Pub Date : 2021-11-18DOI: 10.3389/fcteg.2021.758543
D. Krokavec, A. Filasová
The paper presents the design conditions adequate in design of virtual actuators and utilizable by nominal static output control structures in fault-tolerant control for strictly Metzler systems. The positive stabilization with H ∞ norm performance is also addressed for virtual actuator design for strictly Metzler systems with interval uncertainty matrix representations of single actuator faults. Taking into account disturbance conditions and changes of values of variables after the virtual actuator activation, the design conditions are outlined in the terms of linear matrix inequalities. The approach provides a way to obtain acceptable dynamics of the closed loop system after virtual actuator activation.
{"title":"Virtual Actuator Design for Uncertain Metzler Systems","authors":"D. Krokavec, A. Filasová","doi":"10.3389/fcteg.2021.758543","DOIUrl":"https://doi.org/10.3389/fcteg.2021.758543","url":null,"abstract":"The paper presents the design conditions adequate in design of virtual actuators and utilizable by nominal static output control structures in fault-tolerant control for strictly Metzler systems. The positive stabilization with H ∞ norm performance is also addressed for virtual actuator design for strictly Metzler systems with interval uncertainty matrix representations of single actuator faults. Taking into account disturbance conditions and changes of values of variables after the virtual actuator activation, the design conditions are outlined in the terms of linear matrix inequalities. The approach provides a way to obtain acceptable dynamics of the closed loop system after virtual actuator activation.","PeriodicalId":73076,"journal":{"name":"Frontiers in control engineering","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2021-11-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47069123","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 : 2021-11-17DOI: 10.3389/fcteg.2021.721475
Zhe-Yang Zhu, Chenglin Liu
In this paper, we investigate a pursuit problem with multi-pursuer and single evader in a two-dimensional grid space with obstacles. Taking a different approach to previous studies, this paper aims to address a pursuit problem in which only some pursuers can directly access the evader’s position. It also proposes using a hierarchical Q(λ)-learning with improved reward, with simulation results indicating that the proposed method outperforms Q-learning.
{"title":"Leader-Following Multi-Agent Coordination Control Accompanied With Hierarchical Q(λ)-Learning for Pursuit","authors":"Zhe-Yang Zhu, Chenglin Liu","doi":"10.3389/fcteg.2021.721475","DOIUrl":"https://doi.org/10.3389/fcteg.2021.721475","url":null,"abstract":"In this paper, we investigate a pursuit problem with multi-pursuer and single evader in a two-dimensional grid space with obstacles. Taking a different approach to previous studies, this paper aims to address a pursuit problem in which only some pursuers can directly access the evader’s position. It also proposes using a hierarchical Q(λ)-learning with improved reward, with simulation results indicating that the proposed method outperforms Q-learning.","PeriodicalId":73076,"journal":{"name":"Frontiers in control engineering","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2021-11-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43947510","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 : 2021-11-05DOI: 10.3389/fcteg.2021.710271
Hajer Srihi, T. Guerra, Anh‐Tu Nguyen, P. Pudlo, A. Dequidt
People with spinal cord injury (SCI) suffer from a drastic reduction in sitting stability which negatively impacts their postural control. Thus, sitting balance becomes one of the most challenging everyday exercises. To better understand the consequences of this pathology, we have to work with high-sized non-linear biomechanical models implying both theoretical and numerical difficulties. The main goal being to recover unmeasured inputs, the observer should have limited or no simplification at all to provide a better estimation quality. A Proportional Integral-observer (PI-observer) is designed and its convergence is formulated by linear matrix inequalities (LMI) through convex optimization techniques. Using a unique high-sized observer, the LMI constraints problem can quickly reach current solvers limitations regarding the number of unknown parameters required. A way to solve this issue is to design a cascade observer in order to estimate the unmeasurable torques of a human with SCI. This approach consists in decomposing a biomechanical model into interconnected subsystems and to build “local” observers. The relevance of this approach is demonstrated in simulation and with real-time experimental data.
{"title":"Cascade Descriptor Observers: Application to Understanding Sitting Control of Persons Living With Spinal Cord Injury","authors":"Hajer Srihi, T. Guerra, Anh‐Tu Nguyen, P. Pudlo, A. Dequidt","doi":"10.3389/fcteg.2021.710271","DOIUrl":"https://doi.org/10.3389/fcteg.2021.710271","url":null,"abstract":"People with spinal cord injury (SCI) suffer from a drastic reduction in sitting stability which negatively impacts their postural control. Thus, sitting balance becomes one of the most challenging everyday exercises. To better understand the consequences of this pathology, we have to work with high-sized non-linear biomechanical models implying both theoretical and numerical difficulties. The main goal being to recover unmeasured inputs, the observer should have limited or no simplification at all to provide a better estimation quality. A Proportional Integral-observer (PI-observer) is designed and its convergence is formulated by linear matrix inequalities (LMI) through convex optimization techniques. Using a unique high-sized observer, the LMI constraints problem can quickly reach current solvers limitations regarding the number of unknown parameters required. A way to solve this issue is to design a cascade observer in order to estimate the unmeasurable torques of a human with SCI. This approach consists in decomposing a biomechanical model into interconnected subsystems and to build “local” observers. The relevance of this approach is demonstrated in simulation and with real-time experimental data.","PeriodicalId":73076,"journal":{"name":"Frontiers in control engineering","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2021-11-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46106045","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 : 2021-10-27DOI: 10.3389/fcteg.2021.750190
Alex Gimondi, M. Corno, S. Savaresi
This paper discusses a multi-layer linear parameter varying path tracking controller for autonomous full electric vehicles with 4 wheel drive. Many approaches for path tracking are present in the literature, but the majority of them utilize only the steering wheel. Nowadays, the massive introduction of electric vehicles opens new opportunities for vehicle dynamics control; multiple electric motors, via differential torque, offer an alternative way to influence vehicle motion. The multi-layer structure, managing separately steering wheel and electric motors, permits the exploitation of pre-existing control systems and maintains a straightforward tuning process. Furthermore, the robustness of the path tracking controller is enhanced by introducing tire nonlinearities. Linear parameter varying models offer a direct way to incorporate tire characteristics in the design process. Exploiting H ∞ technique the scheduled controller can be seamlessly synthezised. The proposed strategy has been compared in simulation to a benchmark integrated, i.e., a unique controller that manages all the actuators, approach. During double lane changes beyond the vehicle limits, the multi-layer controller guarantees stability and excellent tracking with an average error of 12 and 24 cm on high and low grip respectively.
{"title":"Linear Parameter Varying Path Tracking Control for Over-Actuated Electric Vehicles","authors":"Alex Gimondi, M. Corno, S. Savaresi","doi":"10.3389/fcteg.2021.750190","DOIUrl":"https://doi.org/10.3389/fcteg.2021.750190","url":null,"abstract":"This paper discusses a multi-layer linear parameter varying path tracking controller for autonomous full electric vehicles with 4 wheel drive. Many approaches for path tracking are present in the literature, but the majority of them utilize only the steering wheel. Nowadays, the massive introduction of electric vehicles opens new opportunities for vehicle dynamics control; multiple electric motors, via differential torque, offer an alternative way to influence vehicle motion. The multi-layer structure, managing separately steering wheel and electric motors, permits the exploitation of pre-existing control systems and maintains a straightforward tuning process. Furthermore, the robustness of the path tracking controller is enhanced by introducing tire nonlinearities. Linear parameter varying models offer a direct way to incorporate tire characteristics in the design process. Exploiting H ∞ technique the scheduled controller can be seamlessly synthezised. The proposed strategy has been compared in simulation to a benchmark integrated, i.e., a unique controller that manages all the actuators, approach. During double lane changes beyond the vehicle limits, the multi-layer controller guarantees stability and excellent tracking with an average error of 12 and 24 cm on high and low grip respectively.","PeriodicalId":73076,"journal":{"name":"Frontiers in control engineering","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2021-10-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47428245","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 : 2021-10-01DOI: 10.3389/fcteg.2021.744027
Ni Zhao, Jiandong Zhu
This paper investigates the robust consensus problem for heterogeneous second-order multi-agent systems with uncertain parameters. Based on the sliding mode control method, novel robust consensus protocols are designed for the linear multi-agent systems with uncertain parameters and a class of uncertain nonlinear multi-agent systems. Finally, numerical simulations are given to verify the effectiveness of the proposed protocols.
{"title":"Robust Consensus Problem of Heterogeneous Uncertain Second-Order Multi-Agent Systems Based on Sliding Mode Control","authors":"Ni Zhao, Jiandong Zhu","doi":"10.3389/fcteg.2021.744027","DOIUrl":"https://doi.org/10.3389/fcteg.2021.744027","url":null,"abstract":"This paper investigates the robust consensus problem for heterogeneous second-order multi-agent systems with uncertain parameters. Based on the sliding mode control method, novel robust consensus protocols are designed for the linear multi-agent systems with uncertain parameters and a class of uncertain nonlinear multi-agent systems. Finally, numerical simulations are given to verify the effectiveness of the proposed protocols.","PeriodicalId":73076,"journal":{"name":"Frontiers in control engineering","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2021-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47590684","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 : 2021-08-19DOI: 10.3389/fcteg.2021.716110
J. Sabatier
This paper first warns about the confusion or rather the implicit link that exists in the literature between fractional behaviours (of physical, biological, thermal, etc. origin) and fractional models. The need in the field of dynamic systems modelling is for tools that can capture fractional behaviours that are ubiquitous. Fractional models are only one class of models among others that can capture fractional behaviours, but with associated drawbacks. Several other modelling tools are proposed in this paper, thus showing that a distinction is needed between fractional behaviours and fractional models.
{"title":"Modelling Fractional Behaviours Without Fractional Models","authors":"J. Sabatier","doi":"10.3389/fcteg.2021.716110","DOIUrl":"https://doi.org/10.3389/fcteg.2021.716110","url":null,"abstract":"This paper first warns about the confusion or rather the implicit link that exists in the literature between fractional behaviours (of physical, biological, thermal, etc. origin) and fractional models. The need in the field of dynamic systems modelling is for tools that can capture fractional behaviours that are ubiquitous. Fractional models are only one class of models among others that can capture fractional behaviours, but with associated drawbacks. Several other modelling tools are proposed in this paper, thus showing that a distinction is needed between fractional behaviours and fractional models.","PeriodicalId":73076,"journal":{"name":"Frontiers in control engineering","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2021-08-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42726484","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 : 2021-08-18DOI: 10.3389/fcteg.2021.734220
Dariush Fooladivanda, Qie Hu, Y. Chang
A timely, accurate, and secure dynamic state estimation is needed for reliable monitoring and efficient control of microgrids. The synchrophasor technology enables system operators to obtain synchronized measurements in real-time and to develop dynamic state estimators for monitoring and control of microgrids. However, in practice, sensor measurements can be corrupted or attacked. In this study, we consider an AC microgrid comprising several synchronous generators and inverter-interface power supplies, and focus on securely estimating the dynamic states of the microgrid from a set of corrupted data. We propose a secure dynamic state estimator which allows the microgrid operator to reconstruct the dynamic states of the microgrid from a set of attacked or corrupted data without any assumption on attacks or corruptions. Finally, we consider an AC microgrid with the same topology as the IEEE 33-bus distribution system, and show that the proposed secure estimation algorithm can accurately reconstruct the attack signals.
{"title":"Secure Dynamic State Estimation for Cyber Security of AC Microgrids","authors":"Dariush Fooladivanda, Qie Hu, Y. Chang","doi":"10.3389/fcteg.2021.734220","DOIUrl":"https://doi.org/10.3389/fcteg.2021.734220","url":null,"abstract":"A timely, accurate, and secure dynamic state estimation is needed for reliable monitoring and efficient control of microgrids. The synchrophasor technology enables system operators to obtain synchronized measurements in real-time and to develop dynamic state estimators for monitoring and control of microgrids. However, in practice, sensor measurements can be corrupted or attacked. In this study, we consider an AC microgrid comprising several synchronous generators and inverter-interface power supplies, and focus on securely estimating the dynamic states of the microgrid from a set of corrupted data. We propose a secure dynamic state estimator which allows the microgrid operator to reconstruct the dynamic states of the microgrid from a set of attacked or corrupted data without any assumption on attacks or corruptions. Finally, we consider an AC microgrid with the same topology as the IEEE 33-bus distribution system, and show that the proposed secure estimation algorithm can accurately reconstruct the attack signals.","PeriodicalId":73076,"journal":{"name":"Frontiers in control engineering","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2021-08-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44928197","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 : 2021-08-16DOI: 10.3389/fcteg.2021.687807
Shahin Tasoujian, Karolos Grigoriadis , Matthew Franchek
The present work examines the delay-dependent gain-scheduling feedback control with guaranteed closed-loop stability and induced L 2 norm performance for continuous-time linear parameter-varying (LPV) systems with arbitrary time-varying delay. An extension of Lyapunov stability utilizing Krasovskii functionals is considered to derive stability analysis and synthesis conditions for delay-dependent dynamic output feedback LPV control design. The main challenges associated with this approach are selecting appropriate Lyapunov-Krasovskii functionals (LKFs) and finding efficient integral inequalities to bound the derivative of the LKF. Accordingly, a novel modified parameter-dependent LKF candidate along with an affine version of Jensen’s inequality bounding technique are employed leading to the derivation of less conservative sufficient conditions expressed in terms of convex linear matrix inequalities (LMIs). The proposed methodology is compared with past work in the literature in terms of conservatism reduction and performance improvement through a numerical example. Finally, the application of the proposed output-feedback LPV control design is evaluated on the automated mean arterial blood pressure (MAP) regulation in critical patient resuscitation via vasoactive drug infusion. Closed-loop simulation results are presented to illustrate the potential of the introduced LPV gain-scheduling design to provide MAP set-point tracking in the presence of disturbances and varying input delays.
{"title":"An Improved Integral Inequality for Delay-Dependent Gain-Scheduled LPV Control","authors":"Shahin Tasoujian, Karolos Grigoriadis , Matthew Franchek ","doi":"10.3389/fcteg.2021.687807","DOIUrl":"https://doi.org/10.3389/fcteg.2021.687807","url":null,"abstract":"The present work examines the delay-dependent gain-scheduling feedback control with guaranteed closed-loop stability and induced L 2 norm performance for continuous-time linear parameter-varying (LPV) systems with arbitrary time-varying delay. An extension of Lyapunov stability utilizing Krasovskii functionals is considered to derive stability analysis and synthesis conditions for delay-dependent dynamic output feedback LPV control design. The main challenges associated with this approach are selecting appropriate Lyapunov-Krasovskii functionals (LKFs) and finding efficient integral inequalities to bound the derivative of the LKF. Accordingly, a novel modified parameter-dependent LKF candidate along with an affine version of Jensen’s inequality bounding technique are employed leading to the derivation of less conservative sufficient conditions expressed in terms of convex linear matrix inequalities (LMIs). The proposed methodology is compared with past work in the literature in terms of conservatism reduction and performance improvement through a numerical example. Finally, the application of the proposed output-feedback LPV control design is evaluated on the automated mean arterial blood pressure (MAP) regulation in critical patient resuscitation via vasoactive drug infusion. Closed-loop simulation results are presented to illustrate the potential of the introduced LPV gain-scheduling design to provide MAP set-point tracking in the presence of disturbances and varying input delays.","PeriodicalId":73076,"journal":{"name":"Frontiers in control engineering","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2021-08-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48521256","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 : 2021-08-06DOI: 10.3389/fcteg.2021.722092
Ashlesha Akella, Chin-Teng Lin
In formation control, a robot (or an agent) learns to align itself in a particular spatial alignment. However, in a few scenarios, it is also vital to learn temporal alignment along with spatial alignment. An effective control system encompasses flexibility, precision, and timeliness. Existing reinforcement learning algorithms excel at learning to select an action given a state. However, executing an optimal action at an appropriate time remains challenging. Building a reinforcement learning agent which can learn an optimal time to act along with an optimal action can address this challenge. Neural networks in which timing relies on dynamic changes in the activity of population neurons have been shown to be a more effective representation of time. In this work, we trained a reinforcement learning agent to create its representation of time using a neural network with a population of recurrently connected nonlinear firing rate neurons. Trained using a reward-based recursive least square algorithm, the agent learned to produce a neural trajectory that peaks at the “time-to-act”; thus, it learns “when” to act. A few control system applications also require the agent to temporally scale its action. We trained the agent so that it could temporally scale its action for different speed inputs. Furthermore, given one state, the agent could learn to plan multiple future actions, that is, multiple times to act without needing to observe a new state.
{"title":"Time and Action Co-Training in Reinforcement Learning Agents","authors":"Ashlesha Akella, Chin-Teng Lin","doi":"10.3389/fcteg.2021.722092","DOIUrl":"https://doi.org/10.3389/fcteg.2021.722092","url":null,"abstract":"In formation control, a robot (or an agent) learns to align itself in a particular spatial alignment. However, in a few scenarios, it is also vital to learn temporal alignment along with spatial alignment. An effective control system encompasses flexibility, precision, and timeliness. Existing reinforcement learning algorithms excel at learning to select an action given a state. However, executing an optimal action at an appropriate time remains challenging. Building a reinforcement learning agent which can learn an optimal time to act along with an optimal action can address this challenge. Neural networks in which timing relies on dynamic changes in the activity of population neurons have been shown to be a more effective representation of time. In this work, we trained a reinforcement learning agent to create its representation of time using a neural network with a population of recurrently connected nonlinear firing rate neurons. Trained using a reward-based recursive least square algorithm, the agent learned to produce a neural trajectory that peaks at the “time-to-act”; thus, it learns “when” to act. A few control system applications also require the agent to temporally scale its action. We trained the agent so that it could temporally scale its action for different speed inputs. Furthermore, given one state, the agent could learn to plan multiple future actions, that is, multiple times to act without needing to observe a new state.","PeriodicalId":73076,"journal":{"name":"Frontiers in control engineering","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2021-08-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49016968","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 : 2021-08-02DOI: 10.3389/fcteg.2021.707729
Kunal Garg, Dimitra Panagou
In this work, we study finite-time stability of hybrid systems with unstable modes. We present sufficient conditions in terms of multiple Lyapunov functions for the origin of a class of hybrid systems to be finite-time stable. More specifically, we show that even if the value of the Lyapunov function increases during continuous flow, i.e., if the unstable modes in the system are active for some time, finite-time stability can be guaranteed if the finite-time convergent mode is active for a sufficient amount of cumulative time. This is the first work on finite-time stability of hybrid systems using multiple Lyapunov functions. Prior work uses a common Lyapunov function approach, and requires the Lyapunov function to be decreasing during the continuous flows and non-increasing at the discrete jumps, thereby, restricting the hybrid system to only have stable modes, or to only evolve along the stable modes. In contrast, we allow Lyapunov functions to increase both during the continuous flows and the discrete jumps. As thus, the derived stability results are less conservative compared to the earlier results in the related literature, and in effect allow the hybrid system to have unstable modes.
{"title":"Finite-Time Stability of Hybrid Systems With Unstable Modes","authors":"Kunal Garg, Dimitra Panagou","doi":"10.3389/fcteg.2021.707729","DOIUrl":"https://doi.org/10.3389/fcteg.2021.707729","url":null,"abstract":"In this work, we study finite-time stability of hybrid systems with unstable modes. We present sufficient conditions in terms of multiple Lyapunov functions for the origin of a class of hybrid systems to be finite-time stable. More specifically, we show that even if the value of the Lyapunov function increases during continuous flow, i.e., if the unstable modes in the system are active for some time, finite-time stability can be guaranteed if the finite-time convergent mode is active for a sufficient amount of cumulative time. This is the first work on finite-time stability of hybrid systems using multiple Lyapunov functions. Prior work uses a common Lyapunov function approach, and requires the Lyapunov function to be decreasing during the continuous flows and non-increasing at the discrete jumps, thereby, restricting the hybrid system to only have stable modes, or to only evolve along the stable modes. In contrast, we allow Lyapunov functions to increase both during the continuous flows and the discrete jumps. As thus, the derived stability results are less conservative compared to the earlier results in the related literature, and in effect allow the hybrid system to have unstable modes.","PeriodicalId":73076,"journal":{"name":"Frontiers in control engineering","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2021-08-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45781904","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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