Pub Date : 2024-10-10DOI: 10.1016/j.ejcon.2024.101124
In this paper, we focus on the control problem of mean square consensus for second-order continuous-time multi-agent systems with multiplicative noises under Markovian switching topologies. A new Lyapunov function based on the Laplacian matrix of the corresponding union topology of all possible topologies is designed for the stochastic stability analysis of consensus. Applying matrix theory and stochastic stability for stochastic differential equations, we can analyze the consensus problem of the considered systems with the designed Lyapunov function. In addition, we present the sufficient conditions of the mean square consensus exponentially for the considered stochastic systems. Finally, we give an simulation example to numerically validate our theoretical results.
{"title":"Consensus for discrete-time second-order multi-agent systems in the presence of noises and semi-Markovian switching topologies","authors":"","doi":"10.1016/j.ejcon.2024.101124","DOIUrl":"10.1016/j.ejcon.2024.101124","url":null,"abstract":"<div><div>In this paper, we focus on the control problem of mean square consensus for second-order continuous-time multi-agent systems with multiplicative noises under Markovian switching topologies. A new Lyapunov function based on the Laplacian matrix of the corresponding union topology of all possible topologies is designed for the stochastic stability analysis of consensus. Applying matrix theory and stochastic stability for stochastic differential equations, we can analyze the consensus problem of the considered systems with the designed Lyapunov function. In addition, we present the sufficient conditions of the mean square consensus exponentially for the considered stochastic systems. Finally, we give an simulation example to numerically validate our theoretical results.</div></div>","PeriodicalId":50489,"journal":{"name":"European Journal of Control","volume":null,"pages":null},"PeriodicalIF":2.5,"publicationDate":"2024-10-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142445392","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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 : 2024-10-10DOI: 10.1016/j.ejcon.2024.101125
Finite-time stability (FTS) has garnered considerable attention within the realm of control theory as a subject of active research. The objective of this paper is to explore the FTS of switched systems by employing a novel approach that relies on the concept of average dwell time (ADT). The ADT serves as a metric for quantifying the average duration a system remains in a specific mode prior to transitioning to a different mode. In this context, a condition that establishes the sufficiency of achieving FTS for a switched system has been derived in terms of the ADT and the corresponding Lyapunov function. Numerical simulations have been conducted to assess the efficacy of the proposed approach. Achieving a stable state within a specific time frame is crucial in many practical applications to meet desired performance requirements. The outcomes of this study have the potential to advance the development of more effective and reliable control systems across various engineering domains, including robotics, power systems, and transportation systems, which are often modeled as switched systems.
{"title":"Finite time stability condition for switched systems under restricted switching","authors":"","doi":"10.1016/j.ejcon.2024.101125","DOIUrl":"10.1016/j.ejcon.2024.101125","url":null,"abstract":"<div><div>Finite-time stability (FTS) has garnered considerable attention within the realm of control theory as a subject of active research. The objective of this paper is to explore the FTS of switched systems by employing a novel approach that relies on the concept of average dwell time (ADT). The ADT serves as a metric for quantifying the average duration a system remains in a specific mode prior to transitioning to a different mode. In this context, a condition that establishes the sufficiency of achieving FTS for a switched system has been derived in terms of the ADT and the corresponding Lyapunov function. Numerical simulations have been conducted to assess the efficacy of the proposed approach. Achieving a stable state within a specific time frame is crucial in many practical applications to meet desired performance requirements. The outcomes of this study have the potential to advance the development of more effective and reliable control systems across various engineering domains, including robotics, power systems, and transportation systems, which are often modeled as switched systems.</div></div>","PeriodicalId":50489,"journal":{"name":"European Journal of Control","volume":null,"pages":null},"PeriodicalIF":2.5,"publicationDate":"2024-10-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142445393","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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 : 2024-10-09DOI: 10.1016/j.ejcon.2024.101119
This paper presents a comprehensive control framework tailored for achieving Prescribed Performance Control (PPC) in the context of complex nonlinear systems, addressing multifaceted challenges prevalent in control design. The focus is on a control scenario characterized by the simultaneous presence of nonlinearity, external disturbances, time delay, and unknown control direction—issues that pose considerable obstacles for existing solutions. To surmount these challenges, our proposed approach integrates well-established techniques, including neural networks, Nussbaum-type gains, and adaptive control strategies within a unified control design framework. The specific technical challenge addressed in this work involves the effective management of these intricate complexities in Single-Input Single-Output (SISO) systems. Our contributions extend the theoretical foundations, presenting an ideal PPC control design and introducing two adaptive neural network-based control methods capable of accommodating both known and unknown control directions. Utilizing Lyapunov–Krasovskii functionals, we showcase a unique integration that surpasses a mere combination of individual techniques. This work advances the theoretical underpinnings of control engineering tailored for real-world scenarios. The proposed controller’s efficacy is validated through rigorous simulations and compared with recent results and benchmark PPC controllers, establishing its superiority in addressing the intricacies of complex control scenarios.
{"title":"A comprehensive control paradigm for prescribed performance attainment in complex nonlinear systems","authors":"","doi":"10.1016/j.ejcon.2024.101119","DOIUrl":"10.1016/j.ejcon.2024.101119","url":null,"abstract":"<div><div>This paper presents a comprehensive control framework tailored for achieving Prescribed Performance Control (PPC) in the context of complex nonlinear systems, addressing multifaceted challenges prevalent in control design. The focus is on a control scenario characterized by the simultaneous presence of nonlinearity, external disturbances, time delay, and unknown control direction—issues that pose considerable obstacles for existing solutions. To surmount these challenges, our proposed approach integrates well-established techniques, including neural networks, Nussbaum-type gains, and adaptive control strategies within a unified control design framework. The specific technical challenge addressed in this work involves the effective management of these intricate complexities in Single-Input Single-Output (SISO) systems. Our contributions extend the theoretical foundations, presenting an ideal PPC control design and introducing two adaptive neural network-based control methods capable of accommodating both known and unknown control directions. Utilizing Lyapunov–Krasovskii functionals, we showcase a unique integration that surpasses a mere combination of individual techniques. This work advances the theoretical underpinnings of control engineering tailored for real-world scenarios. The proposed controller’s efficacy is validated through rigorous simulations and compared with recent results and benchmark PPC controllers, establishing its superiority in addressing the intricacies of complex control scenarios.</div></div>","PeriodicalId":50489,"journal":{"name":"European Journal of Control","volume":null,"pages":null},"PeriodicalIF":2.5,"publicationDate":"2024-10-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142423229","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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.ejcon.2024.101120
This paper studies resilient distributed consensus in networks lacking the structural robustness necessary for achieving consensus in the presence of misbehaving agents. Existing resilient consensus solutions, including widely adapted weighted mean subsequence reduced (WMSR) resilient consensus algorithm, present robustness conditions guaranteeing consensus among normal agents. However, when the graph is less robust than required, they only inform that agents fail to achieve consensus and do not evaluate the network performance comprehensively in such non-ideal scenarios. To address this limitation, we analyze the performance of resilient consensus in non-ideal situations by introducing the concept of non-convergent nodes. These nodes/agents cannot achieve consensus with any arbitrary agent due to the presence of misbehaving agents in the network. This notion enables ordering graphs that lack required robustness and facilitates the assessment of partial performance. Additionally, we demonstrate that among graphs with the same level of robustness (measured by their -robustness), the number of non-convergent nodes varies significantly, indicating differing degrees of non-resilience. We also present numerical evaluation of results. Our approach quantifies the network performance under sub-optimal robustness conditions and offers a comprehensive resilience perspective.
{"title":"On the non-resiliency of subsequence reduced resilient consensus in multiagent networks","authors":"","doi":"10.1016/j.ejcon.2024.101120","DOIUrl":"10.1016/j.ejcon.2024.101120","url":null,"abstract":"<div><div>This paper studies resilient distributed consensus in networks lacking the structural robustness necessary for achieving consensus in the presence of misbehaving agents. Existing resilient consensus solutions, including widely adapted <em>weighted mean subsequence reduced (WMSR)</em> resilient consensus algorithm, present robustness conditions guaranteeing consensus among normal agents. However, when the graph is less robust than required, they only inform that agents fail to achieve consensus and do not evaluate the network performance comprehensively in such non-ideal scenarios. To address this limitation, we analyze the performance of resilient consensus in non-ideal situations by introducing the concept of <em>non-convergent nodes</em>. These nodes/agents cannot achieve consensus with any arbitrary agent due to the presence of misbehaving agents in the network. This notion enables ordering graphs that lack required robustness and facilitates the assessment of partial performance. Additionally, we demonstrate that among graphs with the same level of robustness (measured by their <span><math><mrow><mo>(</mo><mi>r</mi><mo>,</mo><mi>s</mi><mo>)</mo></mrow></math></span>-robustness), the number of non-convergent nodes varies significantly, indicating differing degrees of non-resilience. We also present numerical evaluation of results. Our approach quantifies the network performance under sub-optimal robustness conditions and offers a comprehensive resilience perspective.</div></div>","PeriodicalId":50489,"journal":{"name":"European Journal of Control","volume":null,"pages":null},"PeriodicalIF":2.5,"publicationDate":"2024-09-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142423279","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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 : 2024-09-26DOI: 10.1016/j.ejcon.2024.101118
A common approach in robotics is to learn tasks by generalizing from special cases given by a so-called demonstrator. In this paper, we apply this paradigm and present an algorithm that uses a demonstrator (typically given by a trajectory optimizer) to automatically synthesize feedback controllers for steering a system described by ordinary differential equations into a goal set. The resulting feedback control law switches between the demonstrations that it uses as reference trajectories. In comparison to the direct use of trajectory optimization as a control law, for example, in the form of model predictive control, this allows for a much simpler and more efficient implementation of the controller. The synthesis algorithm comes with rigorous convergence and optimality results, and computational experiments confirm its efficiency.
{"title":"Computation of feedback control laws based on switched tracking of demonstrations","authors":"","doi":"10.1016/j.ejcon.2024.101118","DOIUrl":"10.1016/j.ejcon.2024.101118","url":null,"abstract":"<div><div>A common approach in robotics is to learn tasks by generalizing from special cases given by a so-called demonstrator. In this paper, we apply this paradigm and present an algorithm that uses a demonstrator (typically given by a trajectory optimizer) to automatically synthesize feedback controllers for steering a system described by ordinary differential equations into a goal set. The resulting feedback control law switches between the demonstrations that it uses as reference trajectories. In comparison to the direct use of trajectory optimization as a control law, for example, in the form of model predictive control, this allows for a much simpler and more efficient implementation of the controller. The synthesis algorithm comes with rigorous convergence and optimality results, and computational experiments confirm its efficiency.</div></div>","PeriodicalId":50489,"journal":{"name":"European Journal of Control","volume":null,"pages":null},"PeriodicalIF":2.5,"publicationDate":"2024-09-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142357698","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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 : 2024-09-24DOI: 10.1016/j.ejcon.2024.101117
Precision control of Unmanned Aerial Vehicles (UAVs) is essential for deployment in a wide range of applications. However, real-world flight conditions often deviate from ideal operating scenarios, presenting uncertainties such as external disturbances and unmodeled dynamics. These can dramatically impact tracking accuracy and stability. This study proposes a novel adaptive control technique for quadrotors based on Windowed Dynamic Mode Decomposition (DMDc) techniques. This techniques efficiently identifies dynamic models directly from data, and updates this model in real-time, allowing the controller to compensate for changing conditions. To facilitate realistic validation, the proposed system is integrated within a Hardware-in-the-Loop (HiL) framework. In a series of simulated experiments, the adaptive controller demonstrates improvement in trajectory tracking under disturbances when compared to a conventional inverse dynamics approach. This research underscores the promise of DMDc-based techniques combined with adaptive control to enhance UAV operation, enabling safer and more robust performance in demanding scenarios.
{"title":"Adaptive quadrotor control using online dynamic mode decomposition","authors":"","doi":"10.1016/j.ejcon.2024.101117","DOIUrl":"10.1016/j.ejcon.2024.101117","url":null,"abstract":"<div><div>Precision control of Unmanned Aerial Vehicles (UAVs) is essential for deployment in a wide range of applications. However, real-world flight conditions often deviate from ideal operating scenarios, presenting uncertainties such as external disturbances and unmodeled dynamics. These can dramatically impact tracking accuracy and stability. This study proposes a novel adaptive control technique for quadrotors based on Windowed Dynamic Mode Decomposition (DMDc) techniques. This techniques efficiently identifies dynamic models directly from data, and updates this model in real-time, allowing the controller to compensate for changing conditions. To facilitate realistic validation, the proposed system is integrated within a Hardware-in-the-Loop (HiL) framework. In a series of simulated experiments, the adaptive controller demonstrates improvement in trajectory tracking under disturbances when compared to a conventional inverse dynamics approach. This research underscores the promise of DMDc-based techniques combined with adaptive control to enhance UAV operation, enabling safer and more robust performance in demanding scenarios.</div></div>","PeriodicalId":50489,"journal":{"name":"European Journal of Control","volume":null,"pages":null},"PeriodicalIF":2.5,"publicationDate":"2024-09-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142423228","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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 : 2024-09-21DOI: 10.1016/j.ejcon.2024.101116
Switching on a new or retuned controller while keeping the control loop engaged tends to generate transient “bumps” in the commands and plant outputs. For a linear time-invariant (LTI) controller in state–space form, these bumps can be mitigated or even suppressed by resetting the controller state to an appropriate non-zero value adapted to the pre-switching trajectories of the feedback loop signals. This paper proposes a simple way to compute this adapted controller state by minimizing the difference between the commands actually applied immediately before switching and the virtual command trajectory which the new controller would have generated if it had been activated in parallel. This adapted state can be recursively computed as the output of an LTI system in standard state–space form, the anti-bump adapter. Computing the anti-bump adapter involves only standard matrix algebra and control concepts (e.g., observability and controllability matrices/Gramians). Calculations are very simple and can be translated into compact computer code. This bump suppression procedure is applicable to any discrete-time or continuous-time LTI SISO or MIMO controller, without any assumption on or knowledge of either the previously active controller or the plant. Illustrative applications to continuous-time and discrete-time switching problems and a Matlab® code for computing the anti-bump adapter are presented.
{"title":"Controller switching with the anti-bump adapter","authors":"","doi":"10.1016/j.ejcon.2024.101116","DOIUrl":"10.1016/j.ejcon.2024.101116","url":null,"abstract":"<div><div>Switching on a new or retuned controller while keeping the control loop engaged tends to generate transient “bumps” in the commands and plant outputs. For a linear time-invariant (LTI) controller in state–space form, these bumps can be mitigated or even suppressed by resetting the controller state to an appropriate non-zero value adapted to the pre-switching trajectories of the feedback loop signals. This paper proposes a simple way to compute this adapted controller state by minimizing the difference between the commands actually applied immediately before switching and the virtual command trajectory which the new controller would have generated if it had been activated in parallel. This adapted state can be recursively computed as the output of an LTI system in standard state–space form, the anti-bump adapter. Computing the anti-bump adapter involves only standard matrix algebra and control concepts (e.g., observability and controllability matrices/Gramians). Calculations are very simple and can be translated into compact computer code. This bump suppression procedure is applicable to any discrete-time or continuous-time LTI SISO or MIMO controller, without any assumption on or knowledge of either the previously active controller or the plant. Illustrative applications to continuous-time and discrete-time switching problems and a <span>Matlab</span>® code for computing the anti-bump adapter are presented.</div></div>","PeriodicalId":50489,"journal":{"name":"European Journal of Control","volume":null,"pages":null},"PeriodicalIF":2.5,"publicationDate":"2024-09-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142357699","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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 : 2024-09-18DOI: 10.1016/j.ejcon.2024.101103
This paper proposes an adaptive finite time command filtered backstepping control scheme for single‐input and single‐output (SISO) uncertain strict-feedback nonlinear systems. The problem of the explosion of complexity existing in the adaptive backstepping control design and the singularity problem are solved by using the proposed adaptive finite time control method. In addition, the compensating signals are introduced to deal with the effect of the known filtering errors caused by the command filters. By using the finite time Lyapunov stability theory, the proposed adaptive finite time control strategy guarantees that all the signals in the closed-loop system are practical finite time stable, and the tracking errors converge to an arbitrarily small neighbourhood of the origin in finite time. Simulation and experimental results of the DC-DC buck converter are given to illustrate the effectiveness of the proposed adaptive finite time control scheme.
{"title":"Adaptive finite time command filtered backstepping control scheme of uncertain strict-feedback nonlinear systems","authors":"","doi":"10.1016/j.ejcon.2024.101103","DOIUrl":"10.1016/j.ejcon.2024.101103","url":null,"abstract":"<div><p>This paper proposes an adaptive finite time command filtered backstepping control scheme for single‐input and single‐output (SISO) uncertain strict-feedback nonlinear systems. The problem of the explosion of complexity existing in the adaptive backstepping control design and the singularity problem are solved by using the proposed adaptive finite time control method. In addition, the compensating signals are introduced to deal with the effect of the known filtering errors caused by the command filters. By using the finite time Lyapunov stability theory, the proposed adaptive finite time control strategy guarantees that all the signals in the closed-loop system are practical finite time stable, and the tracking errors converge to an arbitrarily small neighbourhood of the origin in finite time. Simulation and experimental results of the DC-DC buck converter are given to illustrate the effectiveness of the proposed adaptive finite time control scheme.</p></div>","PeriodicalId":50489,"journal":{"name":"European Journal of Control","volume":null,"pages":null},"PeriodicalIF":2.5,"publicationDate":"2024-09-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142239069","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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 : 2024-09-17DOI: 10.1016/j.ejcon.2024.101114
This paper introduces a Practical Fixed-Time Stabilization technique (PFxT) designed for a specific class of nonlinear second-order systems. The closed-loop systems, when appropriately parameterized, exhibit convergence within a predetermined time frame to a confined region near the origin. This outcome is achieved by amalgamating a nonlinear sliding mode approach with a practical fixed-time tracking virtual trajectory. The control algorithmś design incorporates considerations for overshoot reduction and chattering cancellation. Furthermore, the Lyapunov method is employed to establish the practical fixed-time stability of the proposed solution, providing insights into the limits within which the algorithm can be effectively deployed. To complete the algorithm specification, a parameter selection approach is introduced, enabling customization of the desired settling time. Comprehensive simulations are conducted to validate the effectiveness and viability of the proposed PFxT technique.
{"title":"Practical fixed-time non-singular sliding mode control of second order nonlinear dynamic systems with chattering and overshooting avoidance","authors":"","doi":"10.1016/j.ejcon.2024.101114","DOIUrl":"10.1016/j.ejcon.2024.101114","url":null,"abstract":"<div><div>This paper introduces a Practical Fixed-Time Stabilization technique (PFxT) designed for a specific class of nonlinear second-order systems. The closed-loop systems, when appropriately parameterized, exhibit convergence within a predetermined time frame to a confined region near the origin. This outcome is achieved by amalgamating a nonlinear sliding mode approach with a practical fixed-time tracking virtual trajectory. The control algorithmś design incorporates considerations for overshoot reduction and chattering cancellation. Furthermore, the Lyapunov method is employed to establish the practical fixed-time stability of the proposed solution, providing insights into the limits within which the algorithm can be effectively deployed. To complete the algorithm specification, a parameter selection approach is introduced, enabling customization of the desired settling time. Comprehensive simulations are conducted to validate the effectiveness and viability of the proposed PFxT technique.</div></div>","PeriodicalId":50489,"journal":{"name":"European Journal of Control","volume":null,"pages":null},"PeriodicalIF":2.5,"publicationDate":"2024-09-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142323242","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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 : 2024-09-13DOI: 10.1016/j.ejcon.2024.101115
This paper introduces an algorithm for estimating the invariant set of closed-loop controlled dynamical systems identified using single-hidden layer Rectified linear units (ReLU) neural networks or piecewise affine () functions, particularly addressing the challenge of providing safety guarantees for single-hidden layer ReLU networks commonly used in safety–critical applications. The invariant set of dynamical system is estimated using single-hidden layer ReLU networks or its equivalent function. This method entails formulating the barrier function as a function and converting the search process into a linear optimization problem using vertices. We incorporate a domain refinement strategy to increase flexibility in case the optimization does not find a valid barrier function. Moreover, the objective of the optimization is to find a less conservative invariant set based on the current partition. Our experimental results demonstrate the effectiveness and efficiency of our approach, demonstrating its potential for ensuring the safety of dynamical systems.
{"title":"Invariant set estimation for piecewise affine dynamical systems using piecewise affine barrier function","authors":"","doi":"10.1016/j.ejcon.2024.101115","DOIUrl":"10.1016/j.ejcon.2024.101115","url":null,"abstract":"<div><p>This paper introduces an algorithm for estimating the invariant set of closed-loop controlled dynamical systems identified using single-hidden layer Rectified linear units (ReLU) neural networks or piecewise affine (<span><math><mi>PWA</mi></math></span>) functions, particularly addressing the challenge of providing safety guarantees for single-hidden layer ReLU networks commonly used in safety–critical applications. The invariant set of <span><math><mi>PWA</mi></math></span> dynamical system is estimated using single-hidden layer ReLU networks or its equivalent <span><math><mi>PWA</mi></math></span> function. This method entails formulating the barrier function as a <span><math><mi>PWA</mi></math></span> function and converting the search process into a linear optimization problem using vertices. We incorporate a domain refinement strategy to increase flexibility in case the optimization does not find a valid barrier function. Moreover, the objective of the optimization is to find a less conservative invariant set based on the current partition. Our experimental results demonstrate the effectiveness and efficiency of our approach, demonstrating its potential for ensuring the safety of <span><math><mi>PWA</mi></math></span> dynamical systems.</p></div>","PeriodicalId":50489,"journal":{"name":"European Journal of Control","volume":null,"pages":null},"PeriodicalIF":2.5,"publicationDate":"2024-09-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142239071","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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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