Pub Date : 2026-01-15DOI: 10.1016/j.automatica.2026.112838
Juan Javier Palacios Roman , Sigurdur Hafstein , Peter Giesl , Sebastiaan van den Eijnden , Stefania Andersen , W.P.M.H. Heemels
In this paper, we present a method for constructing continuous piecewise quadratic (CPQ) Lyapunov functions for continuous-time switched and conewise linear systems using linear programming (LP). Key in our approach is the formulation of effective sufficient conditions for the copositivity of matrices via diagonal dominance. This formulation consists of linear constraints and can be expressed as an LP. It is shown that the sufficient conditions are also necessary conditions for the existence of a Lyapunov function, given a sufficiently refined CPQ function. We provide an in-depth comparison between our new method and other computational methods in the literature, and provide extensive numerical experiments on various switched and conewise linear systems. In particular, we show that the proposed method is the most accurate of the LP-based methods for constructing Lyapunov functions and is a numerically competitive alternative to LMI-based methods.
{"title":"Constructing piecewise quadratic Lyapunov functions with linear programming for continuous-time switched and conewise linear systems","authors":"Juan Javier Palacios Roman , Sigurdur Hafstein , Peter Giesl , Sebastiaan van den Eijnden , Stefania Andersen , W.P.M.H. Heemels","doi":"10.1016/j.automatica.2026.112838","DOIUrl":"10.1016/j.automatica.2026.112838","url":null,"abstract":"<div><div>In this paper, we present a method for constructing continuous piecewise quadratic (CPQ) Lyapunov functions for continuous-time switched and conewise linear systems using linear programming (LP). Key in our approach is the formulation of effective sufficient conditions for the copositivity of matrices via diagonal dominance. This formulation consists of linear constraints and can be expressed as an LP. It is shown that the sufficient conditions are also necessary conditions for the existence of a Lyapunov function, given a sufficiently refined CPQ function. We provide an in-depth comparison between our new method and other computational methods in the literature, and provide extensive numerical experiments on various switched and conewise linear systems. In particular, we show that the proposed method is the most accurate of the LP-based methods for constructing Lyapunov functions and is a numerically competitive alternative to LMI-based methods.</div></div>","PeriodicalId":55413,"journal":{"name":"Automatica","volume":"186 ","pages":"Article 112838"},"PeriodicalIF":5.9,"publicationDate":"2026-01-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145963137","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 : 2026-01-14DOI: 10.1016/j.automatica.2026.112835
Yuxin Sun, Feng Xu
This paper proposes a new observer-based method suitable for both passive and active fault diagnosis in discrete linear time-invariant systems, developed from an optimization design perspective using state estimation sets. First, based on the output-consistent state sets explicitly expressed as the Minkowski sum of a constrained zonotope and a subspace, this paper establishes an equivalent interpretation of the fault diagnosis criterion using state estimation sets instead of traditional output estimation sets. This provides a novel state estimation set-based design perspective to enhance fault diagnosis. Second, this paper introduces a new quantitative metric named separation tendency that quantifies the geometric relationship between two constrained zonotopes. The observer gain for each mode is optimized to facilitate fault diagnosis by maximizing the separation tendency of the orthogonal projections of the two constructed state estimation sets of that mode. Third, a distinctive feature of our design method compared to existing approaches is that the design of observer gains does not depend on the current system input, enabling the design of inputs after that of observer gains without the counteracting effect on the inputs from the observer gains. At the end of this paper, numerical examples are used to illustrate the effectiveness of the proposed method.
{"title":"Observer-based passive/active fault diagnosis: A new optimization design perspective from state sets","authors":"Yuxin Sun, Feng Xu","doi":"10.1016/j.automatica.2026.112835","DOIUrl":"10.1016/j.automatica.2026.112835","url":null,"abstract":"<div><div>This paper proposes a new observer-based method suitable for both passive and active fault diagnosis in discrete linear time-invariant systems, developed from an optimization design perspective using state estimation sets. First, based on the output-consistent state sets explicitly expressed as the Minkowski sum of a constrained zonotope and a subspace, this paper establishes an equivalent interpretation of the fault diagnosis criterion using state estimation sets instead of traditional output estimation sets. This provides a novel state estimation set-based design perspective to enhance fault diagnosis. Second, this paper introduces a new quantitative metric named separation tendency that quantifies the geometric relationship between two constrained zonotopes. The observer gain for each mode is optimized to facilitate fault diagnosis by maximizing the separation tendency of the orthogonal projections of the two constructed state estimation sets of that mode. Third, a distinctive feature of our design method compared to existing approaches is that the design of observer gains does not depend on the current system input, enabling the design of inputs after that of observer gains without the counteracting effect on the inputs from the observer gains. At the end of this paper, numerical examples are used to illustrate the effectiveness of the proposed method.</div></div>","PeriodicalId":55413,"journal":{"name":"Automatica","volume":"186 ","pages":"Article 112835"},"PeriodicalIF":5.9,"publicationDate":"2026-01-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145963136","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 : 2026-01-14DOI: 10.1016/j.automatica.2026.112834
Ling Ma , Nicolas Vanspranghe , Daniele Astolfi , Vincent Andrieu , Mathieu Bajodek , Xuyang Lou
This paper addresses the feedback stabilization problem for a gantry crane system with input constraints. Such a system is described by a wave equation interconnected at the boundary conditions with a double integrator, which represents the top cart’s position and its speed. We propose a simple nested-saturation proportional derivative feedback which ensures that the control inputs remain within certain given limits. Global asymptotic stability of the origin of the closed-loop system is established. To this end, a new weak Lyapunov functional and a new methodology to study pre-compactness of solutions are introduced. Numerical simulations are presented to illustrate the effectiveness of the proposed control method.
{"title":"Nested saturation proportional–derivative control for conservative PDE–ODE interconnections: The gantry crane example","authors":"Ling Ma , Nicolas Vanspranghe , Daniele Astolfi , Vincent Andrieu , Mathieu Bajodek , Xuyang Lou","doi":"10.1016/j.automatica.2026.112834","DOIUrl":"10.1016/j.automatica.2026.112834","url":null,"abstract":"<div><div>This paper addresses the feedback stabilization problem for a gantry crane system with input constraints. Such a system is described by a wave equation interconnected at the boundary conditions with a double integrator, which represents the top cart’s position and its speed. We propose a simple nested-saturation proportional derivative feedback which ensures that the control inputs remain within certain given limits. Global asymptotic stability of the origin of the closed-loop system is established. To this end, a new weak Lyapunov functional and a new methodology to study pre-compactness of solutions are introduced. Numerical simulations are presented to illustrate the effectiveness of the proposed control method.</div></div>","PeriodicalId":55413,"journal":{"name":"Automatica","volume":"185 ","pages":"Article 112834"},"PeriodicalIF":5.9,"publicationDate":"2026-01-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145962443","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}
In this paper, we propose a novel distributed state-feedback design for robust synchronization of networks of identical discrete-time nonlinear agents under generic time-invariant communication graphs. We focus on the class of almost differentiable (possibly time-varying) dynamics that are linear in the input. By generalizing results on synchronization of linear agents, we build strong links between the solution to the synchronization problem in the linear and nonlinear framework. This is also enabled by the introduction of new results on design of incrementally stabilizing controllers based on contraction analysis. Finally, we propose numerically tractable sufficient conditions for the synchronization of networks of non-smooth Lur’e systems.
{"title":"Incremental stabilization and multi-agent synchronization of discrete-time nonlinear systems","authors":"Samuele Zoboli , Daniele Astolfi , Vincent Andrieu , Giacomo Casadei , Luca Zaccarian","doi":"10.1016/j.automatica.2026.112832","DOIUrl":"10.1016/j.automatica.2026.112832","url":null,"abstract":"<div><div>In this paper, we propose a novel distributed state-feedback design for robust synchronization of networks of identical discrete-time nonlinear agents under generic time-invariant communication graphs. We focus on the class of almost differentiable (possibly time-varying) dynamics that are linear in the input. By generalizing results on synchronization of linear agents, we build strong links between the solution to the synchronization problem in the linear and nonlinear framework. This is also enabled by the introduction of new results on design of incrementally stabilizing controllers based on contraction analysis. Finally, we propose numerically tractable sufficient conditions for the synchronization of networks of non-smooth Lur’e systems.</div></div>","PeriodicalId":55413,"journal":{"name":"Automatica","volume":"185 ","pages":"Article 112832"},"PeriodicalIF":5.9,"publicationDate":"2026-01-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145978176","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 : 2026-01-12DOI: 10.1016/j.automatica.2025.112798
Luke Rickard , Alessandro Abate , Kostas Margellos
We investigate the problem of verifying different properties of discrete time dynamical systems, namely, reachability, safety and reach-while-avoid. To achieve this, we adopt a data-driven perspective and, using past system trajectories as data, we aim at learning a specific function termed certificate for each property we wish to verify. We seek to minimize a loss function, designed to encompass conditions on the certificate to be learned that encode the satisfaction of the associated property. Besides learning a certificate, we quantify probabilistically its generalization properties, namely, how likely it is for a certificate to be valid (and hence for the associated property to be satisfied) when it comes to a new system trajectory not included in the training data set. We view this problem under the realm of probably approximately correct (PAC) learning under the notion of compression, and use recent advancements of the so-called scenario approach to obtain scalable generalization bounds on the learned certificates. To achieve this, we design a novel algorithm that minimizes the loss function and hence constructs a certificate, and at the same time determines a quantity termed compression, which is instrumental in obtaining meaningful probabilistic guarantees. This process is novel per se and provides a constructive mechanism for compression set calculation, thus opening the road for its use to more general non-convex optimization problems. We verify the efficacy of our methodology on several numerical case studies, and compare it (both theoretically and numerically) with closely related results on data-driven property verification.
{"title":"Data-driven certificate synthesis","authors":"Luke Rickard , Alessandro Abate , Kostas Margellos","doi":"10.1016/j.automatica.2025.112798","DOIUrl":"10.1016/j.automatica.2025.112798","url":null,"abstract":"<div><div>We investigate the problem of verifying different properties of discrete time dynamical systems, namely, reachability, safety and reach-while-avoid. To achieve this, we adopt a data-driven perspective and, using past system trajectories as data, we aim at learning a specific function termed <em>certificate</em> for each property we wish to verify. We seek to minimize a loss function, designed to encompass conditions on the certificate to be learned that encode the satisfaction of the associated property. Besides learning a certificate, we quantify probabilistically its generalization properties, namely, how likely it is for a certificate to be valid (and hence for the associated property to be satisfied) when it comes to a new system trajectory not included in the training data set. We view this problem under the realm of probably approximately correct (PAC) learning under the notion of compression, and use recent advancements of the so-called scenario approach to obtain scalable generalization bounds on the learned certificates. To achieve this, we design a novel algorithm that minimizes the loss function and hence constructs a certificate, and at the same time determines a quantity termed compression, which is instrumental in obtaining meaningful probabilistic guarantees. This process is novel per se and provides a constructive mechanism for compression set calculation, thus opening the road for its use to more general non-convex optimization problems. We verify the efficacy of our methodology on several numerical case studies, and compare it (both theoretically and numerically) with closely related results on data-driven property verification.</div></div>","PeriodicalId":55413,"journal":{"name":"Automatica","volume":"185 ","pages":"Article 112798"},"PeriodicalIF":5.9,"publicationDate":"2026-01-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145978177","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 : 2026-01-12DOI: 10.1016/j.automatica.2026.112833
Zhihua Guo, Xinjun Wang, Mingliang Tian, Jianing Hu
This paper investigates the issues of zonotopic-based set-membership state estimation and fault detection for discrete-time linear systems with unknown but bounded (UBB) disturbance and noise under nonperiodic denial-of-service (DoS) attacks. Firstly, a novel zonotopic state observer is designed to obtain point-valued estimations for the considered system. To improve estimation accuracy, a decoupling method is simultaneously proposed to separate the disturbance from the error dynamics. Secondly, the discrete-time linear systems subjected to intermittent nonperiodic DoS attacks are restructured into a class of augmented switched systems, which comprises both a stable subsystem and an unstable subsystem. To guarantee the stability of the augmented system, a switching law is designed, which solves the instability problem of system under long-term or high-frequency DoS attacks. Based on Lyapunov stability theory, the exponential stability analysis and -gain performance analysis are presented for the augmented switched system. Moreover, the reachable set of the system state under nonperiodic DoS attacks and fault-free scenarios is obtained through reachability analysis. In addition, a more reliable set-membership fault detection strategy with the obtained reachable set and the residual signals is developed. Finally, some simulation results are provided to show the advantages of the theoretic results.
{"title":"Zonotopic state estimation and fault detection for discrete-time linear systems under DoS attacks: A switching controller design mechanism","authors":"Zhihua Guo, Xinjun Wang, Mingliang Tian, Jianing Hu","doi":"10.1016/j.automatica.2026.112833","DOIUrl":"10.1016/j.automatica.2026.112833","url":null,"abstract":"<div><div>This paper investigates the issues of zonotopic-based set-membership state estimation and fault detection for discrete-time linear systems with unknown but bounded (UBB) disturbance and noise under nonperiodic denial-of-service (DoS) attacks. Firstly, a novel zonotopic state observer is designed to obtain point-valued estimations for the considered system. To improve estimation accuracy, a decoupling method is simultaneously proposed to separate the disturbance from the error dynamics. Secondly, the discrete-time linear systems subjected to intermittent nonperiodic DoS attacks are restructured into a class of augmented switched systems, which comprises both a stable subsystem and an unstable subsystem. To guarantee the stability of the augmented system, a switching law is designed, which solves the instability problem of system under long-term or high-frequency DoS attacks. Based on Lyapunov stability theory, the exponential stability analysis and <span><math><msub><mrow><mi>l</mi></mrow><mrow><mn>2</mn></mrow></msub></math></span>-gain performance analysis are presented for the augmented switched system. Moreover, the reachable set of the system state under nonperiodic DoS attacks and fault-free scenarios is obtained through reachability analysis. In addition, a more reliable set-membership fault detection strategy with the obtained reachable set and the residual signals is developed. Finally, some simulation results are provided to show the advantages of the theoretic results.</div></div>","PeriodicalId":55413,"journal":{"name":"Automatica","volume":"185 ","pages":"Article 112833"},"PeriodicalIF":5.9,"publicationDate":"2026-01-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145978260","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 : 2026-01-10DOI: 10.1016/j.automatica.2026.112823
Yu-Ang Wang , Zidong Wang , Lei Zou , Fan Wang , Hongli Dong
In this paper, the problem of resilient recursive state estimation is addressed for a class of nonlinear cyber–physical systems operating under token bucket protocols and subject to probabilistic bit flips. Measurement signals are transmitted to the remote estimator only when the token storage surpasses the token consumption required for transmission. The communication process employs a binary encoding scheme, which quantizes measurement outputs into a bit string, transmits them through memoryless binary symmetric channels subject to probabilistic bit flips, and subsequently recovers them at the receiver. To achieve the desired estimation performance, a resilient state estimator is developed to mitigate the adverse effects of random perturbations in the estimator gain during implementation. The aim is to design a recursive state estimation algorithm that effectively manages the token bucket protocol, addresses probabilistic bit flips, and accommodates estimator gain perturbations. An upper bound for the estimation error covariance is derived, and the corresponding estimator gain is recursively calculated to minimize this bound. Finally, numerical simulations are conducted to validate the effectiveness of the proposed algorithm.
{"title":"Resilient state estimation for nonlinear cyber–physical systems under probabilistic bit flips: A token bucket protocol","authors":"Yu-Ang Wang , Zidong Wang , Lei Zou , Fan Wang , Hongli Dong","doi":"10.1016/j.automatica.2026.112823","DOIUrl":"10.1016/j.automatica.2026.112823","url":null,"abstract":"<div><div>In this paper, the problem of resilient recursive state estimation is addressed for a class of nonlinear cyber–physical systems operating under token bucket protocols and subject to probabilistic bit flips. Measurement signals are transmitted to the remote estimator only when the token storage surpasses the token consumption required for transmission. The communication process employs a binary encoding scheme, which quantizes measurement outputs into a bit string, transmits them through memoryless binary symmetric channels subject to probabilistic bit flips, and subsequently recovers them at the receiver. To achieve the desired estimation performance, a resilient state estimator is developed to mitigate the adverse effects of random perturbations in the estimator gain during implementation. The aim is to design a recursive state estimation algorithm that effectively manages the token bucket protocol, addresses probabilistic bit flips, and accommodates estimator gain perturbations. An upper bound for the estimation error covariance is derived, and the corresponding estimator gain is recursively calculated to minimize this bound. Finally, numerical simulations are conducted to validate the effectiveness of the proposed algorithm.</div></div>","PeriodicalId":55413,"journal":{"name":"Automatica","volume":"185 ","pages":"Article 112823"},"PeriodicalIF":5.9,"publicationDate":"2026-01-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145939236","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 : 2026-01-09DOI: 10.1016/j.automatica.2026.112824
Na Li , Lei Zou , Jiayue Sun , Derui Ding
The federated-filtering-based (FFB) fusion estimation problem is investigated in this paper for networked multi-rate systems, where the measurement signals are transmitted over a wireless network with limited transmission power. A probabilistic quantization mechanism is introduced to handle the raw measurement signals for the purpose of facilitating digital communication over network. Certain transmission models are proposed to describe the behaviors under the effects of multi-rate dynamics, probabilistic quantization and limited transmission power. A delicately designed FFB fusion scheme is proposed to acquire the desired state estimates, where the local filters will receive feedback from the fusion center to reset their estimates. The parameters for the local filters are calculated by recursively minimizing their upper-bounds for the estimation error covariances. Furthermore, new conditions have been derived to analyze the ultimately boundedness of the estimation error covariance for the fusion center. Subsequently, a power allocation strategy is designed by minimizing such ultimate bound subject to the given transmission power constraint. Finally, the effectiveness of the proposed fusion estimation strategy and its optimal power allocation scheme is verified through a simulation example.
{"title":"Fusion estimation for multi-rate systems with probabilistic quantization and transmission power constraints: A federated-filtering-based method","authors":"Na Li , Lei Zou , Jiayue Sun , Derui Ding","doi":"10.1016/j.automatica.2026.112824","DOIUrl":"10.1016/j.automatica.2026.112824","url":null,"abstract":"<div><div>The federated-filtering-based (FFB) fusion estimation problem is investigated in this paper for networked multi-rate systems, where the measurement signals are transmitted over a wireless network with limited transmission power. A probabilistic quantization mechanism is introduced to handle the raw measurement signals for the purpose of facilitating digital communication over network. Certain transmission models are proposed to describe the behaviors under the effects of multi-rate dynamics, probabilistic quantization and limited transmission power. A delicately designed FFB fusion scheme is proposed to acquire the desired state estimates, where the local filters will receive feedback from the fusion center to reset their estimates. The parameters for the local filters are calculated by recursively minimizing their upper-bounds for the estimation error covariances. Furthermore, new conditions have been derived to analyze the ultimately boundedness of the estimation error covariance for the fusion center. Subsequently, a power allocation strategy is designed by minimizing such ultimate bound subject to the given transmission power constraint. Finally, the effectiveness of the proposed fusion estimation strategy and its optimal power allocation scheme is verified through a simulation example.</div></div>","PeriodicalId":55413,"journal":{"name":"Automatica","volume":"185 ","pages":"Article 112824"},"PeriodicalIF":5.9,"publicationDate":"2026-01-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145939237","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 : 2026-01-09DOI: 10.1016/j.automatica.2026.112821
Ruiqing Zhang, Huaiyuan Jiang, Bin Zhou
In this paper, a bias-policy iteration (Bias-PI) method is proposed to relax the requirement of the policy iteration method on the initial admissible control and achieve optimal control for unknown continuous-time nonlinear systems. First, a model-based Bias-PI method is introduced that uses a bias value function to ease the constraints of the initial admissible control. The boundedness of the bias value function and the convergence of the algorithm are demonstrated through rigorous mathematical proofs. Further, the data-driven implementation of the Bias-PI method is detailed, highlighting its ability to learn an optimal controller without prior system information, and simultaneously retaining the fast convergence properties of the traditional policy iteration algorithm. The effectiveness of the data-driven Bias-PI method is illustrated through two simulation examples.
{"title":"Adaptive dynamic programming for unknown continuous-time nonlinear systems via bias-policy iteration","authors":"Ruiqing Zhang, Huaiyuan Jiang, Bin Zhou","doi":"10.1016/j.automatica.2026.112821","DOIUrl":"10.1016/j.automatica.2026.112821","url":null,"abstract":"<div><div>In this paper, a bias-policy iteration (Bias-PI) method is proposed to relax the requirement of the policy iteration method on the initial admissible control and achieve optimal control for unknown continuous-time nonlinear systems. First, a model-based Bias-PI method is introduced that uses a bias value function to ease the constraints of the initial admissible control. The boundedness of the bias value function and the convergence of the algorithm are demonstrated through rigorous mathematical proofs. Further, the data-driven implementation of the Bias-PI method is detailed, highlighting its ability to learn an optimal controller without prior system information, and simultaneously retaining the fast convergence properties of the traditional policy iteration algorithm. The effectiveness of the data-driven Bias-PI method is illustrated through two simulation examples.</div></div>","PeriodicalId":55413,"journal":{"name":"Automatica","volume":"185 ","pages":"Article 112821"},"PeriodicalIF":5.9,"publicationDate":"2026-01-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145939238","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 : 2026-01-09DOI: 10.1016/j.automatica.2026.112820
Jingyao Zhang , Deyuan Meng
This paper is aimed at addressing a class of data-based design and analysis problems of optimal iterative learning control (ILC), where the performance index consists of the quadratic terms of the input updating and tracking error over all iterations and time steps. The optimal ILC design is proposed based on the Bellman optimality equation and the convergence analysis of optimal ILC is implemented such that the performance index throughout the whole iterative process is minimized and the perfect tracking objective of ILC is monotonically achieved at an exponential speed. An iterative method for solving the learning gain of optimal ILC is presented based on the input–output data such that the optimal ILC can be executed without any model information. Simulation tests are performed to illustrate the effectiveness and optimality of our proposed ILC method.
{"title":"Data-based optimal learning control minimizing performance indexes throughout iterative processes","authors":"Jingyao Zhang , Deyuan Meng","doi":"10.1016/j.automatica.2026.112820","DOIUrl":"10.1016/j.automatica.2026.112820","url":null,"abstract":"<div><div>This paper is aimed at addressing a class of data-based design and analysis problems of optimal iterative learning control (ILC), where the performance index consists of the quadratic terms of the input updating and tracking error over all iterations and time steps. The optimal ILC design is proposed based on the Bellman optimality equation and the convergence analysis of optimal ILC is implemented such that the performance index throughout the whole iterative process is minimized and the perfect tracking objective of ILC is monotonically achieved at an exponential speed. An iterative method for solving the learning gain of optimal ILC is presented based on the input–output data such that the optimal ILC can be executed without any model information. Simulation tests are performed to illustrate the effectiveness and optimality of our proposed ILC method.</div></div>","PeriodicalId":55413,"journal":{"name":"Automatica","volume":"185 ","pages":"Article 112820"},"PeriodicalIF":5.9,"publicationDate":"2026-01-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145939143","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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