Pub Date : 2024-12-23DOI: 10.1109/LCSYS.2024.3521191
Miguel Castroviejo-Fernandez;Ilya Kolmanovsky
An approach to safe and fast online learning of constraints for a continuous-time linear system subject to linear inequality constraints is developed, assuming that the number of constraints is known and measurements of the constraint signals are available. During the identification phase, a constant reference command input is applied for the duration of an epoch and constraint measurements are collected. Based on these measurements, the set of feasible constraint parameters is refined using set-membership learning techniques. The reference command value is selected so that it minimizes the worst-case uncertainty in the parameters after one epoch while safety is ensured through the use of appropriately defined safe sets. The characterization of safe sets is shown to reduce to a finite set of linear inequality constraints. A numerical case study is reported for the proposed algorithm.
{"title":"Safe Constraint Learning for Reference Governor Implementation in Constrained Linear Systems","authors":"Miguel Castroviejo-Fernandez;Ilya Kolmanovsky","doi":"10.1109/LCSYS.2024.3521191","DOIUrl":"https://doi.org/10.1109/LCSYS.2024.3521191","url":null,"abstract":"An approach to safe and fast online learning of constraints for a continuous-time linear system subject to linear inequality constraints is developed, assuming that the number of constraints is known and measurements of the constraint signals are available. During the identification phase, a constant reference command input is applied for the duration of an epoch and constraint measurements are collected. Based on these measurements, the set of feasible constraint parameters is refined using set-membership learning techniques. The reference command value is selected so that it minimizes the worst-case uncertainty in the parameters after one epoch while safety is ensured through the use of appropriately defined safe sets. The characterization of safe sets is shown to reduce to a finite set of linear inequality constraints. A numerical case study is reported for the proposed algorithm.","PeriodicalId":37235,"journal":{"name":"IEEE Control Systems Letters","volume":"8 ","pages":"3117-3122"},"PeriodicalIF":2.4,"publicationDate":"2024-12-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142962825","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-12-23DOI: 10.1109/LCSYS.2024.3522058
Nathaniel Sisson;K. Merve Dogan
Adaptive control techniques are ubiquitous methods for controlling dynamic systems, particularly because of their ability to improve system performance in the presence of uncertainties. However, a downside to these adaptive controllers is that particular learning rates are often required to ensure system performance requirements, creating high-frequency oscillations in the control input signal. These oscillations can potentially cause the system to become unstable or to have unacceptable performance. Thus, in this letter, we introduce a low-frequency learning adaptive control architecture for a discrete dynamical system with system uncertainties. In this framework, the update law is modified to include a filtered version of the updated parameter, allowing for high-frequency content to be removed while preserving system performance requirements. Lyapunov stability analysis is provided to guarantee asymptotic tracking error convergence of the closed-loop system. The results of a numerical simulation illustrates the reduction of high-frequencies in the system response.
{"title":"Low-Frequency Learning for a Discrete Uncertain System","authors":"Nathaniel Sisson;K. Merve Dogan","doi":"10.1109/LCSYS.2024.3522058","DOIUrl":"https://doi.org/10.1109/LCSYS.2024.3522058","url":null,"abstract":"Adaptive control techniques are ubiquitous methods for controlling dynamic systems, particularly because of their ability to improve system performance in the presence of uncertainties. However, a downside to these adaptive controllers is that particular learning rates are often required to ensure system performance requirements, creating high-frequency oscillations in the control input signal. These oscillations can potentially cause the system to become unstable or to have unacceptable performance. Thus, in this letter, we introduce a low-frequency learning adaptive control architecture for a discrete dynamical system with system uncertainties. In this framework, the update law is modified to include a filtered version of the updated parameter, allowing for high-frequency content to be removed while preserving system performance requirements. Lyapunov stability analysis is provided to guarantee asymptotic tracking error convergence of the closed-loop system. The results of a numerical simulation illustrates the reduction of high-frequencies in the system response.","PeriodicalId":37235,"journal":{"name":"IEEE Control Systems Letters","volume":"8 ","pages":"3111-3116"},"PeriodicalIF":2.4,"publicationDate":"2024-12-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142962830","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-12-23DOI: 10.1109/LCSYS.2024.3522212
Shaurya Shrivastava;Kenshiro Oguri
In this letter, we propose novel LMI-based controller synthesis frameworks for discrete-time Markov-jump systems with periodically time-varying dynamics. We discuss necessary and sufficient conditions for mean square stability and derive Lyapunov-like conditions for stability assurance. To relax strict stability requirements, we introduce a new criterion that does not require the Lyapunov function to decrease at each time step. Further, we incorporate these stability theorems in LMI-based controller synthesis frameworks while considering two separate problems: minimizing an upper bound of a quadratic cost and maximizing the region of attraction, all while guaranteeing stability. Numerical simulations verify the controllers’ stability and showcase its applicability to fault-tolerant control.
{"title":"Robust Controller Synthesis Under Markovian Mode Switching With Periodic LTV Dynamics","authors":"Shaurya Shrivastava;Kenshiro Oguri","doi":"10.1109/LCSYS.2024.3522212","DOIUrl":"https://doi.org/10.1109/LCSYS.2024.3522212","url":null,"abstract":"In this letter, we propose novel LMI-based controller synthesis frameworks for discrete-time Markov-jump systems with periodically time-varying dynamics. We discuss necessary and sufficient conditions for mean square stability and derive Lyapunov-like conditions for stability assurance. To relax strict stability requirements, we introduce a new criterion that does not require the Lyapunov function to decrease at each time step. Further, we incorporate these stability theorems in LMI-based controller synthesis frameworks while considering two separate problems: minimizing an upper bound of a quadratic cost and maximizing the region of attraction, all while guaranteeing stability. Numerical simulations verify the controllers’ stability and showcase its applicability to fault-tolerant control.","PeriodicalId":37235,"journal":{"name":"IEEE Control Systems Letters","volume":"8 ","pages":"3339-3344"},"PeriodicalIF":2.4,"publicationDate":"2024-12-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143184229","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-12-23DOI: 10.1109/LCSYS.2024.3521432
Poorva Shukla;Bassam Bamieh
We study phenomena where some eigenvectors of a graph Laplacian are largely confined in small subsets of the graph. These localization phenomena are similar to those generally termed Anderson Localization in the Physics literature, and are related to the complexity of the structure of large graphs in still unexplored ways. Using perturbation analysis and pseudo-spectrum analysis, we explain how the presence of localized eigenvectors gives rise to fragilities (low robustness margins) to unmodeled node or link dynamics. Our analysis is demonstrated by examples of networks with relatively low complexity, but with features that appear to induce eigenvector localization. The implications of this newly-discovered fragility phenomenon are briefly discussed.
{"title":"Localization Phenomena in Large-Scale Networked Systems: Implications for Fragility","authors":"Poorva Shukla;Bassam Bamieh","doi":"10.1109/LCSYS.2024.3521432","DOIUrl":"https://doi.org/10.1109/LCSYS.2024.3521432","url":null,"abstract":"We study phenomena where some eigenvectors of a graph Laplacian are largely confined in small subsets of the graph. These localization phenomena are similar to those generally termed Anderson Localization in the Physics literature, and are related to the complexity of the structure of large graphs in still unexplored ways. Using perturbation analysis and pseudo-spectrum analysis, we explain how the presence of localized eigenvectors gives rise to fragilities (low robustness margins) to unmodeled node or link dynamics. Our analysis is demonstrated by examples of networks with relatively low complexity, but with features that appear to induce eigenvector localization. The implications of this newly-discovered fragility phenomenon are briefly discussed.","PeriodicalId":37235,"journal":{"name":"IEEE Control Systems Letters","volume":"8 ","pages":"3087-3092"},"PeriodicalIF":2.4,"publicationDate":"2024-12-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142962848","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Soft robots offer a frontier in robotics with enormous potential for safe human-robot interaction and agility in uncertain environments. A stepping stone towards unlocking their potential is a control theory tailored to soft robotics, including a principled framework for gait design. We analyze the problem of optimal gait design for a soft crawling body – the crawler. The crawler is an elastic body with the control signal defined as actuation forces between segments of the body. We consider the simplest such crawler: a two-segmented body with a passive mechanical connection modeling the viscoelastic body dynamics and a symmetric control force modeling actuation between the two body segments. The model accounts for the nonlinear asymmetric friction with the ground, which together with the symmetric actuation forces enable the crawler’s locomotion. Using a describing-function analysis, we show that when the body is forced sinusoidally, the optimal actuator contraction frequency corresponds to the body’s natural frequency when operating with only passive dynamics. We then use the framework of Optimal Periodic Control (OPC) to design optimal force cycles of arbitrary waveform and the corresponding crawling gaits. We provide a hill-climbing algorithm to solve the OPC problem numerically. Our proposed methods and results inform the design of optimal forcing and gaits for more complex and multi-segmented crawling soft bodies.
{"title":"Optimal Gait Design for Nonlinear Soft Robotic Crawlers","authors":"Yenan Shen;Naomi Ehrich Leonard;Bassam Bamieh;Juncal Arbelaiz","doi":"10.1109/LCSYS.2024.3521872","DOIUrl":"https://doi.org/10.1109/LCSYS.2024.3521872","url":null,"abstract":"Soft robots offer a frontier in robotics with enormous potential for safe human-robot interaction and agility in uncertain environments. A stepping stone towards unlocking their potential is a control theory tailored to soft robotics, including a principled framework for gait design. We analyze the problem of optimal gait design for a soft crawling body – the crawler. The crawler is an elastic body with the control signal defined as actuation forces between segments of the body. We consider the simplest such crawler: a two-segmented body with a passive mechanical connection modeling the viscoelastic body dynamics and a symmetric control force modeling actuation between the two body segments. The model accounts for the nonlinear asymmetric friction with the ground, which together with the symmetric actuation forces enable the crawler’s locomotion. Using a describing-function analysis, we show that when the body is forced sinusoidally, the optimal actuator contraction frequency corresponds to the body’s natural frequency when operating with only passive dynamics. We then use the framework of Optimal Periodic Control (OPC) to design optimal force cycles of arbitrary waveform and the corresponding crawling gaits. We provide a hill-climbing algorithm to solve the OPC problem numerically. Our proposed methods and results inform the design of optimal forcing and gaits for more complex and multi-segmented crawling soft bodies.","PeriodicalId":37235,"journal":{"name":"IEEE Control Systems Letters","volume":"8 ","pages":"1-1"},"PeriodicalIF":2.4,"publicationDate":"2024-12-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142937954","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-12-23DOI: 10.1109/LCSYS.2024.3521360
Fat-Hy Omar Rajab;Jeff S. Shamma
A scenario-based risk-sensitive optimization framework is presented to approximate minimax solutions with high confidence. The approach involves first drawing several random samples from the maximizing variable, then solving a sample-based risk-sensitive optimization problem. This letter derives the sample complexity and the required risk-sensitivity level to ensure a specified tolerance and confidence in approximating the minimax solution. The derived sample complexity highlights the impact of the underlying probability distribution of the random samples. The framework is demonstrated through applications to zero-sum games and model predictive control for linear dynamical systems with bounded disturbances.
{"title":"Scenario-Based Risk-Sensitive Computations of Equilibria for Two-Person Zero-Sum Games","authors":"Fat-Hy Omar Rajab;Jeff S. Shamma","doi":"10.1109/LCSYS.2024.3521360","DOIUrl":"https://doi.org/10.1109/LCSYS.2024.3521360","url":null,"abstract":"A scenario-based risk-sensitive optimization framework is presented to approximate minimax solutions with high confidence. The approach involves first drawing several random samples from the maximizing variable, then solving a sample-based risk-sensitive optimization problem. This letter derives the sample complexity and the required risk-sensitivity level to ensure a specified tolerance and confidence in approximating the minimax solution. The derived sample complexity highlights the impact of the underlying probability distribution of the random samples. The framework is demonstrated through applications to zero-sum games and model predictive control for linear dynamical systems with bounded disturbances.","PeriodicalId":37235,"journal":{"name":"IEEE Control Systems Letters","volume":"8 ","pages":"3207-3212"},"PeriodicalIF":2.4,"publicationDate":"2024-12-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142938055","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-12-23DOI: 10.1109/LCSYS.2024.3521187
Ke Wang;Di Wu;Pengyuan Li;Xu Li
In practical aero-engine control systems, saturation constraints on the control input are inherently asymmetric and the engine outputs may exceed their physical or safety limits during the operation. This letter proposes a switching anti-windup compensation for aero-engines incorporating the asymmetric input saturation and output constraint simultaneously. To tackle the asymmetric saturation, we transform the aero-engine linear model with asymmetrically saturated input into a switched system, and all its subsystems possess symmetric saturation property. Based on this transformation, a switching anti-windup compensator with multiple anti-windup gains is developed to mitigate the performance deterioration induced by the saturation constraints. Furthermore, output constraints are also incorporated into the compensation design, which prevents engine outputs from exceeding their allowable limits during the control process. The switching between different anti-windup gains in real time can fully utilize the actuator capability, and further achieving a more desirable engine performance. Finally, hardware-in-loop (HIL) testing and comparative results demonstrate its effectiveness and superiority.
{"title":"Output-Constrained Switching Anti-Windup Compensation for Aero-Engines With Asymmetric Input Saturation","authors":"Ke Wang;Di Wu;Pengyuan Li;Xu Li","doi":"10.1109/LCSYS.2024.3521187","DOIUrl":"https://doi.org/10.1109/LCSYS.2024.3521187","url":null,"abstract":"In practical aero-engine control systems, saturation constraints on the control input are inherently asymmetric and the engine outputs may exceed their physical or safety limits during the operation. This letter proposes a switching anti-windup compensation for aero-engines incorporating the asymmetric input saturation and output constraint simultaneously. To tackle the asymmetric saturation, we transform the aero-engine linear model with asymmetrically saturated input into a switched system, and all its subsystems possess symmetric saturation property. Based on this transformation, a switching anti-windup compensator with multiple anti-windup gains is developed to mitigate the performance deterioration induced by the saturation constraints. Furthermore, output constraints are also incorporated into the compensation design, which prevents engine outputs from exceeding their allowable limits during the control process. The switching between different anti-windup gains in real time can fully utilize the actuator capability, and further achieving a more desirable engine performance. Finally, hardware-in-loop (HIL) testing and comparative results demonstrate its effectiveness and superiority.","PeriodicalId":37235,"journal":{"name":"IEEE Control Systems Letters","volume":"8 ","pages":"3075-3080"},"PeriodicalIF":2.4,"publicationDate":"2024-12-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142962826","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-12-23DOI: 10.1109/LCSYS.2024.3522196
Manali Dutta;Rahul Singh
We consider a remote estimation setup, where data packets containing sensor observations are transmitted over a Gilbert-Elliot channel to a remote estimator, and design scheduling policies that minimize a risk-sensitive cost, which is equal to the expected value of the exponential of the cumulative cost incurred during a finite horizon, that is the sum of the cumulative transmission power consumed, and the cumulative squared estimation error. More specifically, consider a sensor that observes a discrete-time autoregressive Markov process, and at each time decides whether or not to transmit its observations to a remote estimator using an unreliable wireless communication channel after encoding these observations into data packets. Modeling the communication channel as a Gilbert-Elliot channel allows us to take into account the temporal correlations in its fading. We pose this dynamic optimization problem as a Markov decision process (MDP), and show that there exists an optimal policy that has a threshold structure, i.e., at each time t it transmits only when the current channel state is good, and the magnitude of the current “error” exceeds a certain threshold.
{"title":"Optimal Risk-Sensitive Scheduling Policies for Remote Estimation of Autoregressive Markov Processes","authors":"Manali Dutta;Rahul Singh","doi":"10.1109/LCSYS.2024.3522196","DOIUrl":"https://doi.org/10.1109/LCSYS.2024.3522196","url":null,"abstract":"We consider a remote estimation setup, where data packets containing sensor observations are transmitted over a Gilbert-Elliot channel to a remote estimator, and design scheduling policies that minimize a risk-sensitive cost, which is equal to the expected value of the exponential of the cumulative cost incurred during a finite horizon, that is the sum of the cumulative transmission power consumed, and the cumulative squared estimation error. More specifically, consider a sensor that observes a discrete-time autoregressive Markov process, and at each time decides whether or not to transmit its observations to a remote estimator using an unreliable wireless communication channel after encoding these observations into data packets. Modeling the communication channel as a Gilbert-Elliot channel allows us to take into account the temporal correlations in its fading. We pose this dynamic optimization problem as a Markov decision process (MDP), and show that there exists an optimal policy that has a threshold structure, i.e., at each time t it transmits only when the current channel state is good, and the magnitude of the current “error” exceeds a certain threshold.","PeriodicalId":37235,"journal":{"name":"IEEE Control Systems Letters","volume":"8 ","pages":"3099-3104"},"PeriodicalIF":2.4,"publicationDate":"2024-12-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142962831","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
This letter addresses a fundamental issue of time-varying parametric uncertainty affecting unreliable communication links that convey the control commands to actuators in wireless networked control systems. It introduces the polytopic time-inhomogeneous finite-state Markov channel model to account for significant changes in possible propagation channel characteristics and analytically solves the linear quadratic regulation problem under the generalized packet dropout compensation. An example validating the results is presented.
{"title":"Robust Linear Quadratic Regulation Over Polytopic Time-Inhomogeneous Markovian Channels Under Generalized Packet Dropout Compensation","authors":"Yuriy Zacchia Lun;Fortunato Santucci;Alessandro D’Innocenzo","doi":"10.1109/LCSYS.2024.3521656","DOIUrl":"https://doi.org/10.1109/LCSYS.2024.3521656","url":null,"abstract":"This letter addresses a fundamental issue of time-varying parametric uncertainty affecting unreliable communication links that convey the control commands to actuators in wireless networked control systems. It introduces the polytopic time-inhomogeneous finite-state Markov channel model to account for significant changes in possible propagation channel characteristics and analytically solves the linear quadratic regulation problem under the generalized packet dropout compensation. An example validating the results is presented.","PeriodicalId":37235,"journal":{"name":"IEEE Control Systems Letters","volume":"8 ","pages":"3315-3320"},"PeriodicalIF":2.4,"publicationDate":"2024-12-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=10812755","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143184225","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-12-23DOI: 10.1109/LCSYS.2024.3521356
Mohammed Adib Oumer;Vishnu Murali;Ashutosh Trivedi;Majid Zamani
Barrier certificates provide an effective automated approach to verifying the safety of dynamical systems. A barrier certificate is a real-valued function over states of the system whose zero level set separates the unsafe region from all possible trajectories starting from a given set of initial states. Typically, the system dynamics must be nonincreasing in the value of the barrier certificate with each transition. Thus, the states of the system that are nonpositive with respect to the barrier certificate act as an over-approximation of the reachable states. The search for such certificates is typically automated by first fixing a template of functions and then using optimization and satisfiability modulo theory (SMT) solvers to find them. Unfortunately, it may not be possible to find a single function in this fixed template. To tackle this challenge, we propose the notion of interpolation-inspired barrier certificate. Instead of a single function, an interpolation-inspired barrier certificate consists of a set of functions such that the union of their sublevel sets over-approximate the reachable set of states. We show how one may find interpolation-inspired barrier certificates of a fixed template, even when we fail to find standard barrier certificates of the same template. We present sum-of-squares (SOS) programming as a computational method to find this set of functions and demonstrate effectiveness of this method over a case study.
{"title":"Safety Verification of Discrete-Time Systems via Interpolation-Inspired Barrier Certificates","authors":"Mohammed Adib Oumer;Vishnu Murali;Ashutosh Trivedi;Majid Zamani","doi":"10.1109/LCSYS.2024.3521356","DOIUrl":"https://doi.org/10.1109/LCSYS.2024.3521356","url":null,"abstract":"Barrier certificates provide an effective automated approach to verifying the safety of dynamical systems. A barrier certificate is a real-valued function over states of the system whose zero level set separates the unsafe region from all possible trajectories starting from a given set of initial states. Typically, the system dynamics must be nonincreasing in the value of the barrier certificate with each transition. Thus, the states of the system that are nonpositive with respect to the barrier certificate act as an over-approximation of the reachable states. The search for such certificates is typically automated by first fixing a template of functions and then using optimization and satisfiability modulo theory (SMT) solvers to find them. Unfortunately, it may not be possible to find a single function in this fixed template. To tackle this challenge, we propose the notion of interpolation-inspired barrier certificate. Instead of a single function, an interpolation-inspired barrier certificate consists of a set of functions such that the union of their sublevel sets over-approximate the reachable set of states. We show how one may find interpolation-inspired barrier certificates of a fixed template, even when we fail to find standard barrier certificates of the same template. We present sum-of-squares (SOS) programming as a computational method to find this set of functions and demonstrate effectiveness of this method over a case study.","PeriodicalId":37235,"journal":{"name":"IEEE Control Systems Letters","volume":"8 ","pages":"3183-3188"},"PeriodicalIF":2.4,"publicationDate":"2024-12-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142938054","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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