Pub Date : 2025-12-29DOI: 10.1016/j.automatica.2025.112813
Zhijian Hu , Renjie Ma
This paper considers adaptive event-triggered tracking control problem in the presence of uncertainties, including unmodeled dynamics and external disturbances. A novel switching function is introduced, and the compensated tracking error dynamics is constructed via a command filter. Based on the backstepping methodology, virtual controllers are designed together with an adaptive law that estimates the supremum of uncertainty effects, leading to an event-triggered control strategy, such that uniform finite-time stability is established for different switching function scenarios. Finally, a simulation study on a soft robot illustrates the effectiveness of the proposed approach.
{"title":"Adaptive event-triggered tracking control via switching functions","authors":"Zhijian Hu , Renjie Ma","doi":"10.1016/j.automatica.2025.112813","DOIUrl":"10.1016/j.automatica.2025.112813","url":null,"abstract":"<div><div>This paper considers adaptive event-triggered tracking control problem in the presence of uncertainties, including unmodeled dynamics and external disturbances. A novel switching function is introduced, and the compensated tracking error dynamics is constructed via a command filter. Based on the backstepping methodology, virtual controllers are designed together with an adaptive law that estimates the supremum of uncertainty effects, leading to an event-triggered control strategy, such that uniform finite-time stability is established for different switching function scenarios. Finally, a simulation study on a soft robot illustrates the effectiveness of the proposed approach.</div></div>","PeriodicalId":55413,"journal":{"name":"Automatica","volume":"185 ","pages":"Article 112813"},"PeriodicalIF":5.9,"publicationDate":"2025-12-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145884870","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}
Given a network of agents, we say that the agents achieve a -agreement when their state variables converge to a point that corresponds to the projection of the agents’ states onto a -dimensional linear subspace. The -agreement problem generalizes the classical consensus problem; unlike in consensus, where the agents’ states must asymptotically coincide, in -agreement the agents reach an agreement in a generalized sense (within a linear subspace, where the states do not necessarily coincide). In this paper, we investigate which interaction topologies enable a network of agents to reach an agreement on a prescribed -dimensional subspace through local coordination algorithms. We show that achieving -agreement requires communication over highly connected graphs; specifically, the number of edges in the interaction graph must grow linearly with the dimension of the agreement subspace. Our characterization reveals that the presence of cycles in the communication graph (particularly, independent families of cycles) constitutes the fundamental structural feature enabling the agents to achieve -agreement. We also investigate the use of common graph topologies, such as path and circulant graphs, for -agreement, deriving insights into the relationship between the subspace dimension and the required network connectivity. The effectiveness of the proposed framework is demonstrated through simulations in robotic formation control problems.
{"title":"The role of network connectivity in distributed k-agreement protocols","authors":"Gianluca Bianchin , Miguel Vaquero , Jorge Cortés , Emiliano Dall’Anese","doi":"10.1016/j.automatica.2025.112753","DOIUrl":"10.1016/j.automatica.2025.112753","url":null,"abstract":"<div><div>Given a network of agents, we say that the agents achieve a <span><math><mi>k</mi></math></span>-<em>agreement</em> when their state variables converge to a point that corresponds to the projection of the agents’ states onto a <span><math><mi>k</mi></math></span>-dimensional linear subspace. The <span><math><mi>k</mi></math></span>-agreement problem generalizes the classical consensus problem; unlike in consensus, where the agents’ states must asymptotically coincide, in <span><math><mi>k</mi></math></span>-agreement the agents reach an agreement in a generalized sense (within a linear subspace, where the states do not necessarily coincide). In this paper, we investigate which interaction topologies enable a network of agents to reach an agreement on a prescribed <span><math><mi>k</mi></math></span>-dimensional subspace through local coordination algorithms. We show that achieving <span><math><mi>k</mi></math></span>-agreement requires communication over highly connected graphs; specifically, the number of edges in the interaction graph must grow linearly with the dimension <span><math><mi>k</mi></math></span> of the agreement subspace. Our characterization reveals that the presence of cycles in the communication graph (particularly, independent families of cycles) constitutes the fundamental structural feature enabling the agents to achieve <span><math><mi>k</mi></math></span>-agreement. We also investigate the use of common graph topologies, such as path and circulant graphs, for <span><math><mi>k</mi></math></span>-agreement, deriving insights into the relationship between the subspace dimension <span><math><mi>k</mi></math></span> and the required network connectivity. The effectiveness of the proposed framework is demonstrated through simulations in robotic formation control problems.</div></div>","PeriodicalId":55413,"journal":{"name":"Automatica","volume":"185 ","pages":"Article 112753"},"PeriodicalIF":5.9,"publicationDate":"2025-12-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145884874","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 : 2025-12-29DOI: 10.1016/j.automatica.2025.112799
Sebin Gracy , Brian D.O. Anderson , Mengbin Ye , César A. Uribe
The paper studies the simultaneous spread of two competing viruses over a network of population nodes with higher-order interactions (HOI), using a continuous-time time-invariant competitive bivirus networked susceptible–infected–susceptible (SIS) system. In this paper, by HOI, we mean interactions among group sizes of no more than three nodes. The first key contribution is to establish several important general properties for generic systems. Namely, there are a finite number of equilibria, each equilibrium is nondegenerate, and the system is a strongly monotone dynamical system. Put together, we establish that for almost all initial conditions, the system will converge to a stable equilibrium (of which there may be many). We then turn our focus to characterizing the existence and stability of the equilibria of this system, which are (i) the disease-free equilibrium (DFE), (ii) single-virus endemic equilibria, and (iii) coexistence equilibria (where both viruses are present). We present a range of conditions on the existence or nonexistence of various equilibria. Two key features underpin our results: First, we substantially relax the connectivity conditions of the network relative to existing literature. More specifically, for securing several important general properties for generic systems, we do not require strong connectivity of the standard pairwise interaction graph. Second, we identify dynamical phenomena, including multiple stable equilibria, which are known to be impossible without HOI. The latter illustrates the novel insights that are obtained by including HOI into models of epidemic spread. Finally, we illustrate our results using a real-world large-scale network.
{"title":"Networked competitive bivirus SIS spread with higher order interactions","authors":"Sebin Gracy , Brian D.O. Anderson , Mengbin Ye , César A. Uribe","doi":"10.1016/j.automatica.2025.112799","DOIUrl":"10.1016/j.automatica.2025.112799","url":null,"abstract":"<div><div>The paper studies the simultaneous spread of two competing viruses over a network of population nodes with higher-order interactions (HOI), using a continuous-time time-invariant competitive bivirus networked susceptible–infected–susceptible (SIS) system. In this paper, by HOI, we mean interactions among group sizes of no more than three nodes. The first key contribution is to establish several important general properties for generic systems. Namely, there are a finite number of equilibria, each equilibrium is nondegenerate, and the system is a strongly monotone dynamical system. Put together, we establish that for almost all initial conditions, the system will converge to a stable equilibrium (of which there may be many). We then turn our focus to characterizing the existence and stability of the equilibria of this system, which are (i) the disease-free equilibrium (DFE), (ii) single-virus endemic equilibria, and (iii) coexistence equilibria (where both viruses are present). We present a range of conditions on the existence or nonexistence of various equilibria. Two key features underpin our results: First, we substantially relax the connectivity conditions of the network relative to existing literature. More specifically, for securing several important general properties for generic systems, we do <em>not</em> require strong connectivity of the standard pairwise interaction graph. Second, we identify dynamical phenomena, including multiple stable equilibria, which are known to be impossible without HOI. The latter illustrates the novel insights that are obtained by including HOI into models of epidemic spread. Finally, we illustrate our results using a real-world large-scale network.</div></div>","PeriodicalId":55413,"journal":{"name":"Automatica","volume":"185 ","pages":"Article 112799"},"PeriodicalIF":5.9,"publicationDate":"2025-12-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145884867","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 : 2025-12-26DOI: 10.1016/j.automatica.2025.112808
Hai-Tao Zhang , Jiayu Zou , Xingjian Liu
It has long been a challenging task for optimal coverage control of multi-agent systems (MASs) in non-convex surface environments often encountered in real coordinated detection applications. To this end, this paper develops a surface cooperative control scheme for MASs to perform coverage operations. First, a coverage surface partition protocol is devised to divide a non-convex surface into multiple sectorial sub-surfaces. Accordingly, a performance index in surface coverage is established considering the curvature spatial evolution of the surface environments. Thereby, a random-initial-point algorithm is designed to minimize the performance index, and a surface-constrained optimal control law is developed to deploy MASs at niche positions. Significantly, sufficient conditions are derived to guarantee the asymptotical stability of the present scheme. Finally, numerical simulations are conducted to verify the effectiveness of the present surface coverage design.
{"title":"Cooperative optimal surface coverage control of multi-agent systems in non-convex surface environments","authors":"Hai-Tao Zhang , Jiayu Zou , Xingjian Liu","doi":"10.1016/j.automatica.2025.112808","DOIUrl":"10.1016/j.automatica.2025.112808","url":null,"abstract":"<div><div>It has long been a challenging task for optimal coverage control of multi-agent systems (MASs) in non-convex surface environments often encountered in real coordinated detection applications. To this end, this paper develops a surface cooperative control scheme for MASs to perform coverage operations. First, a coverage surface partition protocol is devised to divide a non-convex surface into multiple sectorial sub-surfaces. Accordingly, a performance index in surface coverage is established considering the curvature spatial evolution of the surface environments. Thereby, a random-initial-point algorithm is designed to minimize the performance index, and a surface-constrained optimal control law is developed to deploy MASs at niche positions. Significantly, sufficient conditions are derived to guarantee the asymptotical stability of the present scheme. Finally, numerical simulations are conducted to verify the effectiveness of the present surface coverage design.</div></div>","PeriodicalId":55413,"journal":{"name":"Automatica","volume":"185 ","pages":"Article 112808"},"PeriodicalIF":5.9,"publicationDate":"2025-12-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145841799","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 : 2025-12-24DOI: 10.1016/j.automatica.2025.112761
Licheng Wang , Zidong Wang
This paper investigates the event-based probability guaranteed tracking control problem for a class of discrete-time systems with a relay-aided communication scheme. The uncertainties of the system matrices are taken into account, which is described by mutually independent uniformly distributed random variables. An adaptive event-triggering scheme is introduced during the signal exchange from the sensor to the relay where the triggering threshold is dynamically regulated. Moreover, an amplify-to-forward relay is employed to improve the communication quality between the sensor and the controller. With the help of the Lyapunov stability theory, sufficient conditions are established to guarantee that the tracking error dynamics achieves the asymptotical stability and the performance with probability constraints. The desired controller parameters are derived by means of the solution to certain optimization problem subject to matrix inequality constraints. Finally, a numerical example is provided to show the effectiveness of the developed tracking control scheme.
{"title":"Event-based probability-guaranteed tracking control with amplify-and-forward relay schemes","authors":"Licheng Wang , Zidong Wang","doi":"10.1016/j.automatica.2025.112761","DOIUrl":"10.1016/j.automatica.2025.112761","url":null,"abstract":"<div><div>This paper investigates the event-based probability guaranteed <span><math><msub><mrow><mi>H</mi></mrow><mrow><mi>∞</mi></mrow></msub></math></span> tracking control problem for a class of discrete-time systems with a relay-aided communication scheme. The uncertainties of the system matrices are taken into account, which is described by mutually independent uniformly distributed random variables. An adaptive event-triggering scheme is introduced during the signal exchange from the sensor to the relay where the triggering threshold is dynamically regulated. Moreover, an amplify-to-forward relay is employed to improve the communication quality between the sensor and the controller. With the help of the Lyapunov stability theory, sufficient conditions are established to guarantee that the tracking error dynamics achieves the asymptotical stability and the <span><math><msub><mrow><mi>H</mi></mrow><mrow><mi>∞</mi></mrow></msub></math></span> performance with probability constraints. The desired controller parameters are derived by means of the solution to certain optimization problem subject to matrix inequality constraints. Finally, a numerical example is provided to show the effectiveness of the developed tracking control scheme.</div></div>","PeriodicalId":55413,"journal":{"name":"Automatica","volume":"185 ","pages":"Article 112761"},"PeriodicalIF":5.9,"publicationDate":"2025-12-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145822795","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}
This paper introduces novel companion form realizations for quasi-Linear Parameter Varying (qLPV) state space models obtained from input–output models, which are identified using neural networks (NN). The data for training the NN is generated from a multi-input, multi-output (MIMO) dynamic system. The method, at first, trains a (possibly deep) neural network to minimize one-step or multi-step prediction errors. If the layer activation functions of the NN satisfy a certain property, labeled as Lipschitz factorability, then the NN can be cast into a quasi-linear difference equation that describe the input–output dynamics of the nonlinear MIMO system. Such a NN consisting of Lipschitz factorable activation layers is termed as a Lipschitz factorable NN. Next, the input–output, qLPV difference equation is then realized into qLPV MIMO state space model in companion form via suitable state definitions. To demonstrate the effectiveness of the proposed method, such a realized qLPV state space model, identified from a trained NN, is used as the prediction model in a simulated sub-optimal nonlinear Model Predictive Control (MPC) example for a benchmark quadruple tank system, wherein voltages of two pumps are manipulated to control levels of two tanks.
{"title":"qLPV state space models in companion form via realization of factorable neural networks","authors":"Deepti Khimani , Machhindranath Patil , Sharad Bhartiya","doi":"10.1016/j.automatica.2025.112812","DOIUrl":"10.1016/j.automatica.2025.112812","url":null,"abstract":"<div><div>This paper introduces novel companion form realizations for quasi-Linear Parameter Varying (qLPV) state space models obtained from input–output models, which are identified using neural networks (NN). The data for training the NN is generated from a multi-input, multi-output (MIMO) dynamic system. The method, at first, trains a (possibly deep) neural network to minimize one-step or multi-step prediction errors. If the layer activation functions of the NN satisfy a certain property, labeled as Lipschitz factorability, then the NN can be cast into a quasi-linear difference equation that describe the input–output dynamics of the nonlinear MIMO system. Such a NN consisting of Lipschitz factorable activation layers is termed as a Lipschitz factorable NN. Next, the input–output, qLPV difference equation is then realized into qLPV MIMO state space model in companion form via suitable state definitions. To demonstrate the effectiveness of the proposed method, such a realized qLPV state space model, identified from a trained NN, is used as the prediction model in a simulated sub-optimal nonlinear Model Predictive Control (MPC) example for a benchmark quadruple tank system, wherein voltages of two pumps are manipulated to control levels of two tanks.</div></div>","PeriodicalId":55413,"journal":{"name":"Automatica","volume":"185 ","pages":"Article 112812"},"PeriodicalIF":5.9,"publicationDate":"2025-12-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145822794","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 : 2025-12-23DOI: 10.1016/j.automatica.2025.112780
Mohammed M.J. Alyaseen, Nikolay Atanasov, Jorge Cortes
This paper studies the design of controllers for discontinuous dynamics that ensure the safety of non-smooth sets. The safe set is represented by arbitrarily nested unions and intersections of 0-superlevel sets of differentiable functions. We show that the satisfaction of the point-wise active safety constraints only does not necessarily imply safety. This rules out the standard techniques developed for safety of continuous dynamics. This motivates the introduction of the notion of transition functions, which allow us to incorporate even the inactive safety constraints without falling into unnecessary conservatism. These functions allow system trajectories to leave a component of the nonsmooth safe set to transition to a different one. The resulting controller is then defined as the solution to a convex optimization problem, which we show is feasible and continuous wherever the system dynamics is continuous. We illustrate the effectiveness of the proposed design approach in a multi-agent coverage control problem.
{"title":"Safety-critical control of discontinuous systems with nonsmooth safe sets","authors":"Mohammed M.J. Alyaseen, Nikolay Atanasov, Jorge Cortes","doi":"10.1016/j.automatica.2025.112780","DOIUrl":"10.1016/j.automatica.2025.112780","url":null,"abstract":"<div><div>This paper studies the design of controllers for discontinuous dynamics that ensure the safety of non-smooth sets. The safe set is represented by arbitrarily nested unions and intersections of 0-superlevel sets of differentiable functions. We show that the satisfaction of the point-wise active safety constraints only does not necessarily imply safety. This rules out the standard techniques developed for safety of continuous dynamics. This motivates the introduction of the notion of transition functions, which allow us to incorporate even the inactive safety constraints without falling into unnecessary conservatism. These functions allow system trajectories to leave a component of the nonsmooth safe set to transition to a different one. The resulting controller is then defined as the solution to a convex optimization problem, which we show is feasible and continuous wherever the system dynamics is continuous. We illustrate the effectiveness of the proposed design approach in a multi-agent coverage control problem.</div></div>","PeriodicalId":55413,"journal":{"name":"Automatica","volume":"185 ","pages":"Article 112780"},"PeriodicalIF":5.9,"publicationDate":"2025-12-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145822801","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 : 2025-12-23DOI: 10.1016/j.automatica.2025.112768
David Meister , Duarte J. Antunes , Frank Allgöwer
Event-triggered control is often argued to lower the average triggering rate compared to time-triggered control while still achieving a desired control goal, e.g., the same performance level. However, this property, often called consistency, cannot be taken for granted and can be hard to analyze in many settings. In particular, the performance properties of decentralized event-triggered control schemes with respect to time-triggered control remain mostly unexplored. Therefore, in this paper, we examine these performance properties for a consensus problem considering single-integrator agent dynamics, a level-triggering rule, and a complete communication graph. We consider the long-term average quadratic deviation from consensus as a performance measure. For this setting, we show that enriching the information the local controllers use improves the performance of the consensus algorithm but renders a previously consistent event-triggered control scheme inconsistent. In addition, we do so while deploying optimal control inputs which we derive for both information cases and triggering schemes. With this insight, we can furthermore explain the relationship between two seemingly contrasting consistency results from the literature.
{"title":"How improving performance may imply losing consistency in event-triggered consensus","authors":"David Meister , Duarte J. Antunes , Frank Allgöwer","doi":"10.1016/j.automatica.2025.112768","DOIUrl":"10.1016/j.automatica.2025.112768","url":null,"abstract":"<div><div>Event-triggered control is often argued to lower the average triggering rate compared to time-triggered control while still achieving a desired control goal, e.g., the same performance level. However, this property, often called consistency, cannot be taken for granted and can be hard to analyze in many settings. In particular, the performance properties of decentralized event-triggered control schemes with respect to time-triggered control remain mostly unexplored. Therefore, in this paper, we examine these performance properties for a consensus problem considering single-integrator agent dynamics, a level-triggering rule, and a complete communication graph. We consider the long-term average quadratic deviation from consensus as a performance measure. For this setting, we show that enriching the information the local controllers use improves the performance of the consensus algorithm but renders a previously consistent event-triggered control scheme inconsistent. In addition, we do so while deploying optimal control inputs which we derive for both information cases and triggering schemes. With this insight, we can furthermore explain the relationship between two seemingly contrasting consistency results from the literature.</div></div>","PeriodicalId":55413,"journal":{"name":"Automatica","volume":"185 ","pages":"Article 112768"},"PeriodicalIF":5.9,"publicationDate":"2025-12-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145822800","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 : 2025-12-23DOI: 10.1016/j.automatica.2025.112760
Reza Samsami, Mohammad Mehdi Arefi
This paper introduces a novel policy iteration (PI) reinforcement learning (RL) technique for a hierarchical Stackelberg dynamic game for a class of continuous-time nonlinear dynamical systems including one-leader-multi-followers that concurrently handles both zero-sum (ZS) and nonzero-sum (NZS) games in the game model. At first, the leader makes decisions to learn optimal strategies of all followers. Meanwhile, each follower independently reacts optimally to the leader’s strategy by playing a Nash game with followers and a ZS game with the disturbances simultaneously. To overcome the difficulty of solving the Hamilton–Jacobi (HJ) equation resulting from this hierarchical game, and consequently finding the multiplayer Stackelberg–Nash-saddle (MSNS) equilibrium solution of the game, an adaptive dynamic programming (ADP) algorithm that employs neural network (NN) is developed. An actor-critic NNs framework is presented to solve HJ equations by estimating value functions, control policies, and disturbances. To obtain the leader’s optimal strategy, an optimal adaptive control method using NN is proposed. The convergence of NN weights and the states of the closed-loop optimal system are shown to be uniformly ultimately bounded (UUB). Finally, an example is provided to show the effectiveness of the proposed algorithm in solving the MSNS equilibrium solution with input constraints.
{"title":"Robust reinforcement learning-based controller for a class of nonlinear multiplayer Stackelberg game with input constraints","authors":"Reza Samsami, Mohammad Mehdi Arefi","doi":"10.1016/j.automatica.2025.112760","DOIUrl":"10.1016/j.automatica.2025.112760","url":null,"abstract":"<div><div>This paper introduces a novel policy iteration (PI) reinforcement learning (RL) technique for a hierarchical Stackelberg dynamic game for a class of continuous-time nonlinear dynamical systems including one-leader-multi-followers that concurrently handles both zero-sum (ZS) and nonzero-sum (NZS) games in the game model. At first, the leader makes decisions to learn optimal strategies of all followers. Meanwhile, each follower independently reacts optimally to the leader’s strategy by playing a Nash game with followers and a ZS game with the disturbances simultaneously. To overcome the difficulty of solving the Hamilton–Jacobi (HJ) equation resulting from this hierarchical game, and consequently finding the multiplayer Stackelberg–Nash-saddle (MSNS) equilibrium solution of the game, an adaptive dynamic programming (ADP) algorithm that employs neural network (NN) is developed. An actor-critic NNs framework is presented to solve HJ equations by estimating value functions, control policies, and disturbances. To obtain the leader’s optimal strategy, an optimal adaptive control method using NN is proposed. The convergence of NN weights and the states of the closed-loop optimal system are shown to be uniformly ultimately bounded (UUB). Finally, an example is provided to show the effectiveness of the proposed algorithm in solving the MSNS equilibrium solution with input constraints.</div></div>","PeriodicalId":55413,"journal":{"name":"Automatica","volume":"185 ","pages":"Article 112760"},"PeriodicalIF":5.9,"publicationDate":"2025-12-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145822797","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 : 2025-12-23DOI: 10.1016/j.automatica.2025.112769
Zhuyuan Li , Steven X. Ding , Linlin Li , Ying Yang
This article investigates the analysis and design of cyber attacks in the unified control and detection framework for cyber–physical systems (CPSs). Based on the Bezout identity, it is proved that there exists a one-to-one mapping between the I/O signals and I/O residuals. The input residual and output residual depend on cyber attacks and plant faults respectively, which is a major difference between these two factors impairing systems. Moreover, it is concluded that cyber attacks compromise the I/O signals within the plant’s image subspace. To facilitate strictly stealthy attack design, a novel image attack with a latent variable to be designed is proposed, decoupling the realization of attack objectives from stealthiness conditions. It is worth pointing out that the image attack parameterizes strictly stealthy attacks undetectable to any observer-based detector and affects the plant in the form of altering the input residual. Further, an offline attack intended to modify system operation points and an online attack aimed at moving system states to desired ones are presented to illustrate the advantages of the image attack model. Finally, a case study is demonstrated on the longitudinal flight control system to validate the proposed scheme.
{"title":"A novel cyber attack design scheme based on system subspace analysis","authors":"Zhuyuan Li , Steven X. Ding , Linlin Li , Ying Yang","doi":"10.1016/j.automatica.2025.112769","DOIUrl":"10.1016/j.automatica.2025.112769","url":null,"abstract":"<div><div>This article investigates the analysis and design of cyber attacks in the unified control and detection framework for cyber–physical systems (CPSs). Based on the Bezout identity, it is proved that there exists a one-to-one mapping between the I/O signals and I/O residuals. The input residual and output residual depend on cyber attacks and plant faults respectively, which is a major difference between these two factors impairing systems. Moreover, it is concluded that cyber attacks compromise the I/O signals within the plant’s image subspace. To facilitate strictly stealthy attack design, a novel image attack with a latent variable to be designed is proposed, decoupling the realization of attack objectives from stealthiness conditions. It is worth pointing out that the image attack parameterizes strictly stealthy attacks undetectable to any observer-based detector and affects the plant in the form of altering the input residual. Further, an offline attack intended to modify system operation points and an online attack aimed at moving system states to desired ones are presented to illustrate the advantages of the image attack model. Finally, a case study is demonstrated on the longitudinal flight control system to validate the proposed scheme.</div></div>","PeriodicalId":55413,"journal":{"name":"Automatica","volume":"185 ","pages":"Article 112769"},"PeriodicalIF":5.9,"publicationDate":"2025-12-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145822798","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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