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}
Pub Date : 2025-12-23DOI: 10.1016/j.automatica.2025.112771
Hang Xu , Kaihong Lu , Yu-Long Wang , Qixin Zhu
In this paper, the mixed equilibrium problem with coupled inequality constraints in dynamic environments is solved by employing a multi-agent system, where each agent only has access to its own bifunction, its own constraint function, and can communicate with its immediate neighbors via a time-varying digraph. At each time, the goal of agents is to cooperatively find a point in the constraint set such that the sum of local bifunctions with a free variable is non-negative. Different from existing works, here the bifunctions and the constraint functions are time-varying and only available to agents after decisions are made. To tackle this problem, first, an online distributed algorithm involving the accurate gradient information is proposed based on mirror descent algorithms and primal–dual strategies. Of particular interest is that dynamic regrets, whose offline benchmarks are to find the solution at each time, are employed to measure the performance of the algorithm. Under mild assumptions on the graph and the bifunctions, we prove that if the deviation in the solution sequence grows within a certain rate, then both the dynamic regret and the violation of coupled inequality constraints increase sublinearly. Second, considering the case where each agent only has access to a noisy estimate on the accurate gradient, we propose an online distributed algorithm involving the stochastic gradients. The result shows that under the same conditions as in the first case, if the noise distribution satisfies the sub-Gaussian condition, then dynamic regrets, as well as constraint violations, increase sublinearly with high probability. Finally, several simulation examples are presented to corroborate the validity of our results.
{"title":"Online distributed algorithms for mixed equilibrium problems in dynamic environments","authors":"Hang Xu , Kaihong Lu , Yu-Long Wang , Qixin Zhu","doi":"10.1016/j.automatica.2025.112771","DOIUrl":"10.1016/j.automatica.2025.112771","url":null,"abstract":"<div><div>In this paper, the mixed equilibrium problem with coupled inequality constraints in dynamic environments is solved by employing a multi-agent system, where each agent only has access to its own bifunction, its own constraint function, and can communicate with its immediate neighbors via a time-varying digraph. At each time, the goal of agents is to cooperatively find a point in the constraint set such that the sum of local bifunctions with a free variable is non-negative. Different from existing works, here the bifunctions and the constraint functions are time-varying and only available to agents after decisions are made. To tackle this problem, first, an online distributed algorithm involving the accurate gradient information is proposed based on mirror descent algorithms and primal–dual strategies. Of particular interest is that dynamic regrets, whose offline benchmarks are to find the solution at each time, are employed to measure the performance of the algorithm. Under mild assumptions on the graph and the bifunctions, we prove that if the deviation in the solution sequence grows within a certain rate, then both the dynamic regret and the violation of coupled inequality constraints increase sublinearly. Second, considering the case where each agent only has access to a noisy estimate on the accurate gradient, we propose an online distributed algorithm involving the stochastic gradients. The result shows that under the same conditions as in the first case, if the noise distribution satisfies the sub-Gaussian condition, then dynamic regrets, as well as constraint violations, increase sublinearly with high probability. Finally, several simulation examples are presented to corroborate the validity of our results.</div></div>","PeriodicalId":55413,"journal":{"name":"Automatica","volume":"185 ","pages":"Article 112771"},"PeriodicalIF":5.9,"publicationDate":"2025-12-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145822799","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-12-22DOI: 10.1016/j.automatica.2025.112796
Fatemeh Fardno , S. Rasoul Etesami
Motivated by applications in job scheduling, queuing networks, and load balancing in cyber–physical systems, we develop and analyze a game-theoretic framework to balance the load among servers in static and dynamic settings. In these applications, jobs/tasks are held by selfish entities that do not want to coordinate with each other, yet the goal is to balance the load among servers in a distributed manner. First, we provide a static game formulation in which each player holds a job with a specific processing requirement and wants to schedule it fractionally among a set of heterogeneous servers to minimize its average processing time. We show that this static game is a potential game with a pure Nash equilibrium (NE). In particular, the best-response dynamics converge to such an NE after iterations, where is the number of players. Additionally, we bound the price of anarchy (PoA) of the static game in terms of game parameters. We then extend our results to a dynamic game setting, where jobs arrive and get processed, and players observe the load on the servers to decide how to schedule their jobs. In this setting, we show that if the players update their strategies using dynamic best-response, the system eventually becomes fully load-balanced and the players’ strategies converge to the pure NE of the static game. In particular, we show that the convergence time scales only polynomially with respect to the game parameters. Finally, we provide numerical results to evaluate the performance of our proposed algorithms.
{"title":"A game-theoretic framework for distributed load balancing: Static and dynamic game models","authors":"Fatemeh Fardno , S. Rasoul Etesami","doi":"10.1016/j.automatica.2025.112796","DOIUrl":"10.1016/j.automatica.2025.112796","url":null,"abstract":"<div><div>Motivated by applications in job scheduling, queuing networks, and load balancing in cyber–physical systems, we develop and analyze a game-theoretic framework to balance the load among servers in static and dynamic settings. In these applications, jobs/tasks are held by selfish entities that do not want to coordinate with each other, yet the goal is to balance the load among servers in a distributed manner. First, we provide a static game formulation in which each player holds a job with a specific processing requirement and wants to schedule it fractionally among a set of heterogeneous servers to minimize its average processing time. We show that this static game is a potential game with a pure Nash equilibrium (NE). In particular, the best-response dynamics converge to such an NE after <span><math><mi>n</mi></math></span> iterations, where <span><math><mi>n</mi></math></span> is the number of players. Additionally, we bound the price of anarchy (PoA) of the static game in terms of game parameters. We then extend our results to a dynamic game setting, where jobs arrive and get processed, and players observe the load on the servers to decide how to schedule their jobs. In this setting, we show that if the players update their strategies using dynamic best-response, the system eventually becomes fully load-balanced and the players’ strategies converge to the pure NE of the static game. In particular, we show that the convergence time scales only polynomially with respect to the game parameters. Finally, we provide numerical results to evaluate the performance of our proposed algorithms.</div></div>","PeriodicalId":55413,"journal":{"name":"Automatica","volume":"185 ","pages":"Article 112796"},"PeriodicalIF":5.9,"publicationDate":"2025-12-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145841282","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-12-22DOI: 10.1016/j.automatica.2025.112783
Linghuan Kong , Wei He , Carlos Silvestre
This paper proposes a novel two-layer prescribed performance control strategy for underactuated unmanned aerial vehicles (UAVs) with unknown mass. Unlike conventional approaches that heavily rely on barrier functions—often producing large control signals and potential instability due to actuator limitations—the proposed method introduces soft and hard performance bounds on position and velocity errors. A smooth switching mechanism selectively activates the barrier function, thereby reducing its usage and enhancing system robustness. To accommodate these bounds, a new integral-multiplicative barrier-like (IMBL) Lyapunov function is developed to determine the desired thrust. Second-order linear systems are employed as low-pass filters in the backstepping design, lowering computational complexity and improving robustness against disturbances. An adaptive law is integrated into the framework for real-time mass estimation, and torque inputs are derived accordingly. Simulation results demonstrate the effectiveness of the method and validate the theoretical analysis.
{"title":"A two-layer adaptive control framework for prescribed performance in unmanned aerial vehicles","authors":"Linghuan Kong , Wei He , Carlos Silvestre","doi":"10.1016/j.automatica.2025.112783","DOIUrl":"10.1016/j.automatica.2025.112783","url":null,"abstract":"<div><div>This paper proposes a novel two-layer prescribed performance control strategy for underactuated unmanned aerial vehicles (UAVs) with unknown mass. Unlike conventional approaches that heavily rely on barrier functions—often producing large control signals and potential instability due to actuator limitations—the proposed method introduces soft and hard performance bounds on position and velocity errors. A smooth switching mechanism selectively activates the barrier function, thereby reducing its usage and enhancing system robustness. To accommodate these bounds, a new integral-multiplicative barrier-like (IMBL) Lyapunov function is developed to determine the desired thrust. Second-order linear systems are employed as low-pass filters in the backstepping design, lowering computational complexity and improving robustness against disturbances. An adaptive law is integrated into the framework for real-time mass estimation, and torque inputs are derived accordingly. Simulation results demonstrate the effectiveness of the method and validate the theoretical analysis.</div></div>","PeriodicalId":55413,"journal":{"name":"Automatica","volume":"185 ","pages":"Article 112783"},"PeriodicalIF":5.9,"publicationDate":"2025-12-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145841800","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-12-22DOI: 10.1016/j.automatica.2025.112765
Liuliu Zhang, Xianglin Liu, Changchun Hua
This paper focuses on the problem of the prescribed-time output feedback control for a class of uncertain nonlinear systems subjected to unknown non-differentiable measurement sensitivity along with the presence of an arbitrary large sensitivity error. To deal with the obstacle arising from such a severe sensitivity condition for prescribed-time control, a pair of novel non-homogeneous order prescribed-time functions and asymmetric state transformations are introduced. And the dual dynamic gain is constructed to compensate for the uncertainty and the polynomial growth rate of the system online. Then, a novel multi-gain-based prescribed-time output feedback control scheme is developed based on the proposed multi-gain, which ensures the boundedness of all closed-loop system signals and drives the states to reach the equilibrium point at any prescribed time. Finally, a simulation example based on the real system demonstrates the effectiveness of the algorithm.
{"title":"Prescribed-time output feedback control for nonlinear systems with unknown measurement sensitivity","authors":"Liuliu Zhang, Xianglin Liu, Changchun Hua","doi":"10.1016/j.automatica.2025.112765","DOIUrl":"10.1016/j.automatica.2025.112765","url":null,"abstract":"<div><div>This paper focuses on the problem of the prescribed-time output feedback control for a class of uncertain nonlinear systems subjected to unknown non-differentiable measurement sensitivity along with the presence of an arbitrary large sensitivity error. To deal with the obstacle arising from such a severe sensitivity condition for prescribed-time control, a pair of novel non-homogeneous order prescribed-time functions and asymmetric state transformations are introduced. And the dual dynamic gain is constructed to compensate for the uncertainty and the polynomial growth rate of the system online. Then, a novel multi-gain-based prescribed-time output feedback control scheme is developed based on the proposed multi-gain, which ensures the boundedness of all closed-loop system signals and drives the states to reach the equilibrium point at any prescribed time. Finally, a simulation example based on the real system demonstrates the effectiveness of the algorithm.</div></div>","PeriodicalId":55413,"journal":{"name":"Automatica","volume":"185 ","pages":"Article 112765"},"PeriodicalIF":5.9,"publicationDate":"2025-12-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145841726","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-12-22DOI: 10.1016/j.automatica.2025.112749
Zhenhua Deng , Xiang-Peng Xie
As cyber–physical systems march toward intelligence, physical systems have the ability to execute distributed game tasks autonomously. Hence this paper focuses on multi-coalition games (MCGs) of autonomous high-order nonlinear players (HNPs). The intra-coalition communication networks are not connected in our problem, distinct from almost all existing MCGs. Moreover, here there are local nonlinear convex inequalities, intra-coalition and inter-coalition coupling nonlinear convex inequalities, different from most of works about MCGs of physical systems. Mainly attributed to the high-order nonlinear dynamics, the unconnected intra-coalition communications and/or the nonlinear convex constraints, existing methods cannot solve our problem. Also, these characteristics put a crime in the strategy design and analysis of our problem. For the purpose of steering the heterogeneous HNPs to autonomously seek the variational generalized Nash equilibrium (vGNE) of MCGs, a distributed strategy is proposed by utilizing primal–dual methods and state feedback. Supported by Lasalle invariance principle, our strategy is analyzed rigorously. Under our strategy, all HNPs globally converge to the exact vGNE. Finally, the merits of our strategy are verified by two examples.
{"title":"Distributed strategy for autonomous nonlinear multi-coalition games of high-order players over unconnected intra-coalition communications","authors":"Zhenhua Deng , Xiang-Peng Xie","doi":"10.1016/j.automatica.2025.112749","DOIUrl":"10.1016/j.automatica.2025.112749","url":null,"abstract":"<div><div>As cyber–physical systems march toward intelligence, physical systems have the ability to execute distributed game tasks autonomously. Hence this paper focuses on multi-coalition games (MCGs) of autonomous high-order nonlinear players (HNPs). The intra-coalition communication networks are not connected in our problem, distinct from almost all existing MCGs. Moreover, here there are local nonlinear convex inequalities, intra-coalition and inter-coalition coupling nonlinear convex inequalities, different from most of works about MCGs of physical systems. Mainly attributed to the high-order nonlinear dynamics, the unconnected intra-coalition communications and/or the nonlinear convex constraints, existing methods cannot solve our problem. Also, these characteristics put a crime in the strategy design and analysis of our problem. For the purpose of steering the heterogeneous HNPs to autonomously seek the variational generalized Nash equilibrium (vGNE) of MCGs, a distributed strategy is proposed by utilizing primal–dual methods and state feedback. Supported by Lasalle invariance principle, our strategy is analyzed rigorously. Under our strategy, all HNPs globally converge to the exact vGNE. Finally, the merits of our strategy are verified by two examples.</div></div>","PeriodicalId":55413,"journal":{"name":"Automatica","volume":"185 ","pages":"Article 112749"},"PeriodicalIF":5.9,"publicationDate":"2025-12-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145841797","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-12-22DOI: 10.1016/j.automatica.2025.112784
Laura Menini, Corrado Possieri, Antonio Tornambe
In this communique, an algorithm is proposed to solve symbolically the model matching problem for single input single output systems. A solution to such a problem has been proposed in Doyle et al. (1990) using the Nevanlinna–Pick theory. However, when implementing such a procedure numerically, some issues may arise due to imperfect cancellations among the numerator and the denominator of the obtained controller. The proposed algorithm overcomes such issues by using some algebraic geometry results to solve exactly the problem.
{"title":"An algebraic approach to solve the model matching problem for single input single output systems","authors":"Laura Menini, Corrado Possieri, Antonio Tornambe","doi":"10.1016/j.automatica.2025.112784","DOIUrl":"10.1016/j.automatica.2025.112784","url":null,"abstract":"<div><div>In this communique, an algorithm is proposed to solve symbolically the model matching problem for single input single output systems. A solution to such a problem has been proposed in Doyle et al. (1990) using the Nevanlinna–Pick theory. However, when implementing such a procedure numerically, some issues may arise due to imperfect cancellations among the numerator and the denominator of the obtained controller. The proposed algorithm overcomes such issues by using some algebraic geometry results to solve exactly the problem.</div></div>","PeriodicalId":55413,"journal":{"name":"Automatica","volume":"185 ","pages":"Article 112784"},"PeriodicalIF":5.9,"publicationDate":"2025-12-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145841801","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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