Pub Date : 2026-03-01Epub Date: 2025-12-29DOI: 10.1016/j.automatica.2025.112801
Yu Xiao , Yuan Yuan , Biao Huang , Xiaodong Xu
The constrained output regulation problem has been addressed by the output feedback model predictive control (MPC) algorithm for deterministic system without random disturbances in recent years. This paper further considers the case with the presence of unknown-but-bounded random disturbances in the linear systems performing iterative regulation tasks, which have not been considered. When pursuing infinite-horizon optimization, unknown random disturbances give rise to an infinite horizon policy optimization problem in the MPC controller, and the problem cannot be directly solved. Moreover, the recursive feasibility in dealing with iterative tasks for the deterministic system cannot be guaranteed for uncertain systems, which renders the solution of this paper nontrivial. To this end, we develop a novel robust learning-based MPC algorithm such that the problem of linear iterative output regulation in the presence of unknown-but-bounded random disturbances along with state and input constraints is addressed.
{"title":"Constrained output regulation for linear systems performing iterative tasks via robust learning MPC","authors":"Yu Xiao , Yuan Yuan , Biao Huang , Xiaodong Xu","doi":"10.1016/j.automatica.2025.112801","DOIUrl":"10.1016/j.automatica.2025.112801","url":null,"abstract":"<div><div>The constrained output regulation problem has been addressed by the output feedback model predictive control (MPC) algorithm for deterministic system without random disturbances in recent years. This paper further considers the case with the presence of unknown-but-bounded random disturbances in the linear systems performing iterative regulation tasks, which have not been considered. When pursuing infinite-horizon optimization, unknown random disturbances give rise to an infinite horizon policy optimization problem in the MPC controller, and the problem cannot be directly solved. Moreover, the recursive feasibility in dealing with iterative tasks for the deterministic system cannot be guaranteed for uncertain systems, which renders the solution of this paper nontrivial. To this end, we develop a novel robust learning-based MPC algorithm such that the problem of linear iterative output regulation in the presence of unknown-but-bounded random disturbances along with state and input constraints is addressed.</div></div>","PeriodicalId":55413,"journal":{"name":"Automatica","volume":"185 ","pages":"Article 112801"},"PeriodicalIF":5.9,"publicationDate":"2026-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145884872","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 : 2026-03-01Epub Date: 2025-12-22DOI: 10.1016/j.automatica.2025.112749
Zhenhua Deng , Xiang-Peng Xie
As cyber–physical systems march toward intelligence, physical systems have the ability to execute distributed game tasks autonomously. Hence this paper focuses on multi-coalition games (MCGs) of autonomous high-order nonlinear players (HNPs). The intra-coalition communication networks are not connected in our problem, distinct from almost all existing MCGs. Moreover, here there are local nonlinear convex inequalities, intra-coalition and inter-coalition coupling nonlinear convex inequalities, different from most of works about MCGs of physical systems. Mainly attributed to the high-order nonlinear dynamics, the unconnected intra-coalition communications and/or the nonlinear convex constraints, existing methods cannot solve our problem. Also, these characteristics put a crime in the strategy design and analysis of our problem. For the purpose of steering the heterogeneous HNPs to autonomously seek the variational generalized Nash equilibrium (vGNE) of MCGs, a distributed strategy is proposed by utilizing primal–dual methods and state feedback. Supported by Lasalle invariance principle, our strategy is analyzed rigorously. Under our strategy, all HNPs globally converge to the exact vGNE. Finally, the merits of our strategy are verified by two examples.
{"title":"Distributed strategy for autonomous nonlinear multi-coalition games of high-order players over unconnected intra-coalition communications","authors":"Zhenhua Deng , Xiang-Peng Xie","doi":"10.1016/j.automatica.2025.112749","DOIUrl":"10.1016/j.automatica.2025.112749","url":null,"abstract":"<div><div>As cyber–physical systems march toward intelligence, physical systems have the ability to execute distributed game tasks autonomously. Hence this paper focuses on multi-coalition games (MCGs) of autonomous high-order nonlinear players (HNPs). The intra-coalition communication networks are not connected in our problem, distinct from almost all existing MCGs. Moreover, here there are local nonlinear convex inequalities, intra-coalition and inter-coalition coupling nonlinear convex inequalities, different from most of works about MCGs of physical systems. Mainly attributed to the high-order nonlinear dynamics, the unconnected intra-coalition communications and/or the nonlinear convex constraints, existing methods cannot solve our problem. Also, these characteristics put a crime in the strategy design and analysis of our problem. For the purpose of steering the heterogeneous HNPs to autonomously seek the variational generalized Nash equilibrium (vGNE) of MCGs, a distributed strategy is proposed by utilizing primal–dual methods and state feedback. Supported by Lasalle invariance principle, our strategy is analyzed rigorously. Under our strategy, all HNPs globally converge to the exact vGNE. Finally, the merits of our strategy are verified by two examples.</div></div>","PeriodicalId":55413,"journal":{"name":"Automatica","volume":"185 ","pages":"Article 112749"},"PeriodicalIF":5.9,"publicationDate":"2026-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145841797","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 : 2026-03-01Epub Date: 2025-12-22DOI: 10.1016/j.automatica.2025.112784
Laura Menini, Corrado Possieri, Antonio Tornambe
In this communique, an algorithm is proposed to solve symbolically the model matching problem for single input single output systems. A solution to such a problem has been proposed in Doyle et al. (1990) using the Nevanlinna–Pick theory. However, when implementing such a procedure numerically, some issues may arise due to imperfect cancellations among the numerator and the denominator of the obtained controller. The proposed algorithm overcomes such issues by using some algebraic geometry results to solve exactly the problem.
{"title":"An algebraic approach to solve the model matching problem for single input single output systems","authors":"Laura Menini, Corrado Possieri, Antonio Tornambe","doi":"10.1016/j.automatica.2025.112784","DOIUrl":"10.1016/j.automatica.2025.112784","url":null,"abstract":"<div><div>In this communique, an algorithm is proposed to solve symbolically the model matching problem for single input single output systems. A solution to such a problem has been proposed in Doyle et al. (1990) using the Nevanlinna–Pick theory. However, when implementing such a procedure numerically, some issues may arise due to imperfect cancellations among the numerator and the denominator of the obtained controller. The proposed algorithm overcomes such issues by using some algebraic geometry results to solve exactly the problem.</div></div>","PeriodicalId":55413,"journal":{"name":"Automatica","volume":"185 ","pages":"Article 112784"},"PeriodicalIF":5.9,"publicationDate":"2026-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145841801","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 : 2026-03-01Epub 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":"2026-03-01","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 : 2026-03-01Epub Date: 2025-12-22DOI: 10.1016/j.automatica.2025.112765
Liuliu Zhang, Xianglin Liu, Changchun Hua
This paper focuses on the problem of the prescribed-time output feedback control for a class of uncertain nonlinear systems subjected to unknown non-differentiable measurement sensitivity along with the presence of an arbitrary large sensitivity error. To deal with the obstacle arising from such a severe sensitivity condition for prescribed-time control, a pair of novel non-homogeneous order prescribed-time functions and asymmetric state transformations are introduced. And the dual dynamic gain is constructed to compensate for the uncertainty and the polynomial growth rate of the system online. Then, a novel multi-gain-based prescribed-time output feedback control scheme is developed based on the proposed multi-gain, which ensures the boundedness of all closed-loop system signals and drives the states to reach the equilibrium point at any prescribed time. Finally, a simulation example based on the real system demonstrates the effectiveness of the algorithm.
{"title":"Prescribed-time output feedback control for nonlinear systems with unknown measurement sensitivity","authors":"Liuliu Zhang, Xianglin Liu, Changchun Hua","doi":"10.1016/j.automatica.2025.112765","DOIUrl":"10.1016/j.automatica.2025.112765","url":null,"abstract":"<div><div>This paper focuses on the problem of the prescribed-time output feedback control for a class of uncertain nonlinear systems subjected to unknown non-differentiable measurement sensitivity along with the presence of an arbitrary large sensitivity error. To deal with the obstacle arising from such a severe sensitivity condition for prescribed-time control, a pair of novel non-homogeneous order prescribed-time functions and asymmetric state transformations are introduced. And the dual dynamic gain is constructed to compensate for the uncertainty and the polynomial growth rate of the system online. Then, a novel multi-gain-based prescribed-time output feedback control scheme is developed based on the proposed multi-gain, which ensures the boundedness of all closed-loop system signals and drives the states to reach the equilibrium point at any prescribed time. Finally, a simulation example based on the real system demonstrates the effectiveness of the algorithm.</div></div>","PeriodicalId":55413,"journal":{"name":"Automatica","volume":"185 ","pages":"Article 112765"},"PeriodicalIF":5.9,"publicationDate":"2026-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145841726","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 : 2026-03-01Epub Date: 2025-12-19DOI: 10.1016/j.automatica.2025.112795
Alexander Yu. Pogromsky , Alexey S. Matveev
This paper addresses the problem of robust remote state estimation for uncertain nonlinear discrete-time systems when sensor data are transmitted through a digital communication channel of finite bit-rate capacity. The goal is to determine the minimal channel rate required to guarantee a prescribed estimation accuracy in the presence of bounded model uncertainty. We derive an explicit, tractable lower bound on the channel bit rate that ensures this accuracy for any admissible uncertainty level. The bound highlights the fundamental role of the accuracy-to-uncertainty ratio in remote estimation. The analysis relies on a quadratic dissipation inequality describing system uncertainty within the framework of incremental input-to-state stability, leading to a constructive Lyapunov-based characterization. The proposed conditions admit a closed-form analytical expression for a class of systems, including the uncertain Lozi map, which serves as an illustrative example.
{"title":"Remote robust state estimation for nonlinear systems","authors":"Alexander Yu. Pogromsky , Alexey S. Matveev","doi":"10.1016/j.automatica.2025.112795","DOIUrl":"10.1016/j.automatica.2025.112795","url":null,"abstract":"<div><div>This paper addresses the problem of robust remote state estimation for uncertain nonlinear discrete-time systems when sensor data are transmitted through a digital communication channel of finite bit-rate capacity. The goal is to determine the minimal channel rate required to guarantee a prescribed estimation accuracy in the presence of bounded model uncertainty. We derive an explicit, tractable lower bound on the channel bit rate that ensures this accuracy for any admissible uncertainty level. The bound highlights the fundamental role of the accuracy-to-uncertainty ratio in remote estimation. The analysis relies on a quadratic dissipation inequality describing system uncertainty within the framework of incremental input-to-state stability, leading to a constructive Lyapunov-based characterization. The proposed conditions admit a closed-form analytical expression for a class of systems, including the uncertain Lozi map, which serves as an illustrative example.</div></div>","PeriodicalId":55413,"journal":{"name":"Automatica","volume":"185 ","pages":"Article 112795"},"PeriodicalIF":5.9,"publicationDate":"2026-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145784445","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 : 2026-03-01Epub Date: 2025-12-18DOI: 10.1016/j.automatica.2025.112774
Changxin Liu , Xiao Tan , Xuyang Wu , Dimos V. Dimarogonas , Karl H. Johansson
Constraint satisfaction is a critical component in a wide range of engineering applications, including safe multi-agent control and economic dispatch in power systems. This study explores violation-free distributed optimization techniques for problems characterized by separable objective functions and coupling constraints. First, we incorporate auxiliary decision variables together with a network-dependent linear mapping to each coupling constraint. For the reformulated problem, we show that the projection of its feasible set onto the space of primal variables is identical to that of the original problem, which is the key to achieving all-time constraint satisfaction. Upon treating the reformulated problem as a min-min optimization problem with respect to auxiliary and primal variables, we demonstrate that the gradients in the outer minimization problem have a locally computable closed-form. Then, two violation-free distributed optimization algorithms are developed and their convergence under reasonable assumptions is analyzed. Finally, the proposed algorithm is applied to implement a control barrier function based controller in a distributed manner, and the results verify its effectiveness.
{"title":"Achieving violation-free distributed optimization under coupling constraints","authors":"Changxin Liu , Xiao Tan , Xuyang Wu , Dimos V. Dimarogonas , Karl H. Johansson","doi":"10.1016/j.automatica.2025.112774","DOIUrl":"10.1016/j.automatica.2025.112774","url":null,"abstract":"<div><div>Constraint satisfaction is a critical component in a wide range of engineering applications, including safe multi-agent control and economic dispatch in power systems. This study explores violation-free distributed optimization techniques for problems characterized by separable objective functions and coupling constraints. First, we incorporate auxiliary decision variables together with a network-dependent linear mapping to each coupling constraint. For the reformulated problem, we show that the projection of its feasible set onto the space of primal variables is identical to that of the original problem, which is the key to achieving all-time constraint satisfaction. Upon treating the reformulated problem as a min-min optimization problem with respect to auxiliary and primal variables, we demonstrate that the gradients in the outer minimization problem have a locally computable closed-form. Then, two violation-free distributed optimization algorithms are developed and their convergence under reasonable assumptions is analyzed. Finally, the proposed algorithm is applied to implement a control barrier function based controller in a distributed manner, and the results verify its effectiveness.</div></div>","PeriodicalId":55413,"journal":{"name":"Automatica","volume":"185 ","pages":"Article 112774"},"PeriodicalIF":5.9,"publicationDate":"2026-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145799191","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 : 2026-03-01Epub Date: 2026-01-02DOI: 10.1016/j.automatica.2025.112817
Han Wang, Zheng Chen
This paper is concerned with real-time generation of optimal flight trajectories for Minimum-Effort Control Problems (MECPs), which is fundamentally important for autonomous flight of aerospace vehicles. Although existing optimal control methods, such as indirect methods and direct methods, can be amended to solve MECPs, it is very challenging to obtain, in real time, the solution trajectories since those methods suffer the issue of convergence. As the artificial neural network can generate its output within a constant time, it has been alternative for real-time generation of optimal trajectories in the literature. The usual way is to train neural networks by solutions from indirect or direct methods, which, however, cannot ensure sufficient conditions for local optimality to be met. As a result, the trained neural networks cannot be guaranteed to generate at least locally optimal trajectories. To address this issue, a parametrization approach is developed in the paper so that not only necessary but also sufficient conditions for local optimality are embedded into a parameterized set of differential equations. This allows generating the dataset of at least locally optimal trajectories through solving some initial value problems. Once a neural network is trained by the dataset constructed by the parametrization approach, it not only can generate optimal trajectories within milliseconds but also ensure the generated trajectories to be at least locally optimal, as finally demonstrated by two conventional MECPs in aerospace engineering.
{"title":"Parametrization approach for real-time generation of minimum-effort trajectories via neural network","authors":"Han Wang, Zheng Chen","doi":"10.1016/j.automatica.2025.112817","DOIUrl":"10.1016/j.automatica.2025.112817","url":null,"abstract":"<div><div>This paper is concerned with real-time generation of optimal flight trajectories for Minimum-Effort Control Problems (MECPs), which is fundamentally important for autonomous flight of aerospace vehicles. Although existing optimal control methods, such as indirect methods and direct methods, can be amended to solve MECPs, it is very challenging to obtain, in real time, the solution trajectories since those methods suffer the issue of convergence. As the artificial neural network can generate its output within a constant time, it has been alternative for real-time generation of optimal trajectories in the literature. The usual way is to train neural networks by solutions from indirect or direct methods, which, however, cannot ensure sufficient conditions for local optimality to be met. As a result, the trained neural networks cannot be guaranteed to generate at least locally optimal trajectories. To address this issue, a parametrization approach is developed in the paper so that not only necessary but also sufficient conditions for local optimality are embedded into a parameterized set of differential equations. This allows generating the dataset of at least locally optimal trajectories through solving some initial value problems. Once a neural network is trained by the dataset constructed by the parametrization approach, it not only can generate optimal trajectories within milliseconds but also ensure the generated trajectories to be at least locally optimal, as finally demonstrated by two conventional MECPs in aerospace engineering.</div></div>","PeriodicalId":55413,"journal":{"name":"Automatica","volume":"185 ","pages":"Article 112817"},"PeriodicalIF":5.9,"publicationDate":"2026-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145884871","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 : 2026-03-01Epub Date: 2026-01-07DOI: 10.1016/j.automatica.2026.112819
Yao Li , Chengpu Yu , Hao Fang , Jie Chen
This paper addresses the inverse optimal control for the linear quadratic tracking problem with a fixed but unknown target state, which aims to estimate the possible triplets comprising the target state, the state weight matrix, and the input weight matrix from observed optimal control input and the corresponding state trajectories. Sufficient conditions have been provided for the unique determination of both the linear quadratic cost function as well as the target state. A computationally efficient and numerically reliable parameter identification algorithm is proposed by equating optimal control strategies with a system of linear equations, and the associated relative error upper bound is derived in terms of data volume and signal-to-noise ratio (SNR). Moreover, the proposed inverse optimal control algorithm is applied for the joint cluster coordination and intent identification of a multi-agent system. By incorporating the structural constraint of the Laplace matrix, the relative error upper bound can be reduced accordingly. Finally, the algorithm’s efficiency and accuracy are validated by a vehicle-on-a-lever example and a multi-agent formation control example.
{"title":"Inverse optimal control for linear quadratic tracking with unknown target states","authors":"Yao Li , Chengpu Yu , Hao Fang , Jie Chen","doi":"10.1016/j.automatica.2026.112819","DOIUrl":"10.1016/j.automatica.2026.112819","url":null,"abstract":"<div><div>This paper addresses the inverse optimal control for the linear quadratic tracking problem with a fixed but unknown target state, which aims to estimate the possible triplets comprising the target state, the state weight matrix, and the input weight matrix from observed optimal control input and the corresponding state trajectories. Sufficient conditions have been provided for the unique determination of both the linear quadratic cost function as well as the target state. A computationally efficient and numerically reliable parameter identification algorithm is proposed by equating optimal control strategies with a system of linear equations, and the associated relative error upper bound is derived in terms of data volume and signal-to-noise ratio (SNR). Moreover, the proposed inverse optimal control algorithm is applied for the joint cluster coordination and intent identification of a multi-agent system. By incorporating the structural constraint of the Laplace matrix, the relative error upper bound can be reduced accordingly. Finally, the algorithm’s efficiency and accuracy are validated by a vehicle-on-a-lever example and a multi-agent formation control example.</div></div>","PeriodicalId":55413,"journal":{"name":"Automatica","volume":"185 ","pages":"Article 112819"},"PeriodicalIF":5.9,"publicationDate":"2026-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145939142","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 : 2026-03-01Epub 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":"2026-03-01","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}
扫码关注我们
求助内容：
应助结果提醒方式：
京公网安备 11010802042870号