This paper considers robust-safety notions for differential inclusions. A general framework is proposed to certify the considered notions in terms of barrier functions. While most existing literature has focused solely on what we designate as uniform robust safety, in this paper, we make a clear distinction between uniform and non-uniform robust safety. For both cases, we establish sufficient conditions on the nominal (unperturbed) system. Our conditions involve only the barrier function and the system’s right-hand side. Our results allow for unbounded safety regions as well as non-smooth barrier functions. The paper concludes with applications to safety-critical self-triggered control and fast-slow dynamics as well as assume–guarantee contracts.
{"title":"Sufficient conditions for robust safety in differential inclusions using barrier functions","authors":"Mohamed Adlene Maghenem , Masoumeh Ghanbarpour Mamaghani , Adnane Saoud","doi":"10.1016/j.automatica.2024.111938","DOIUrl":"10.1016/j.automatica.2024.111938","url":null,"abstract":"<div><div>This paper considers <em>robust-safety</em> notions for differential inclusions. A general framework is proposed to certify the considered notions in terms of barrier functions. While most existing literature has focused solely on what we designate as <em>uniform robust safety</em>, in this paper, we make a clear distinction between uniform and non-uniform robust safety. For both cases, we establish sufficient conditions on the nominal (unperturbed) system. Our conditions involve only the barrier function and the system’s right-hand side. Our results allow for unbounded safety regions as well as non-smooth barrier functions. The paper concludes with applications to safety-critical self-triggered control and fast-slow dynamics as well as assume–guarantee contracts.</div></div>","PeriodicalId":55413,"journal":{"name":"Automatica","volume":"171 ","pages":"Article 111938"},"PeriodicalIF":4.8,"publicationDate":"2024-09-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142356711","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 : 2024-09-30DOI: 10.1016/j.automatica.2024.111962
Zirui Chen , Zongyu Zuo
The present article introduces the concept of a non-singular cooperative guiding vector field under a homotopy equivalence transformation. Initially, an innovative non-singular guiding vector field is derived, which is capable of guiding the controlled robot to follow a path in a moving frame. Furthermore, the properties of homotopy equivalence transformation are explored to establish the existence of the aforementioned vector field. Subsequently, a cooperative vector field, based on an extensive parameter consensus protocol, is introduced, including an in-depth analysis of the impact of vector field parameters. Then, the practical implementation of this innovative vector field is demonstrated through its application to cooperative path following in both 2-D and 3-D scenarios, showcasing its effectiveness. Finally, for a non-holonomic robot at constant speed, a moving path following control law based on the guiding vector field is presented, along with a discussion on speed constraint.
{"title":"Non-singular cooperative guiding vector field under a homotopy equivalence transformation","authors":"Zirui Chen , Zongyu Zuo","doi":"10.1016/j.automatica.2024.111962","DOIUrl":"10.1016/j.automatica.2024.111962","url":null,"abstract":"<div><div>The present article introduces the concept of a non-singular cooperative guiding vector field under a homotopy equivalence transformation. Initially, an innovative non-singular guiding vector field is derived, which is capable of guiding the controlled robot to follow a path in a moving frame. Furthermore, the properties of homotopy equivalence transformation are explored to establish the existence of the aforementioned vector field. Subsequently, a cooperative vector field, based on an extensive parameter consensus protocol, is introduced, including an in-depth analysis of the impact of vector field parameters. Then, the practical implementation of this innovative vector field is demonstrated through its application to cooperative path following in both 2-D and 3-D scenarios, showcasing its effectiveness. Finally, for a non-holonomic robot at constant speed, a moving path following control law based on the guiding vector field is presented, along with a discussion on speed constraint.</div></div>","PeriodicalId":55413,"journal":{"name":"Automatica","volume":"171 ","pages":"Article 111962"},"PeriodicalIF":4.8,"publicationDate":"2024-09-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142356911","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 : 2024-09-30DOI: 10.1016/j.automatica.2024.111960
Bao Wang , Quanxin Zhu
This paper studies the stabilization problem for a class of discrete-time semi-Markov jump singular systems with mode-dependent singular matrix. Since our model is mode-dependent singular matrix, the previous methods are unable to achieve the stability. To overcome this difficulty, the novel and less conservative stability conditions with the original system coefficient matrices are constructed by developing new theories and methods. Based on the above conditions, the linear matrix inequality (LMI) based stabilizing controller design method is proposed.
{"title":"The stabilization problem for a class of discrete-time semi-Markov jump singular systems","authors":"Bao Wang , Quanxin Zhu","doi":"10.1016/j.automatica.2024.111960","DOIUrl":"10.1016/j.automatica.2024.111960","url":null,"abstract":"<div><div>This paper studies the stabilization problem for a class of discrete-time semi-Markov jump singular systems with mode-dependent singular matrix. Since our model is mode-dependent singular matrix, the previous methods are unable to achieve the stability. To overcome this difficulty, the novel and less conservative stability conditions with the original system coefficient matrices are constructed by developing new theories and methods. Based on the above conditions, the linear matrix inequality (LMI) based stabilizing controller design method is proposed.</div></div>","PeriodicalId":55413,"journal":{"name":"Automatica","volume":"171 ","pages":"Article 111960"},"PeriodicalIF":4.8,"publicationDate":"2024-09-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142356821","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 : 2024-09-30DOI: 10.1016/j.automatica.2024.111966
Jianqi Chen
This study initially addresses the state estimation problem for discrete-time linear time-invariant systems under the influence of both exogenous attacks and random noises. As the filtering side, we make no prior assumptions or have any prior knowledge about the nature of attacks. We employ a specific unknown input filtering approach, which has been examined in prior research, to simultaneously estimate both the system states and attacks. Differing from existing works, our emphasis on full accessibility attacks, a particular class of unknown inputs, reveals that the dynamic estimation gains of the adopted filtering reduce directly to static ones. The second contribution of this study is to mitigate the influence of attacks by utilizing the estimated attack signals. Under this strategy, the deviation between nominal states and attacked states is characterized by evaluating the upper bound of the covariance matrix of the errors.
{"title":"Unknown input filtering under full accessibility attacks","authors":"Jianqi Chen","doi":"10.1016/j.automatica.2024.111966","DOIUrl":"10.1016/j.automatica.2024.111966","url":null,"abstract":"<div><div>This study initially addresses the state estimation problem for discrete-time linear time-invariant systems under the influence of both exogenous attacks and random noises. As the filtering side, we make no prior assumptions or have any prior knowledge about the nature of attacks. We employ a specific unknown input filtering approach, which has been examined in prior research, to simultaneously estimate both the system states and attacks. Differing from existing works, our emphasis on full accessibility attacks, a particular class of unknown inputs, reveals that the dynamic estimation gains of the adopted filtering reduce directly to static ones. The second contribution of this study is to mitigate the influence of attacks by utilizing the estimated attack signals. Under this strategy, the deviation between nominal states and attacked states is characterized by evaluating the upper bound of the covariance matrix of the errors.</div></div>","PeriodicalId":55413,"journal":{"name":"Automatica","volume":"171 ","pages":"Article 111966"},"PeriodicalIF":4.8,"publicationDate":"2024-09-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142356665","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 : 2024-09-30DOI: 10.1016/j.automatica.2024.111956
Ren-Xi Zhao , Bao-Zhu Guo , Lassi Paunonen
Over the past few years, the internal model principle has been extended to some systems described by one-dimensional partial differential equations (PDEs) from the PDE perspective. However, robustness has remained limited to specific cases, primarily due to the challenges in formulating it within the PDE framework. In this paper, we explore output regulation for a multi-dimensional heat equation under boundary control, where the output space is infinite-dimensional. We not only derive an analytic tracking error feedback control but also demonstrate robustness. This is achieved by leveraging abstract results and PDE design techniques.
{"title":"Robust output regulation for multi-dimensional heat equation under boundary control","authors":"Ren-Xi Zhao , Bao-Zhu Guo , Lassi Paunonen","doi":"10.1016/j.automatica.2024.111956","DOIUrl":"10.1016/j.automatica.2024.111956","url":null,"abstract":"<div><div>Over the past few years, the internal model principle has been extended to some systems described by one-dimensional partial differential equations (PDEs) from the PDE perspective. However, robustness has remained limited to specific cases, primarily due to the challenges in formulating it within the PDE framework. In this paper, we explore output regulation for a multi-dimensional heat equation under boundary control, where the output space is infinite-dimensional. We not only derive an analytic tracking error feedback control but also demonstrate robustness. This is achieved by leveraging abstract results and PDE design techniques.</div></div>","PeriodicalId":55413,"journal":{"name":"Automatica","volume":"171 ","pages":"Article 111956"},"PeriodicalIF":4.8,"publicationDate":"2024-09-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142356668","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 : 2024-09-28DOI: 10.1016/j.automatica.2024.111916
Daniel E. Ochoa, Jorge I. Poveda
It is well known that smooth autonomous dynamical systems modeled by ordinary differential equations (ODEs) cannot robustly and globally stabilize a point on compact, boundaryless manifolds. This obstruction, which is topological in nature, has significant implications for optimization problems, rendering traditional continuous-time algorithms incapable of robustly solving global optimization problems in such spaces. In turn, gradient-free optimization algorithms, which usually inherit their stability and convergence properties from their gradient-based counterparts, can also suffer from similar topological obstructions. For instance, this is the case in zeroth-order methods and perturbation-based techniques, where gradients and Hessian matrices are usually estimated in real-time via measurements or evaluations of the cost function. To address this problem, in this paper we introduce a novel class of hybrid gradient-free optimization dynamics that combine continuous-time and discrete-time feedback to overcome the obstructions that emerge in traditional ODE-based optimization algorithms evolving on smooth compact manifolds. The proposed hybrid dynamics switch between different gradient-free feedback-laws obtained by applying suitable exploratory geodesic dithers to a family of synergistic diffeomorphisms adapted to the cost function that defines the optimization problem. The use of geodesic dithers enables a suitable exploration of the manifold while simultaneously preserving its forward invariance, a property that is fundamental for many practical applications with physics-based constraints. The hybrid dynamics exploit the information obtained from the geodesic dithers to achieve robust global practical stability of the set of minimizers of the cost function. This stabilization is achieved without having direct access to the gradients of the cost functions, but rather using only real-time and continuous evaluations of the cost. Examples and numerical results are presented to illustrate the main ideas and advantages of the method.
{"title":"Robust global optimization on smooth compact manifolds via hybrid gradient-free dynamics","authors":"Daniel E. Ochoa, Jorge I. Poveda","doi":"10.1016/j.automatica.2024.111916","DOIUrl":"10.1016/j.automatica.2024.111916","url":null,"abstract":"<div><div>It is well known that smooth autonomous dynamical systems modeled by ordinary differential equations (ODEs) cannot robustly and globally stabilize a point on compact, boundaryless manifolds. This obstruction, which is topological in nature, has significant implications for optimization problems, rendering traditional continuous-time algorithms incapable of robustly solving <em>global</em> optimization problems in such spaces. In turn, <em>gradient-free</em> optimization algorithms, which usually inherit their stability and convergence properties from their gradient-based counterparts, can also suffer from similar topological obstructions. For instance, this is the case in zeroth-order methods and perturbation-based techniques, where gradients and Hessian matrices are usually estimated in real-time via measurements or evaluations of the cost function. To address this problem, in this paper we introduce a novel class of <em>hybrid gradient-free optimization dynamics</em> that combine continuous-time and discrete-time feedback to overcome the obstructions that emerge in traditional ODE-based optimization algorithms evolving on smooth compact manifolds. The proposed hybrid dynamics switch between different gradient-free feedback-laws obtained by applying suitable exploratory <em>geodesic dithers</em> to a family of synergistic diffeomorphisms adapted to the cost function that defines the optimization problem. The use of geodesic dithers enables a suitable exploration of the manifold while simultaneously preserving its forward invariance, a property that is fundamental for many practical applications with physics-based constraints. The hybrid dynamics exploit the information obtained from the geodesic dithers to achieve robust global practical stability of the set of minimizers of the cost function. This stabilization is achieved without having direct access to the gradients of the cost functions, but rather using only real-time and continuous evaluations of the cost. Examples and numerical results are presented to illustrate the main ideas and advantages of the method.</div></div>","PeriodicalId":55413,"journal":{"name":"Automatica","volume":"171 ","pages":"Article 111916"},"PeriodicalIF":4.8,"publicationDate":"2024-09-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142356710","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-09-28DOI: 10.1016/j.automatica.2024.111927
Lechen Feng, Yuan-Hua Ni
This paper introduces an accelerated optimization framework of handling the linear–quadratic regulator (LQR) problem. Firstly, a Lipschitz Hessian property of LQR cost is presented, which turns out to be a crucial property for the application of modern optimization techniques. Secondly, a Nesterov-type method with a restarting rule is proposed for state-feedback LQR problem, which can converge exponentially to the optimal feedback gain with Nesterov-optimal order . Thirdly, a Hessian-free two-procedure accelerated framework is proposed for output-feedback LQR problem, which can find an -stationary point with second-order guarantee.
{"title":"Accelerated optimization landscape of linear–quadratic regulator","authors":"Lechen Feng, Yuan-Hua Ni","doi":"10.1016/j.automatica.2024.111927","DOIUrl":"10.1016/j.automatica.2024.111927","url":null,"abstract":"<div><div>This paper introduces an accelerated optimization framework of handling the linear–quadratic regulator (LQR) problem. Firstly, a Lipschitz Hessian property of LQR cost is presented, which turns out to be a crucial property for the application of modern optimization techniques. Secondly, a Nesterov-type method with a restarting rule is proposed for state-feedback LQR problem, which can converge exponentially to the optimal feedback gain with Nesterov-optimal order <span><math><mrow><mn>1</mn><mo>−</mo><mn>1</mn><mo>/</mo><msqrt><mrow><mi>κ</mi></mrow></msqrt></mrow></math></span>. Thirdly, a Hessian-free two-procedure accelerated framework is proposed for output-feedback LQR problem, which can find an <span><math><mi>ϵ</mi></math></span>-stationary point with second-order guarantee.</div></div>","PeriodicalId":55413,"journal":{"name":"Automatica","volume":"171 ","pages":"Article 111927"},"PeriodicalIF":4.8,"publicationDate":"2024-09-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142356822","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 : 2024-09-27DOI: 10.1016/j.automatica.2024.111923
Francisco J. Vargas , Marco A. Gordon , Andrés A. Peters , Alejandro I. Maass
This paper addresses the string stabilization of vehicular platooning when stochastic phenomena are inherent in inter-vehicle communication. To achieve this, we first provide two definitions to analytically assess the string stability in stochastic scenarios, considering the mean and variance of tracking errors as the platoon size grows. Subsequently, we analytically derive necessary and sufficient conditions to achieve this notion of string stability in predecessor-following linear platoons that communicate through additive white noise channels. We conclude that the condition ensuring string stability with ideal communication is essentially the same that achieves stochastic string stability when additive noise channels are in place and guarantees that the tracking error means and variances converge.
{"title":"On stochastic string stability with applications to platooning over additive noise channels","authors":"Francisco J. Vargas , Marco A. Gordon , Andrés A. Peters , Alejandro I. Maass","doi":"10.1016/j.automatica.2024.111923","DOIUrl":"10.1016/j.automatica.2024.111923","url":null,"abstract":"<div><div>This paper addresses the string stabilization of vehicular platooning when stochastic phenomena are inherent in inter-vehicle communication. To achieve this, we first provide two definitions to analytically assess the string stability in stochastic scenarios, considering the mean and variance of tracking errors as the platoon size grows. Subsequently, we analytically derive necessary and sufficient conditions to achieve this notion of string stability in predecessor-following linear platoons that communicate through additive white noise channels. We conclude that the condition ensuring string stability with ideal communication is essentially the same that achieves stochastic string stability when additive noise channels are in place and guarantees that the tracking error means and variances converge.</div></div>","PeriodicalId":55413,"journal":{"name":"Automatica","volume":"171 ","pages":"Article 111923"},"PeriodicalIF":4.8,"publicationDate":"2024-09-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142324022","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 : 2024-09-27DOI: 10.1016/j.automatica.2024.111925
Dong Wang, Jiaxun Liu, Jie Lian, Wei Wang
This paper studies the design of accelerated distributed algorithms for seeking the Nash Equilibrium (NE) of multiple cluster games over time-varying unbalanced digraphs, where players in the same cluster cooperatively minimize the summation of the local cost function and do not concern the interest of other clusters. In this game, the players have limited access to others’ decisions, while they can communicate with others over the inter-cluster and intra-cluster topologies. Accelerated distributed algorithms are proposed based on the decision estimation, Nesterov acceleration, and pseudo gradient estimation to seek the NE of multiple cluster games. We prove that the proposed algorithm linearly converges to the NE using the multistep contraction and linear systems of inequalities. Moreover, three variants of the proposed algorithm are also given for dealing with cases where only partial communication topologies are time-varying and gossip-type. Lastly, the effectiveness of proposed algorithms and the acceleration effect are verified by solving the intrusion–interception confrontation problem of Unmanned Vehicle (UV) swarms in simulations.
{"title":"Gradient-tracking-based distributed Nesterov accelerated algorithms for multiple cluster games over time-varying unbalanced digraphs","authors":"Dong Wang, Jiaxun Liu, Jie Lian, Wei Wang","doi":"10.1016/j.automatica.2024.111925","DOIUrl":"10.1016/j.automatica.2024.111925","url":null,"abstract":"<div><div>This paper studies the design of accelerated distributed algorithms for seeking the Nash Equilibrium (NE) of multiple cluster games over time-varying unbalanced digraphs, where players in the same cluster cooperatively minimize the summation of the local cost function and do not concern the interest of other clusters. In this game, the players have limited access to others’ decisions, while they can communicate with others over the inter-cluster and intra-cluster topologies. Accelerated distributed algorithms are proposed based on the decision estimation, Nesterov acceleration, and pseudo gradient estimation to seek the NE of multiple cluster games. We prove that the proposed algorithm linearly converges to the NE using the multistep contraction and linear systems of inequalities. Moreover, three variants of the proposed algorithm are also given for dealing with cases where only partial communication topologies are time-varying and gossip-type. Lastly, the effectiveness of proposed algorithms and the acceleration effect are verified by solving the intrusion–interception confrontation problem of Unmanned Vehicle (UV) swarms in simulations.</div></div>","PeriodicalId":55413,"journal":{"name":"Automatica","volume":"171 ","pages":"Article 111925"},"PeriodicalIF":4.8,"publicationDate":"2024-09-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142324023","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 : 2024-09-27DOI: 10.1016/j.automatica.2024.111931
Xiang Xu , Bin Li
This paper addresses the semi-global stabilization problem of parabolic PDE–ODE systems with input saturation. Two low-gain controllers are proposed for two types of systems. It is shown that the proposed controllers can solve the semi-global stabilization problem of the concerned parabolic PDE–ODE systems with input saturation. Distributed-diffusion, counter-convection and Robin boundary condition are simultaneously considered. Moreover, the controllability of PDE–ODE systems with input saturation is discussed. It is shown that semi-global stabilization is impossible if the open-loop ODE system is exponentially unstable, which is another distinctive contribution of this work. Two illustrative examples are given to show the effectiveness of our proposed low-gain controllers.
{"title":"Semi-global stabilization of parabolic PDE–ODE systems with input saturation","authors":"Xiang Xu , Bin Li","doi":"10.1016/j.automatica.2024.111931","DOIUrl":"10.1016/j.automatica.2024.111931","url":null,"abstract":"<div><div>This paper addresses the semi-global stabilization problem of parabolic PDE–ODE systems with input saturation. Two low-gain controllers are proposed for two types of systems. It is shown that the proposed controllers can solve the semi-global stabilization problem of the concerned parabolic PDE–ODE systems with input saturation. Distributed-diffusion, counter-convection and Robin boundary condition are simultaneously considered. Moreover, the controllability of PDE–ODE systems with input saturation is discussed. It is shown that semi-global stabilization is impossible if the open-loop ODE system is exponentially unstable, which is another distinctive contribution of this work. Two illustrative examples are given to show the effectiveness of our proposed low-gain controllers.</div></div>","PeriodicalId":55413,"journal":{"name":"Automatica","volume":"171 ","pages":"Article 111931"},"PeriodicalIF":4.8,"publicationDate":"2024-09-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142328328","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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