Pub Date : 2025-12-22DOI: 10.1016/j.automatica.2025.112789
Giulio Fattore, Maria Elena Valcher
Given an autonomous exosystem generating a reference output, we consider the problem of designing a distributed data-driven control law for a network of discrete-time heterogeneous LTI agents, to synchronize the agents’ outputs to the reference one. The agents split into two groups: leaders, with direct access to the exosystem output, and followers, which only receive information from their neighbors. Each agent implements a state feedback strategy relying on its own state and on an estimate of the exogenous system state, provided by an internal state observer. Necessary and sufficient conditions for the existence of a solution are first derived in the model-based setup and then in a data-driven context. An algorithm is provided to design from data the matrices of the distributed control law. A numerical example illustrates the effectiveness of the proposed approach.
{"title":"Distributed output synchronization of discrete-time multi-agent systems: A data-driven approach","authors":"Giulio Fattore, Maria Elena Valcher","doi":"10.1016/j.automatica.2025.112789","DOIUrl":"10.1016/j.automatica.2025.112789","url":null,"abstract":"<div><div>Given an autonomous exosystem generating a reference output, we consider the problem of designing a distributed data-driven control law for a network of discrete-time heterogeneous LTI agents, to synchronize the agents’ outputs to the reference one. The agents split into two groups: leaders, with direct access to the exosystem output, and followers, which only receive information from their neighbors. Each agent implements a state feedback strategy relying on its own state and on an estimate of the exogenous system state, provided by an internal state observer. Necessary and sufficient conditions for the existence of a solution are first derived in the model-based setup and then in a data-driven context. An algorithm is provided to design from data the matrices of the distributed control law. A numerical example illustrates the effectiveness of the proposed approach.</div></div>","PeriodicalId":55413,"journal":{"name":"Automatica","volume":"185 ","pages":"Article 112789"},"PeriodicalIF":5.9,"publicationDate":"2025-12-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145841802","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}
Pub Date : 2025-12-22DOI: 10.1016/j.automatica.2025.112762
Yangyang Qian , Zongli Lin , Yacov A. Shamash
We investigate the primary/secondary control problem for battery units with adaptive droop control in DC microgrids. A majority of existing control methods for state-of-charge (SoC) balancing among battery units require that the terminal voltage of each battery unit remains constant. To remove such a requirement, at the primary control level, we propose an improved adaptive droop control method by introducing an auxiliary battery state in terms of the battery parameters, the terminal voltage, and a power function of the SoC. The designed droop coefficient is inversely proportional to the auxiliary battery state. It is shown that the proposed adaptive droop control achieves proportional power sharing and SoC balancing, albeit at a cost of compromised voltage regulation. A salient feature of the proposed adaptive droop control method is that the battery’s terminal voltage is allowed to be time-varying. Moreover, to compensate for the voltage deviation caused by the improved adaptive droop control, we propose a consensus-based distributed control scheme at the secondary control level. It is shown that the resulting hierarchical control framework, consisting of the primary and secondary control levels, guarantees that the control objectives of voltage regulation, proportional power sharing, and SoC balancing are all achieved. Simulation studies based on an accurate electrical battery model validate the effectiveness of our multi-objective hierarchical control framework.
{"title":"A multi-objective hierarchical control framework for battery units in DC microgrids using improved adaptive droop control","authors":"Yangyang Qian , Zongli Lin , Yacov A. Shamash","doi":"10.1016/j.automatica.2025.112762","DOIUrl":"10.1016/j.automatica.2025.112762","url":null,"abstract":"<div><div>We investigate the primary/secondary control problem for battery units with adaptive droop control in DC microgrids. A majority of existing control methods for state-of-charge (SoC) balancing among battery units require that the terminal voltage of each battery unit remains constant. To remove such a requirement, at the primary control level, we propose an improved adaptive droop control method by introducing an auxiliary battery state in terms of the battery parameters, the terminal voltage, and a power function of the SoC. The designed droop coefficient is inversely proportional to the auxiliary battery state. It is shown that the proposed adaptive droop control achieves proportional power sharing and SoC balancing, albeit at a cost of compromised voltage regulation. A salient feature of the proposed adaptive droop control method is that the battery’s terminal voltage is allowed to be time-varying. Moreover, to compensate for the voltage deviation caused by the improved adaptive droop control, we propose a consensus-based distributed control scheme at the secondary control level. It is shown that the resulting hierarchical control framework, consisting of the primary and secondary control levels, guarantees that the control objectives of voltage regulation, proportional power sharing, and SoC balancing are all achieved. Simulation studies based on an accurate electrical battery model validate the effectiveness of our multi-objective hierarchical control framework.</div></div>","PeriodicalId":55413,"journal":{"name":"Automatica","volume":"185 ","pages":"Article 112762"},"PeriodicalIF":5.9,"publicationDate":"2025-12-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145841798","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}
Pub Date : 2025-12-22DOI: 10.1016/j.automatica.2025.112722
Masih Haseli , Jorge Cortés
This paper introduces the Koopman Control Family (KCF), a mathematical framework for modeling general (not necessarily control-affine) discrete-time nonlinear control systems with the aim of providing a solid theoretical foundation for the use of Koopman-based methods in systems with inputs. We demonstrate that the concept of KCF captures the behavior of nonlinear control systems on a (potentially infinite-dimensional) function space. By employing a generalized notion of subspace invariance under the KCF, we establish a universal form for finite-dimensional models, which encompasses the commonly used lifted linear, bilinear, and linear switched models as specific instances. In cases where the subspace is not invariant under the KCF, we propose a method for approximating models in general form and characterize the model’s accuracy using the concept of invariance proximity. We end by discussing how the proposed framework naturally lends itself to data-driven modeling of control systems.
{"title":"Modeling nonlinear control systems via Koopman Control Family: Universal forms and subspace invariance proximity","authors":"Masih Haseli , Jorge Cortés","doi":"10.1016/j.automatica.2025.112722","DOIUrl":"10.1016/j.automatica.2025.112722","url":null,"abstract":"<div><div>This paper introduces the Koopman Control Family (KCF), a mathematical framework for modeling general (not necessarily control-affine) discrete-time nonlinear control systems with the aim of providing a solid theoretical foundation for the use of Koopman-based methods in systems with inputs. We demonstrate that the concept of KCF captures the behavior of nonlinear control systems on a (potentially infinite-dimensional) function space. By employing a generalized notion of subspace invariance under the KCF, we establish a universal form for finite-dimensional models, which encompasses the commonly used lifted linear, bilinear, and linear switched models as specific instances. In cases where the subspace is not invariant under the KCF, we propose a method for approximating models in general form and characterize the model’s accuracy using the concept of invariance proximity. We end by discussing how the proposed framework naturally lends itself to data-driven modeling of control systems.</div></div>","PeriodicalId":55413,"journal":{"name":"Automatica","volume":"185 ","pages":"Article 112722"},"PeriodicalIF":5.9,"publicationDate":"2025-12-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145841742","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}
Pub Date : 2025-12-22DOI: 10.1016/j.automatica.2025.112800
Chao Zhou, Zehui Mao, Bin Jiang
In this paper, the fault-tolerant consensus tracking control problem is investigated for a class of discrete-time strict-feedback nonlinear multi-agent systems with sensor faults. The sensor faults are described by the first-order difference equations. By leveraging the augmented state observer structure, an auxiliary nonlinear system is first constructed in a non-strict feedback form, based on which a backstepping-based control framework is established. The consensus tracking errors are directly incorporated into the virtual control to preserve the distributed structure of the controller. Furthermore, in order to alleviate the communication burden and enhance the transmission security, an encoding–decoding scheme is adopted during the information exchange among agents. Accordingly, an encoding–decoding-based distributed controller is proposed, guaranteeing that the output tracking error is uniformly ultimately bounded and the transmitted data is conditionally bounded. Finally, a numerical example is provided to validate the effectiveness of the proposed backstepping-based control framework.
{"title":"Backstepping-based fault-tolerant control for strict-feedback nonlinear multi-agent systems: An encoding–decoding scheme","authors":"Chao Zhou, Zehui Mao, Bin Jiang","doi":"10.1016/j.automatica.2025.112800","DOIUrl":"10.1016/j.automatica.2025.112800","url":null,"abstract":"<div><div>In this paper, the fault-tolerant consensus tracking control problem is investigated for a class of discrete-time strict-feedback nonlinear multi-agent systems with sensor faults. The sensor faults are described by the first-order difference equations. By leveraging the augmented state observer structure, an auxiliary nonlinear system is first constructed in a non-strict feedback form, based on which a backstepping-based control framework is established. The consensus tracking errors are directly incorporated into the virtual control to preserve the distributed structure of the controller. Furthermore, in order to alleviate the communication burden and enhance the transmission security, an encoding–decoding scheme is adopted during the information exchange among agents. Accordingly, an encoding–decoding-based distributed controller is proposed, guaranteeing that the output tracking error is uniformly ultimately bounded and the transmitted data is conditionally bounded. Finally, a numerical example is provided to validate the effectiveness of the proposed backstepping-based control framework.</div></div>","PeriodicalId":55413,"journal":{"name":"Automatica","volume":"185 ","pages":"Article 112800"},"PeriodicalIF":5.9,"publicationDate":"2025-12-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145841796","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}
Pub Date : 2025-12-22DOI: 10.1016/j.automatica.2025.112776
Joel A. Rosenfeld , Benjamin P. Russo , Rushikesh Kamalapurkar
Conventionally, data driven identification and control problems for higher order dynamical systems are solved by augmenting the system state by the derivatives of the output to formulate first order dynamical systems in higher dimensions. However, solution of the augmented problem typically requires knowledge of the full augmented state, which requires numerical differentiation of the original output, frequently resulting in noisy signals. This manuscript develops the theory necessary for a direct analysis of higher order dynamical systems using higher order Liouville operators. Fundamental to this theoretical development is the introduction of signal valued RKHSs and new operators posed over these spaces. Ultimately, it is observed that despite the added abstractions, the necessary computations are remarkably similar to that of first order DMD methods using occupation kernels.
{"title":"Dynamic mode decomposition of higher order systems","authors":"Joel A. Rosenfeld , Benjamin P. Russo , Rushikesh Kamalapurkar","doi":"10.1016/j.automatica.2025.112776","DOIUrl":"10.1016/j.automatica.2025.112776","url":null,"abstract":"<div><div>Conventionally, data driven identification and control problems for higher order dynamical systems are solved by augmenting the system state by the derivatives of the output to formulate first order dynamical systems in higher dimensions. However, solution of the augmented problem typically requires knowledge of the full augmented state, which requires numerical differentiation of the original output, frequently resulting in noisy signals. This manuscript develops the theory necessary for a direct analysis of higher order dynamical systems using higher order Liouville operators. Fundamental to this theoretical development is the introduction of signal valued RKHSs and new operators posed over these spaces. Ultimately, it is observed that despite the added abstractions, the necessary computations are remarkably similar to that of first order DMD methods using occupation kernels.</div></div>","PeriodicalId":55413,"journal":{"name":"Automatica","volume":"185 ","pages":"Article 112776"},"PeriodicalIF":5.9,"publicationDate":"2025-12-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145841803","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}
Pub Date : 2025-12-22DOI: 10.1016/j.automatica.2025.112775
Lijun Long , Chunxiao Huang , Zhendong Sun
This paper investigates the problem of safety-critical optimal control for switched systems via weak topology. A novel safety-critical optimal control framework is established for finding an optimal switching signal and an optimal controller that minimize a switched cost function and ensure safety along the whole optimization time interval. A necessary and sufficient condition is presented to reveal the essence of the safety for switched systems. Also, a single barrier function (SBF) method is proposed to ensure safety of switched systems, where each subsystem does not necessarily possess the safety in the whole safe set. In order to analyze the safety of switched systems and asymptotic stability of the safe set, a new version of the comparison function result is presented, which handles a class of extended comparison functions. Moreover, an optimization algorithm based on weak topology is developed to solve the safety-critical optimal control problem of switched systems, where additional dynamics are introduced to overcome the limitations caused by the unavailability of the traditional weak topology. Finally, two examples including a continuously stirred tank reactor system are given to verify the effectiveness of the methods proposed.
{"title":"Safety-critical optimal control of switched systems","authors":"Lijun Long , Chunxiao Huang , Zhendong Sun","doi":"10.1016/j.automatica.2025.112775","DOIUrl":"10.1016/j.automatica.2025.112775","url":null,"abstract":"<div><div>This paper investigates the problem of safety-critical optimal control for switched systems via weak topology. A novel safety-critical optimal control framework is established for finding an optimal switching signal and an optimal controller that minimize a switched cost function and ensure safety along the whole optimization time interval. A necessary and sufficient condition is presented to reveal the essence of the safety for switched systems. Also, a single barrier function (SBF) method is proposed to ensure safety of switched systems, where each subsystem does not necessarily possess the safety in the whole safe set. In order to analyze the safety of switched systems and asymptotic stability of the safe set, a new version of the comparison function result is presented, which handles a class of extended comparison functions. Moreover, an optimization algorithm based on weak topology is developed to solve the safety-critical optimal control problem of switched systems, where additional dynamics are introduced to overcome the limitations caused by the unavailability of the traditional weak topology. Finally, two examples including a continuously stirred tank reactor system are given to verify the effectiveness of the methods proposed.</div></div>","PeriodicalId":55413,"journal":{"name":"Automatica","volume":"185 ","pages":"Article 112775"},"PeriodicalIF":5.9,"publicationDate":"2025-12-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145813909","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}
Pub Date : 2025-12-20DOI: 10.1016/j.automatica.2025.112792
Sibren Lagauw, Lukas Vanpoucke, Bart De Moor
We consider the least squares (LS) realization of an autonomous single-output linear time-invariant dynamical model for a given sequence of output data. As opposed to standard system identification practices, which often rely on (heuristic) iterative optimization techniques, we propose an exact solution to this non-convex optimization problem: the globally optimal solution(s) are identified by means of a deterministic eigenvalue procedure. In particular, we illustrate that for all (local) minimizers, the corresponding misfit can be characterized as the result of filtering an unknown signal twice through a finite-impulse response filter. Exploiting this insight, we propose a novel (rectangular) multiparameter eigenvalue problem (MEP), the eigentuples of which allow to retrieve all local and global minimizers of the identification problem. The proposed MEP is of great theoretical interest and offers new insights into the structure of the LS realization problem, which we explore in detail. We provide numerical examples to illustrate our findings.
{"title":"Exact solution to the least squares realization problem as a multiparameter eigenvalue problem","authors":"Sibren Lagauw, Lukas Vanpoucke, Bart De Moor","doi":"10.1016/j.automatica.2025.112792","DOIUrl":"10.1016/j.automatica.2025.112792","url":null,"abstract":"<div><div>We consider the least squares (LS) realization of an autonomous single-output linear time-invariant dynamical model for a given sequence of output data. As opposed to standard system identification practices, which often rely on (heuristic) iterative optimization techniques, we propose an exact solution to this non-convex optimization problem: the <em>globally optimal</em> solution(s) are identified by means of a <em>deterministic</em> eigenvalue procedure. In particular, we illustrate that for all (local) minimizers, the corresponding misfit can be characterized as the result of filtering an unknown signal twice through a finite-impulse response filter. Exploiting this insight, we propose a novel (rectangular) multiparameter eigenvalue problem (MEP), the eigentuples of which allow to retrieve all local and global minimizers of the identification problem. The proposed MEP is of great theoretical interest and offers new insights into the structure of the LS realization problem, which we explore in detail. We provide numerical examples to illustrate our findings.</div></div>","PeriodicalId":55413,"journal":{"name":"Automatica","volume":"185 ","pages":"Article 112792"},"PeriodicalIF":5.9,"publicationDate":"2025-12-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145784437","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}
Pub Date : 2025-12-20DOI: 10.1016/j.automatica.2025.112781
Zhihe Zhuang , Rodrigo A. González , Hongfeng Tao , Wojciech Paszke , Tom Oomen
Iterative learning control (ILC) is an intelligent control methodology for tackling iteration-invariant exogenous inputs. It is of great significance to develop its extrapolation for more general repetitive tasks with mutual similarity, e.g., tasks with different time scales. In practice, discrete-time ILC with sampling behavior for time-scale-varying tasks suffers from the failure of perfect corresponding learning and environment-dependent iteration-varying disturbances. This paper develops a novel direct data-based ILC algorithm using off-policy Q-learning for tasks with varying time scales, enabling the robust learning of an optimal ILC policy from experimental input/output (I/O) data. From a two-player zero-sum game perspective, the iteration-varying disturbance generated from the varying time scales of repetitive tasks is tackled quantitatively with a preset disturbance attenuation level. Further, to emphasize the importance of theoretical guarantees of reinforcement learning (RL)-based ILC designs, the data efficiency of the developed algorithm is enhanced based on Willems’ Fundamental Lemma, and a rigorous convergence analysis is given. The simulation model of an F-16 aircraft autopilot is employed to show the effectiveness of the developed approach.
{"title":"Data-enabled iterative learning control: A zero-sum game design for time-scale-varying tasks","authors":"Zhihe Zhuang , Rodrigo A. González , Hongfeng Tao , Wojciech Paszke , Tom Oomen","doi":"10.1016/j.automatica.2025.112781","DOIUrl":"10.1016/j.automatica.2025.112781","url":null,"abstract":"<div><div>Iterative learning control (ILC) is an intelligent control methodology for tackling iteration-invariant exogenous inputs. It is of great significance to develop its extrapolation for more general repetitive tasks with mutual similarity, e.g., tasks with different time scales. In practice, discrete-time ILC with sampling behavior for time-scale-varying tasks suffers from the failure of perfect corresponding learning and environment-dependent iteration-varying disturbances. This paper develops a novel direct data-based ILC algorithm using off-policy Q-learning for tasks with varying time scales, enabling the robust learning of an optimal ILC policy from experimental input/output (I/O) data. From a two-player zero-sum game perspective, the iteration-varying disturbance generated from the varying time scales of repetitive tasks is tackled quantitatively with a preset disturbance attenuation level. Further, to emphasize the importance of theoretical guarantees of reinforcement learning (RL)-based ILC designs, the data efficiency of the developed algorithm is enhanced based on Willems’ Fundamental Lemma, and a rigorous convergence analysis is given. The simulation model of an F-16 aircraft autopilot is employed to show the effectiveness of the developed approach.</div></div>","PeriodicalId":55413,"journal":{"name":"Automatica","volume":"185 ","pages":"Article 112781"},"PeriodicalIF":5.9,"publicationDate":"2025-12-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145784438","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}
Pub Date : 2025-12-20DOI: 10.1016/j.automatica.2025.112773
Giordano Pola, Elena De Santis, Maria Domenica Di Benedetto
In this paper we consider a pair of interconnected, nondeterministic and metric finite state systems and address a control problem where controllers are designed for enforcing local specifications expressed in terms of regular languages, up to a desired accuracy. The control architecture considered is decentralized, that is each controller can only communicate with the corresponding plant. Since plant systems are interconnected, the part of the specification that can be enforced on one system depends on the part that can be applied on the other one. We show how this dependency can be formalized in terms of equilibria, by extending game theory to the present framework. We introduce notions of equilibria, Nash equilibria and dominant equilibria. When controlled plants are at an equilibrium, they satisfy a part of their specification; when they are at a Nash equilibrium, deviation of each plant from its control strategy may correspond to a loss in terms of the part of specification enforced; when they are at a dominant equilibrium, there is no other equilibrium where plants can achieve larger parts of the corresponding specifications. A characterization of these notions is derived and checkable conditions are discussed. An example in the context of multi-agent systems with shared resources is also included.
{"title":"Decentralized control of finite state systems: A game theoretic approach","authors":"Giordano Pola, Elena De Santis, Maria Domenica Di Benedetto","doi":"10.1016/j.automatica.2025.112773","DOIUrl":"10.1016/j.automatica.2025.112773","url":null,"abstract":"<div><div>In this paper we consider a pair of interconnected, nondeterministic and metric finite state systems and address a control problem where controllers are designed for enforcing local specifications expressed in terms of regular languages, up to a desired accuracy. The control architecture considered is decentralized, that is each controller can only communicate with the corresponding plant. Since plant systems are interconnected, the part of the specification that can be enforced on one system depends on the part that can be applied on the other one. We show how this dependency can be formalized in terms of equilibria, by extending game theory to the present framework. We introduce notions of equilibria, Nash equilibria and dominant equilibria. When controlled plants are at an equilibrium, they satisfy a part of their specification; when they are at a Nash equilibrium, deviation of each plant from its control strategy may correspond to a loss in terms of the part of specification enforced; when they are at a dominant equilibrium, there is no other equilibrium where plants can achieve larger parts of the corresponding specifications. A characterization of these notions is derived and checkable conditions are discussed. An example in the context of multi-agent systems with shared resources is also included.</div></div>","PeriodicalId":55413,"journal":{"name":"Automatica","volume":"185 ","pages":"Article 112773"},"PeriodicalIF":5.9,"publicationDate":"2025-12-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145784432","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}
Pub Date : 2025-12-19DOI: 10.1016/j.automatica.2025.112787
Lapo Frascati , Alberto Bemporad
This paper proposes a novel combination of extended Kalman filtering (EKF) with the alternating direction method of multipliers (ADMM) for learning parametric nonlinear models online under non-smooth regularization terms, including and penalties and bound constraints on model parameters. For the case of linear time-varying models and non-smooth convex regularization terms, we provide a sublinear regret bound that ensures the proper behavior of the online learning strategy. The approach is computationally efficient for a wide range of regularization terms, which makes it appealing for its use in embedded control applications for online model adaptation. We show the performance of the proposed method in three simulation examples, highlighting its effectiveness compared to other batch and online algorithms.
{"title":"Online learning of nonlinear parametric models under non-smooth regularization using EKF and ADMM","authors":"Lapo Frascati , Alberto Bemporad","doi":"10.1016/j.automatica.2025.112787","DOIUrl":"10.1016/j.automatica.2025.112787","url":null,"abstract":"<div><div>This paper proposes a novel combination of extended Kalman filtering (EKF) with the alternating direction method of multipliers (ADMM) for learning parametric nonlinear models online under non-smooth regularization terms, including <span><math><msub><mrow><mi>ℓ</mi></mrow><mrow><mn>1</mn></mrow></msub></math></span> and <span><math><msub><mrow><mi>ℓ</mi></mrow><mrow><mn>0</mn></mrow></msub></math></span> penalties and bound constraints on model parameters. For the case of linear time-varying models and non-smooth convex regularization terms, we provide a sublinear regret bound that ensures the proper behavior of the online learning strategy. The approach is computationally efficient for a wide range of regularization terms, which makes it appealing for its use in embedded control applications for online model adaptation. We show the performance of the proposed method in three simulation examples, highlighting its effectiveness compared to other batch and online algorithms.</div></div>","PeriodicalId":55413,"journal":{"name":"Automatica","volume":"185 ","pages":"Article 112787"},"PeriodicalIF":5.9,"publicationDate":"2025-12-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145784442","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}
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