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}
Pub Date : 2026-01-08DOI: 10.1016/j.automatica.2026.112822
Renshuo Cheng, Chengpu Yu, Yao Li
This paper studies the inverse optimal control for discrete-time finite-horizon linear quadratic tracking with unknown target states. Due to the time-varying feedback policies caused by the finite-horizon setting and the unknown system dynamics, the concerned inverse optimal control becomes challenging. To deal with it, a novel data driven inverse identification approach is developed, for which the corresponding identifiability conditions are provided and the statistical consistency is analyzed in the presence of observation noise. Compared to the existing solutions, the proposed approach requires only optimal trajectories, possibly corrupted by additive observation noise with zero mean and bounded covariance, and achieves consistent results without knowledge of the noise covariance. Finally, simulation examples are presented to show the effectiveness of the proposed approach.
{"title":"Data-driven inverse optimal control for linear quadratic tracking with unknown target states","authors":"Renshuo Cheng, Chengpu Yu, Yao Li","doi":"10.1016/j.automatica.2026.112822","DOIUrl":"10.1016/j.automatica.2026.112822","url":null,"abstract":"<div><div>This paper studies the inverse optimal control for discrete-time finite-horizon linear quadratic tracking with unknown target states. Due to the time-varying feedback policies caused by the finite-horizon setting and the unknown system dynamics, the concerned inverse optimal control becomes challenging. To deal with it, a novel data driven inverse identification approach is developed, for which the corresponding identifiability conditions are provided and the statistical consistency is analyzed in the presence of observation noise. Compared to the existing solutions, the proposed approach requires only optimal trajectories, possibly corrupted by additive observation noise with zero mean and bounded covariance, and achieves consistent results without knowledge of the noise covariance. Finally, simulation examples are presented to show the effectiveness of the proposed approach.</div></div>","PeriodicalId":55413,"journal":{"name":"Automatica","volume":"185 ","pages":"Article 112822"},"PeriodicalIF":5.9,"publicationDate":"2026-01-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145939140","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 : 2026-01-07DOI: 10.1016/j.automatica.2026.112825
Zhaoming Qin, Alireza Karimi
In this paper, we propose a data-driven approach to robust feedback controller design for unknown linear time-invariant (LTI) dynamic systems. Using input-state trajectories and prior knowledge of unknown-but-bounded disturbances, the objective is to synthesize a state-feedback controller that achieves robust stabilization and performance while employing a common quadratic Lyapunov function. Previous works have exclusively considered bounded disturbances described by quadratic matrix inequalities (QMIs) and pointwise or constraints. In contrast, this paper introduces a more general framework that characterizes disturbance bounds using compact basic semi-algebraic (BSA) sets, thereby capturing both time-domain and frequency-domain properties. We cast the necessary and sufficient conditions for quadratic stabilization and performance as convex sum-of-squares (SOS) optimization problems. Additionally, we propose relaxation methods to reduce computational complexity by leveraging the geometric and structural properties of the polynomials defining the BSA sets. Simulation results demonstrate the efficiency and flexibility of the proposed approach.
{"title":"Efficient sum-of-squares approach to data-driven robust controller design under generalized bounded disturbances","authors":"Zhaoming Qin, Alireza Karimi","doi":"10.1016/j.automatica.2026.112825","DOIUrl":"10.1016/j.automatica.2026.112825","url":null,"abstract":"<div><div>In this paper, we propose a data-driven approach to robust feedback controller design for unknown linear time-invariant (LTI) dynamic systems. Using input-state trajectories and prior knowledge of unknown-but-bounded disturbances, the objective is to synthesize a state-feedback controller that achieves robust stabilization and <span><math><msub><mrow><mi>H</mi></mrow><mrow><mn>2</mn></mrow></msub></math></span> performance while employing a common quadratic Lyapunov function. Previous works have exclusively considered bounded disturbances described by quadratic matrix inequalities (QMIs) and pointwise <span><math><msub><mrow><mi>ℓ</mi></mrow><mrow><mn>2</mn></mrow></msub></math></span> or <span><math><msub><mrow><mi>ℓ</mi></mrow><mrow><mi>∞</mi></mrow></msub></math></span> constraints. In contrast, this paper introduces a more general framework that characterizes disturbance bounds using compact basic semi-algebraic (BSA) sets, thereby capturing both time-domain and frequency-domain properties. We cast the necessary and sufficient conditions for quadratic stabilization and <span><math><msub><mrow><mi>H</mi></mrow><mrow><mn>2</mn></mrow></msub></math></span> performance as convex sum-of-squares (SOS) optimization problems. Additionally, we propose relaxation methods to reduce computational complexity by leveraging the geometric and structural properties of the polynomials defining the BSA sets. Simulation results demonstrate the efficiency and flexibility of the proposed approach.</div></div>","PeriodicalId":55413,"journal":{"name":"Automatica","volume":"185 ","pages":"Article 112825"},"PeriodicalIF":5.9,"publicationDate":"2026-01-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145939141","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 : 2026-01-07DOI: 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":"2026-01-07","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 : 2026-01-05DOI: 10.1016/j.automatica.2025.112748
Mario Di Ferdinando , Alessandro Borri , Stefano Di Gennaro , Pierdomenico Pepe
In this paper, the digital event-based stabilization problem under safety constraints is studied for nonlinear systems with state delays. In particular, a methodology for the design of quantized sampled-data event-triggered safe stabilizers is provided for nonlinear systems affected by state delays. The proposed design procedure relies on the notion of Safe Steepest Descent Feedback (SSDF) which is based on the combination of Steepest Descent Feedbacks and Barrier functions. The stabilization in the sample-and-hold sense theory is used as a tool to show the existence of a suitably fast sampling and of an accurate quantization of the input/output channels such that: the digital implementation of SSDFs, updated through a proposed event-triggered mechanism, ensures the semi-global practical safe stability property of the related closed-loop system with arbitrarily small final target ball of the origin. A first order spline approximation is used to cope with the possible unavailability in the buffer of required past values of the state measurements. In the theory here developed, time-varying sampling periods and the non-uniform quantization of both input/output channels are allowed. The proposed theoretical results are validated through an application concerning the plasma glucose regulation problem in Type-2 diabetic patients via artificial pancreas.
{"title":"Safety constrained digital control of nonlinear systems with state delays","authors":"Mario Di Ferdinando , Alessandro Borri , Stefano Di Gennaro , Pierdomenico Pepe","doi":"10.1016/j.automatica.2025.112748","DOIUrl":"10.1016/j.automatica.2025.112748","url":null,"abstract":"<div><div>In this paper, the digital event-based stabilization problem under safety constraints is studied for nonlinear systems with state delays. In particular, a methodology for the design of quantized sampled-data event-triggered safe stabilizers is provided for nonlinear systems affected by state delays. The proposed design procedure relies on the notion of Safe Steepest Descent Feedback (SSDF) which is based on the combination of Steepest Descent Feedbacks and Barrier functions. The stabilization in the sample-and-hold sense theory is used as a tool to show the existence of a suitably fast sampling and of an accurate quantization of the input/output channels such that: the digital implementation of SSDFs, updated through a proposed event-triggered mechanism, ensures the semi-global practical safe stability property of the related closed-loop system with arbitrarily small final target ball of the origin. A first order spline approximation is used to cope with the possible unavailability in the buffer of required past values of the state measurements. In the theory here developed, time-varying sampling periods and the non-uniform quantization of both input/output channels are allowed. The proposed theoretical results are validated through an application concerning the plasma glucose regulation problem in Type-2 diabetic patients via artificial pancreas.</div></div>","PeriodicalId":55413,"journal":{"name":"Automatica","volume":"185 ","pages":"Article 112748"},"PeriodicalIF":5.9,"publicationDate":"2026-01-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145902328","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 : 2026-01-03DOI: 10.1016/j.automatica.2025.112809
Yihuai Zhang , Jean Auriol , Huan Yu
This paper addresses the problem of robust stabilization for linear hyperbolic Partial Differential Equations (PDEs) with Markov-jumping parameter uncertainty. We consider a 2 × 2 heterogeneous hyperbolic PDE and propose a control law using operator learning and the backstepping method. Specifically, the backstepping kernels used to construct the control law are approximated with neural operators (NO) in order to improve computational efficiency. The key challenge lies in deriving the stability conditions with respect to the Markov-jumping parameter uncertainty and NO approximation errors. The mean-square exponential stability of the stochastic system is achieved through Lyapunov analysis, indicating that the system can be stabilized if the random parameters are sufficiently close to the nominal parameters on average, and NO approximation errors are small enough. The theoretical results are applied to freeway traffic control under stochastic upstream demands and then validated through numerical simulations.
{"title":"Operator learning for robust stabilization of linear Markov-jumping hyperbolic PDEs","authors":"Yihuai Zhang , Jean Auriol , Huan Yu","doi":"10.1016/j.automatica.2025.112809","DOIUrl":"10.1016/j.automatica.2025.112809","url":null,"abstract":"<div><div>This paper addresses the problem of robust stabilization for linear hyperbolic Partial Differential Equations (PDEs) with Markov-jumping parameter uncertainty. We consider a 2 × 2 heterogeneous hyperbolic PDE and propose a control law using operator learning and the backstepping method. Specifically, the backstepping kernels used to construct the control law are approximated with neural operators (NO) in order to improve computational efficiency. The key challenge lies in deriving the stability conditions with respect to the Markov-jumping parameter uncertainty and NO approximation errors. The mean-square exponential stability of the stochastic system is achieved through Lyapunov analysis, indicating that the system can be stabilized if the random parameters are sufficiently close to the nominal parameters on average, and NO approximation errors are small enough. The theoretical results are applied to freeway traffic control under stochastic upstream demands and then validated through numerical simulations.</div></div>","PeriodicalId":55413,"journal":{"name":"Automatica","volume":"185 ","pages":"Article 112809"},"PeriodicalIF":5.9,"publicationDate":"2026-01-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145884873","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 : 2026-01-02DOI: 10.1016/j.automatica.2025.112810
Bin Zhou
This paper addresses the problems of exact prescribed-time stabilization and observer design for a class of multi-input-multi-output (MIMO) nonlinear systems. By introducing the concept of left and right clustered matrices and exploring their properties, solutions to two classes of parametric Lyapunov equations (PLEs) associated with the coefficients of the linear part of the MIMO nonlinear systems are thoroughly investigated. These two PLEs are then utilized as the key tool to solve respectively the exact prescribed-time stabilization of the MIMO nonlinear system where the nonlinear functions satisfy a linear growth condition with unknown coefficients, and the exact prescribed-time observer design of the MIMO nonlinear system where the nonlinear functions are known and satisfy the Lipschitz condition. The approach is also extended to solve the problem of prescribed-time stabilization of a class of MIMO nonlinear systems by observer-based output feedback. Finally, two numerical examples demonstrate the effectiveness of the proposed approaches.
{"title":"Exact prescribed-time stabilization and observer design for a class of MIMO nonlinear systems","authors":"Bin Zhou","doi":"10.1016/j.automatica.2025.112810","DOIUrl":"10.1016/j.automatica.2025.112810","url":null,"abstract":"<div><div>This paper addresses the problems of exact prescribed-time stabilization and observer design for a class of multi-input-multi-output (MIMO) nonlinear systems. By introducing the concept of left and right clustered matrices and exploring their properties, solutions to two classes of parametric Lyapunov equations (PLEs) associated with the coefficients of the linear part of the MIMO nonlinear systems are thoroughly investigated. These two PLEs are then utilized as the key tool to solve respectively the exact prescribed-time stabilization of the MIMO nonlinear system where the nonlinear functions satisfy a linear growth condition with unknown coefficients, and the exact prescribed-time observer design of the MIMO nonlinear system where the nonlinear functions are known and satisfy the Lipschitz condition. The approach is also extended to solve the problem of prescribed-time stabilization of a class of MIMO nonlinear systems by observer-based output feedback. Finally, two numerical examples demonstrate the effectiveness of the proposed approaches.</div></div>","PeriodicalId":55413,"journal":{"name":"Automatica","volume":"185 ","pages":"Article 112810"},"PeriodicalIF":5.9,"publicationDate":"2026-01-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145884869","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 : 2026-01-02DOI: 10.1016/j.automatica.2025.112816
Jialing Zhou , Guanghui Wen , Yuezu Lv , Xinlei Yi , Tao Yang , Karl Henrik Johansson
The existing distributed resource allocation (DRA) algorithms for multi-agent networks can rarely be implemented for multiple interacting groups of agents with conflicts of interest. The directed interaction, together with the hard balance constraint that follows from maintaining supply–demand balance during the execution process, make the DRA more challenging. To address this problem, the paper studies DRA over multiple interacting groups from a game-theoretic perspective, introducing the resource allocation game (RAG). A novel out-Laplacian matrix based methodology is developed for distributed Nash equilibrium (NE) computation. Following this methodology, distributed algorithms are designed using leader-follower tracking protocols to estimate partial derivatives of individual objective functions for the RAG. A reduced-order distributed algorithm is further developed for the RAG by integrating a gradient-tracking mechanism for estimating partial derivatives of group-level objective functions. It is shown that agent states converge to the NE of the games linearly while satisfying the balance constraint during the whole execution process under the proposed algorithms. The effectiveness of the proposed algorithms is illustrated through numerical examples.
{"title":"Distributed Nash equilibrium computation in multi-group resource allocation games over digraphs","authors":"Jialing Zhou , Guanghui Wen , Yuezu Lv , Xinlei Yi , Tao Yang , Karl Henrik Johansson","doi":"10.1016/j.automatica.2025.112816","DOIUrl":"10.1016/j.automatica.2025.112816","url":null,"abstract":"<div><div>The existing distributed resource allocation (DRA) algorithms for multi-agent networks can rarely be implemented for multiple interacting groups of agents with conflicts of interest. The directed interaction, together with the hard balance constraint that follows from maintaining supply–demand balance during the execution process, make the DRA more challenging. To address this problem, the paper studies DRA over multiple interacting groups from a game-theoretic perspective, introducing the resource allocation game (RAG). A novel out-Laplacian matrix based methodology is developed for distributed Nash equilibrium (NE) computation. Following this methodology, distributed algorithms are designed using leader-follower tracking protocols to estimate partial derivatives of individual objective functions for the RAG. A reduced-order distributed algorithm is further developed for the RAG by integrating a gradient-tracking mechanism for estimating partial derivatives of group-level objective functions. It is shown that agent states converge to the NE of the games linearly while satisfying the balance constraint during the whole execution process under the proposed algorithms. The effectiveness of the proposed algorithms is illustrated through numerical examples.</div></div>","PeriodicalId":55413,"journal":{"name":"Automatica","volume":"185 ","pages":"Article 112816"},"PeriodicalIF":5.9,"publicationDate":"2026-01-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145884850","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 : 2026-01-02DOI: 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":"2026-01-02","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 : 2025-12-31DOI: 10.1016/j.automatica.2025.112815
Qian Liu , Yong He , Chongyang Ning
In this paper, we explore the almost sure input-to-state stability (ISS) and the almost sure integral input-to-state stability (iISS) of nonlinear randomly switched time-varying systems. We begin with defining almost sure ISS and almost sure iISS by combining almost sure uniform stability with a novel almost sure uniform asymptotic gain property. Next, we derive criteria for almost sure ISS and iISS by constructing an ISS-Lyapunov function and an iISS-Lyapunov function for each time-varying subsystem with the help of indefinite multiple Lyapunov functions (iMLFs). In the process of deriving the criteria, the Lyapunov functions are relaxed by integrating mean uniformly stable functions into iMLFs such that the criteria are available to the systems with unstable subsystems. Additionally, we provide numerical examples to illustrate the advantages and the effectiveness of our approach.
{"title":"Almost sure notions of input-to-state stability and integral input-to-state stability for randomly switched time-varying systems","authors":"Qian Liu , Yong He , Chongyang Ning","doi":"10.1016/j.automatica.2025.112815","DOIUrl":"10.1016/j.automatica.2025.112815","url":null,"abstract":"<div><div>In this paper, we explore the almost sure input-to-state stability (ISS) and the almost sure integral input-to-state stability (iISS) of nonlinear randomly switched time-varying systems. We begin with defining almost sure ISS and almost sure iISS by combining almost sure uniform stability with a novel almost sure uniform asymptotic gain property. Next, we derive criteria for almost sure ISS and iISS by constructing an ISS-Lyapunov function and an iISS-Lyapunov function for each time-varying subsystem with the help of indefinite multiple Lyapunov functions (iMLFs). In the process of deriving the criteria, the Lyapunov functions are relaxed by integrating mean uniformly stable functions into iMLFs such that the criteria are available to the systems with unstable subsystems. Additionally, we provide numerical examples to illustrate the advantages and the effectiveness of our approach.</div></div>","PeriodicalId":55413,"journal":{"name":"Automatica","volume":"185 ","pages":"Article 112815"},"PeriodicalIF":5.9,"publicationDate":"2025-12-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145884852","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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