicalIF":5.9,"publicationDate":"2025-09-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145106130","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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":"Reducing real-time complexity via sub-control Lyapunov functions: From theory to experiments","authors":"Huu-Thinh Do , Franco Blanchini , Stefano Miani , Ionela Prodan","doi":"10.1016/j.automatica.2025.112592","DOIUrl":"10.1016/j.automatica.2025.112592","url":null,"abstract":"<div><div>The techniques to design control Lyapunov functions (CLF), along with a proper stabilizing feedback, possibly in the presence of constraints, often provide control laws that are too complex for proper implementation online, especially when an optimization problem is involved. In this work, we show how to acquire an alternative, computationally attractive feedback. Given a nominal CLF and a nominal state feedback, we say that a different positive definite function is a Sub-control Lyapunov function (SCLF) if its Lyapunov derivative is negative-definite and bounded above by the Lyapunov derivative of the nominal function with the nominal control. It turns out that if we consider a family of basis functions, then an SCLF can be computed by linear programming, with an infinite number of constraints. The idea is that although the offline computational burden to achieve the new controller and solve the linear program is considerable, the online computational burden is drastically reduced. Comprehensive simulations and experiments on drone control are conducted to demonstrate the effectiveness of the study.</div></div>","PeriodicalId":55413,"journal":{"name":"Automatica","volume":"183 ","pages":"Article 112592"},"PeriodicalIF":5.9,"publicationDate":"2025-09-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145106627","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
AutomaticaPub Date : 2025-09-17DOI: 10.1016/j.automatica.2025.112594
Yao Xu, Linna Zhou, Jianguo Zhao, Lei Ma, Chunyu Yang
{"title":"Data-model-hybrid-driven near-optimal operational control of two-time-scale industrial systems with unknown operational model","authors":"Yao Xu, Linna Zhou, Jianguo Zhao, Lei Ma, Chunyu Yang","doi":"10.1016/j.automatica.2025.112594","DOIUrl":"10.1016/j.automatica.2025.112594","url":null,"abstract":"<div><div>This article discusses the optimal operational control (OOC) problem of two-time-scale (TTS) industrial systems with unknown operation model. Based on the singular perturbation theory (SPT), the OOC problem of TTS industrial systems is decomposed into an optimal regulation problem in fast time-scale and an optimal set-point tracking problem in slow time-scale. Then, by convex duality, the obtained optimization problems are equivalently transformed into convex optimization (CO) problems, and a data-model-hybrid-driven composite controller is designed. The design method of this composite controller avoids the potential numerical stiffness problems, and does not need complete system dynamics information while ensuring the steady-state output tracking error converges to zero. Finally, an example of mixed separation thickening process (MSTP) of hematite beneficiation is given to show the effectiveness of the proposed scheme.</div></div>","PeriodicalId":55413,"journal":{"name":"Automatica","volume":"183 ","pages":"Article 112594"},"PeriodicalIF":5.9,"publicationDate":"2025-09-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145106628","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
AutomaticaPub Date : 2025-09-16DOI: 10.1016/j.automatica.2025.112545
Lidong Li , Andrea Bisoffi , Claudio De Persis , Nima Monshizadeh
{"title":"Controller synthesis from noisy-input noisy-output data","authors":"Lidong Li , Andrea Bisoffi , Claudio De Persis , Nima Monshizadeh","doi":"10.1016/j.automatica.2025.112545","DOIUrl":"10.1016/j.automatica.2025.112545","url":null,"abstract":"<div><div>We consider the problem of synthesizing a dynamic output-feedback controller for a linear system, using solely input–output data corrupted by measurement noise. To handle input–output data, an auxiliary representation of the original system is utilized. By exploiting the structure of the auxiliary system, we design a controller that robustly stabilizes all possible systems consistent with data. Notably, we also provide a novel solution to extend the results to generic multi-input multi-output systems. The findings are illustrated by numerical examples.</div></div>","PeriodicalId":55413,"journal":{"name":"Automatica","volume":"183 ","pages":"Article 112545"},"PeriodicalIF":5.9,"publicationDate":"2025-09-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145106624","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
AutomaticaPub Date : 2025-09-12DOI: 10.1016/j.automatica.2025.112543
Fahim Shakib , Johan Schoukens , Alexander Yu. Pogromsky , Alexey Pavlov , Nathan van de Wouw
{"title":"Accuracy bounds for the simulation of a class of continuous-time nonlinear models","authors":"Fahim Shakib , Johan Schoukens , Alexander Yu. Pogromsky , Alexey Pavlov , Nathan van de Wouw","doi":"10.1016/j.automatica.2025.112543","DOIUrl":"10.1016/j.automatica.2025.112543","url":null,"abstract":"<div><div>Real-world dynamic systems evolve in the continuous-time world, while their models are simulated in the digital world using discrete-time numerical simulation algorithms. Such simulation is essential for a variety of system and control problems such as system identification and performance analysis of (control) systems. Ideally, the simulated model response should be identical to the system response. However, this is typically not the case in practice, even when the effects of unmodelled dynamics and parametric uncertainty are excluded. Even in that scenario, a mismatch exists between the response of the system and the model due to the interface between the physical world and the digital computer, unknown disturbances, and simulation inaccuracies. For the class of continuous-time, nonlinear Lur’e-type systems, this paper analyses the mismatch between the steady-state system response and the steady-state model response computed using the so-called mixed time–frequency algorithm. Firstly, a bound on the mismatch between the steady-state system response and the computed steady-state model response based on continuous-time signals is derived. Secondly, a bound for the same mismatch is derived for a sampled version of the signals. The bounds are further decomposed into several components, each given an interpretation that can be used to reduce the bounds on the mismatch. In a numerical case study, we show that reducing the bounds also reduces the actual mismatch.</div></div>","PeriodicalId":55413,"journal":{"name":"Automatica","volume":"183 ","pages":"Article 112543"},"PeriodicalIF":5.9,"publicationDate":"2025-09-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145049717","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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":"Orchestrating on-board sensors for global hybrid robust stabilization of unicycles","authors":"Riccardo Ballaben , Alessandro Astolfi , Philipp Braun , Luca Zaccarian","doi":"10.1016/j.automatica.2025.112502","DOIUrl":"10.1016/j.automatica.2025.112502","url":null,"abstract":"<div><div>We consider mobile robots described through unicycle dynamics equipped with on-board range sensors and cameras, one facing forward and one facing backward, providing measurements of the distance and misalignment to a target. We propose a hybrid control law combining the two on-board measurements and discuss stability results for the closed-loop expressed in the on-board camera-based coordinates, using Lyapunov-based arguments. We prove robustness of the stability properties to uncertainties affecting the sensors and external perturbations acting on the robot. The results are illustrated via simulations.</div></div>","PeriodicalId":55413,"journal":{"name":"Automatica","volume":"183 ","pages":"Article 112502"},"PeriodicalIF":5.9,"publicationDate":"2025-09-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145049718","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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 consensus Kalman filter on L2 spaces","authors":"Stefano Battilotti , Alessandro Borri , Filippo Cacace , Massimiliano d’Angelo , Alfredo Germani","doi":"10.1016/j.automatica.2025.112530","DOIUrl":"10.1016/j.automatica.2025.112530","url":null,"abstract":"<div><div>We study the estimation problem of infinite dimensional discrete-time stochastic linear systems with finite dimensional measurements on sensor networks modeled by connected undirected graphs. The framework encompasses discretized PDEs with sampled measurements. A new scheme of distributed consensus on measurements is extended to systems evolving in <span><math><msub><mrow><mi>L</mi></mrow><mrow><mn>2</mn></mrow></msub></math></span> spaces in order to limit the information exchange to finite-dimensional vectors. We show that, in analogy to the finite-dimensional case, at each node the variance of the estimation error tends to the one of the centralized Kalman filter for systems is <span><math><msub><mrow><mi>L</mi></mrow><mrow><mn>2</mn></mrow></msub></math></span> when the number of consensus steps increases.</div></div>","PeriodicalId":55413,"journal":{"name":"Automatica","volume":"183 ","pages":"Article 112530"},"PeriodicalIF":5.9,"publicationDate":"2025-09-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145049716","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
AutomaticaPub Date : 2025-09-09DOI: 10.1016/j.automatica.2025.112572
Rafael Vazquez , Jean Auriol , Federico Bribiesca-Argomedo , Miroslav Krstic
{"title":"Backstepping for partial differential equations: A survey","authors":"Rafael Vazquez , Jean Auriol , Federico Bribiesca-Argomedo , Miroslav Krstic","doi":"10.1016/j.automatica.2025.112572","DOIUrl":"10.1016/j.automatica.2025.112572","url":null,"abstract":"<div><div>Systems modeled by partial differential equations (PDEs) are at least as ubiquitous as those by nature finite-dimensional and modeled by ordinary differential equations (ODEs). And yet, systematic and readily usable methodologies, for such a significant portion of real systems, have been historically scarce. Around the year 2000, the backstepping approach to PDE control began to offer not only a less abstract alternative to PDE control techniques replicating optimal and spectrum assignment techniques of the 1960s, but also enabled the methodologies of adaptive and nonlinear control, matured in the 1980s and 1990s, to be extended from ODEs to PDEs, allowing feedback synthesis for systems that are uncertain, nonlinear, and infinite-dimensional. The PDE backstepping literature has since grown to hundreds of papers and nearly a dozen books. This survey aims to facilitate the entry into this thriving area of overwhelming size and topical diversity. Designs of controllers and observers, for parabolic, hyperbolic, and other classes of PDEs, in one or more dimensions, with nonlinear, adaptive, sampled-data, and event-triggered extensions, are covered in the survey. The lifeblood of control are technology and physics. The survey places a particular emphasis on applications that have motivated the development of the theory and which have benefited from the theory and designs: flows, flexible structures, materials, thermal and chemically reacting dynamics, energy (from oil drilling to batteries and magnetic confinement fusion), and vehicles.</div></div>","PeriodicalId":55413,"journal":{"name":"Automatica","volume":"183 ","pages":"Article 112572"},"PeriodicalIF":5.9,"publicationDate":"2025-09-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145020257","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
AutomaticaPub Date : 2025-09-09DOI: 10.1016/j.automatica.2025.112568
Sara Sepasiahooyi, Shu-Xia Tang
{"title":"State estimation for lithium-ion batteries based on electrolyte–electrode PDE observers","authors":"Sara Sepasiahooyi, Shu-Xia Tang","doi":"10.1016/j.automatica.2025.112568","DOIUrl":"10.1016/j.automatica.2025.112568","url":null,"abstract":"<div><div>Accurate information about the states of an electrochemical battery model facilitates a deeper understanding of battery behavior and enables performance enhancement. This paper first proposes backstepping Partial Differential Equation (PDE) observers for lithium concentration in the electrolyte phase within the negative electrode, positive electrode, and separator. Reverse sensitivity analysis is conducted to identify the most suitable measurable parameter for obtaining the electrolyte lithium concentration at the boundaries, which is used in the design of the electrolyte-phase observer. Subsequently, enhanced observers for the solid-phase lithium concentration in the negative and positive electrodes are developed. The proposed solid-phase observer enables more accurate State-of-Charge (SoC) estimation by leveraging the closed-loop electrolyte-phase observer. Simulations of the reverse sensitivity analysis and state observers are performed on a commercial cylindrical lithium iron phosphate (<span><math><msub><mrow><mtext>LiFePO</mtext></mrow><mrow><mn>4</mn></mrow></msub></math></span>) cell to validate the effectiveness of the proposed approach.</div></div>","PeriodicalId":55413,"journal":{"name":"Automatica","volume":"183 ","pages":"Article 112568"},"PeriodicalIF":5.9,"publicationDate":"2025-09-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145027485","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}