Pub Date : 2017-05-24DOI: 10.23919/ACC.2017.7963778
A. Taha, Nikolaos Gatsis, T. Summers, Sebastian A. Nugroho
In cyber-physical systems (CPS), the problem of controlling resources can be depicted as an actuator selection problem. Given a large library of actuators and a control objective, what is the least number of actuators to be selected, and what is the corresponding optimal control law? These dynamic design questions are inherently coupled. In this paper, we show that a breadth of actuator selection and optimal control problems (stabilizability, robust and LQR control routines, control of uncertain, nonlinear systems) that do not satisfy the submodularity property lead to the formulation of two classes of combinatorial optimization routines for unstable CPSs: mixed-integer semidefinite programs and mixed-integer bilinear matrix inequalities. Branch-and-bound and greedy algorithms are proposed to address the computational complexity, and numerical results are given to illustrate the proposed formulations.
{"title":"Actuator selection for cyber-physical systems","authors":"A. Taha, Nikolaos Gatsis, T. Summers, Sebastian A. Nugroho","doi":"10.23919/ACC.2017.7963778","DOIUrl":"https://doi.org/10.23919/ACC.2017.7963778","url":null,"abstract":"In cyber-physical systems (CPS), the problem of controlling resources can be depicted as an actuator selection problem. Given a large library of actuators and a control objective, what is the least number of actuators to be selected, and what is the corresponding optimal control law? These dynamic design questions are inherently coupled. In this paper, we show that a breadth of actuator selection and optimal control problems (stabilizability, robust and LQR control routines, control of uncertain, nonlinear systems) that do not satisfy the submodularity property lead to the formulation of two classes of combinatorial optimization routines for unstable CPSs: mixed-integer semidefinite programs and mixed-integer bilinear matrix inequalities. Branch-and-bound and greedy algorithms are proposed to address the computational complexity, and numerical results are given to illustrate the proposed formulations.","PeriodicalId":422926,"journal":{"name":"2017 American Control Conference (ACC)","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2017-05-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126716299","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 : 2017-05-24DOI: 10.23919/ACC.2017.7963788
Punit Tulpule, A. Rezaeian, Aditya Karumanchi, S. Midlam-Mohler
Model Based Design (MBD) and systems engineering topics have been separately included in the engineering undergraduate curriculum for many years. Dynamical systems, modeling, optimization, and control, and statistical methods for Validation and Verification (V&V) are typically separate courses, but when it comes to industrial applications, all of these topics need to be considered together using systems engineering principles. Hardware-In-the-Loop (HIL) is a commonly followed practice for V&V, but it was not a part of engineering curriculum at the Ohio State University (OSU). In order to better prepare future engineers for industry requirements, it is necessary to bridge the gaps between the knowledge students gain in different courses. Hence, a pilot course was developed and taught at The OSU, which includes MBD and V&V from a systems engineering perspective. A laboratory project and assignments were designed which used virtual HIL allowing the students hands on experience. The small size pilot class allowed each student access to the virtual HIL setup.
多年来，基于模型的设计(MBD)和系统工程主题已经分别包含在工程本科课程中。动态系统，建模，优化和控制，以及验证和验证(V&V)的统计方法通常是单独的课程，但是当涉及到工业应用时，所有这些主题都需要使用系统工程原理一起考虑。硬件在环(hardware - in - loop, HIL)是V&V通常遵循的实践，但它并不是俄亥俄州立大学(Ohio State University, OSU)工程课程的一部分。为了使未来的工程师更好地为行业需求做好准备，有必要弥合学生在不同课程中获得的知识之间的差距。因此，俄勒冈州立大学开发并教授了一个试点课程，从系统工程的角度来看，它包括MBD和V&V。设计了一个实验室项目和作业，使用虚拟HIL让学生动手体验。小规模的试点班级允许每个学生访问虚拟HIL设置。
{"title":"Model Based Design (MBD) and Hardware In the Loop (HIL) validation: Curriculum development","authors":"Punit Tulpule, A. Rezaeian, Aditya Karumanchi, S. Midlam-Mohler","doi":"10.23919/ACC.2017.7963788","DOIUrl":"https://doi.org/10.23919/ACC.2017.7963788","url":null,"abstract":"Model Based Design (MBD) and systems engineering topics have been separately included in the engineering undergraduate curriculum for many years. Dynamical systems, modeling, optimization, and control, and statistical methods for Validation and Verification (V&V) are typically separate courses, but when it comes to industrial applications, all of these topics need to be considered together using systems engineering principles. Hardware-In-the-Loop (HIL) is a commonly followed practice for V&V, but it was not a part of engineering curriculum at the Ohio State University (OSU). In order to better prepare future engineers for industry requirements, it is necessary to bridge the gaps between the knowledge students gain in different courses. Hence, a pilot course was developed and taught at The OSU, which includes MBD and V&V from a systems engineering perspective. A laboratory project and assignments were designed which used virtual HIL allowing the students hands on experience. The small size pilot class allowed each student access to the virtual HIL setup.","PeriodicalId":422926,"journal":{"name":"2017 American Control Conference (ACC)","volume":"435 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2017-05-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115957269","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 : 2017-05-24DOI: 10.23919/ACC.2017.7963569
Yi Cheng, V. Ugrinovskii
This paper considers the event-triggered leader-follower tracking control for interconnected systems. Unlike the large body of existing work, here we consider systems which are physically coupled with uncertain norm-bounded coupling between the subsystems. We propose a model based event-triggered tracking control strategy and an event triggering rule with a time-dependent threshold which guarantees that the tracking errors in the systems asymptotically converge to zero. With the proposed event triggering rule, we prove that the systems do not exhibit Zeno behavior. In addition, the proposed event-triggered tracking control strategy is also employed to decoupled multi-agent systems. The efficacy of the proposed method is discussed using a simulation example.
{"title":"Event-triggered leader-follower tracking control for interconnected systems with undirected communication graphs","authors":"Yi Cheng, V. Ugrinovskii","doi":"10.23919/ACC.2017.7963569","DOIUrl":"https://doi.org/10.23919/ACC.2017.7963569","url":null,"abstract":"This paper considers the event-triggered leader-follower tracking control for interconnected systems. Unlike the large body of existing work, here we consider systems which are physically coupled with uncertain norm-bounded coupling between the subsystems. We propose a model based event-triggered tracking control strategy and an event triggering rule with a time-dependent threshold which guarantees that the tracking errors in the systems asymptotically converge to zero. With the proposed event triggering rule, we prove that the systems do not exhibit Zeno behavior. In addition, the proposed event-triggered tracking control strategy is also employed to decoupled multi-agent systems. The efficacy of the proposed method is discussed using a simulation example.","PeriodicalId":422926,"journal":{"name":"2017 American Control Conference (ACC)","volume":"50 6 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2017-05-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123832992","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 : 2017-05-24DOI: 10.23919/ACC.2017.7963815
Jing Yan, Yan Wan, Junfei Xie, Shengli Fu, Songwei Li
Aerial networking using directional antennas (ANDA) is considered as a promising solution for the networking of unmanned aerial vehicles (UAVs) over long distance. The cyber constraints on communication channel characteristics and physical constraints on the payload, power, and mobility of UAVs produce challenges to achieve a robust ANDA. In this paper, an RSSI and fuzzy logic based control algorithm is developed to control directional antennas mounted on two moving UAVs to achieve a robust broad-band long-distance communication channel. In particular, the self-alignment of UAV-mounted directional antennas over a long distance is achieved through fusing GPS and communication channel characteristic measured by received signal strength indicator (RSSI), using unscented Kalman filter and fuzzy logic strategies. Simulations are performed to validate the RSSI and fuzzy logic based directional antenna control approach. The solution developed in this paper can significantly enhance the performance of wireless communication channel in imperfect environment subject to the unavailability of GPS and unstable strength of wireless signals.
{"title":"RSSI-based heading control for robust long-range aerial networking using directional antennas","authors":"Jing Yan, Yan Wan, Junfei Xie, Shengli Fu, Songwei Li","doi":"10.23919/ACC.2017.7963815","DOIUrl":"https://doi.org/10.23919/ACC.2017.7963815","url":null,"abstract":"Aerial networking using directional antennas (ANDA) is considered as a promising solution for the networking of unmanned aerial vehicles (UAVs) over long distance. The cyber constraints on communication channel characteristics and physical constraints on the payload, power, and mobility of UAVs produce challenges to achieve a robust ANDA. In this paper, an RSSI and fuzzy logic based control algorithm is developed to control directional antennas mounted on two moving UAVs to achieve a robust broad-band long-distance communication channel. In particular, the self-alignment of UAV-mounted directional antennas over a long distance is achieved through fusing GPS and communication channel characteristic measured by received signal strength indicator (RSSI), using unscented Kalman filter and fuzzy logic strategies. Simulations are performed to validate the RSSI and fuzzy logic based directional antenna control approach. The solution developed in this paper can significantly enhance the performance of wireless communication channel in imperfect environment subject to the unavailability of GPS and unstable strength of wireless signals.","PeriodicalId":422926,"journal":{"name":"2017 American Control Conference (ACC)","volume":"51 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2017-05-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122999882","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 : 2017-05-24DOI: 10.23919/ACC.2017.7963773
Mahyar Fazlyab, Alec Koppel, V. Preciado, Alejandro Ribeiro
We approach linearly constrained convex optimization problems through their dual reformulation. Specifically, we derive a family of accelerated dual algorithms by adopting a variational perspective in which the dual function of the problem represents the scaled potential energy of a synthetic mechanical system, and the kinetic energy is defined by the Bregman divergence induced by the dual velocity flow. Through application of Hamilton's principle, we derive a continuous-time dynamical system which exponentially converges to the saddle point of the Lagrangian. Moreover, this dynamical system only admits a stable discretization through accelerated higher-order gradient methods, which precisely corresponds to accelerated dual mirror ascent. In particular, we obtain discrete-time convergence rate O(1/kp), where p − 1 is the truncation index of the Taylor expansion of the dual function. For practicality sake, we consider p = 2 and p = 3 only, respectively corresponding to dual Nesterov acceleration and a dual variant of Nesterov's cubic regularized Newton method. This analysis provides an explanation from whence dual acceleration comes as the discretization of the Euler-Lagrange dynamics associated with the constrained convex program. We demonstrate the performance of the aforementioned continuous-time framework with numerical simulations.
{"title":"A variational approach to dual methods for constrained convex optimization","authors":"Mahyar Fazlyab, Alec Koppel, V. Preciado, Alejandro Ribeiro","doi":"10.23919/ACC.2017.7963773","DOIUrl":"https://doi.org/10.23919/ACC.2017.7963773","url":null,"abstract":"We approach linearly constrained convex optimization problems through their dual reformulation. Specifically, we derive a family of accelerated dual algorithms by adopting a variational perspective in which the dual function of the problem represents the scaled potential energy of a synthetic mechanical system, and the kinetic energy is defined by the Bregman divergence induced by the dual velocity flow. Through application of Hamilton's principle, we derive a continuous-time dynamical system which exponentially converges to the saddle point of the Lagrangian. Moreover, this dynamical system only admits a stable discretization through accelerated higher-order gradient methods, which precisely corresponds to accelerated dual mirror ascent. In particular, we obtain discrete-time convergence rate O(1/kp), where p − 1 is the truncation index of the Taylor expansion of the dual function. For practicality sake, we consider p = 2 and p = 3 only, respectively corresponding to dual Nesterov acceleration and a dual variant of Nesterov's cubic regularized Newton method. This analysis provides an explanation from whence dual acceleration comes as the discretization of the Euler-Lagrange dynamics associated with the constrained convex program. We demonstrate the performance of the aforementioned continuous-time framework with numerical simulations.","PeriodicalId":422926,"journal":{"name":"2017 American Control Conference (ACC)","volume":"2 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2017-05-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131262524","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 : 2017-05-24DOI: 10.23919/ACC.2017.7963476
Michael Izbicki, Sajjad Amini, C. Shelton, Hamed Mohsenian Rad
In a destabilizing attack against a power system, the adversary hacks into generators or load control mechanisms to insert positive feedback into the power system dynamics. The implementation of destabilizing attacks, both on the generation and load sides, have recently been studied. There are also recent advances on how to detect, i.e., realize the presence of, destabilizing attacks in power systems. However, identifying the location(s) of the compromised buses is still an open problem. This is particularly challenging if, as in practice, one does not even know the number of compromised buses. Another challenge is to keep the computational complexity low to allow fast attack identification with high accuracy. To address these various issues, we observe in this paper that destabilizing attacks can be modeled as a reparameterization of the power system's dynamical model. Therefore, we propose an attack detection method that uses the unscented Kalman filter to jointly estimate both the system states and parameters of the attack. We also propose a low-rank modification to the Kalman filter that improves computational efficiency while maintaining the detection accuracy. We show empirically that this method successfully identifies complex attacks involving many buses.
{"title":"Identification of destabilizing attacks in power systems","authors":"Michael Izbicki, Sajjad Amini, C. Shelton, Hamed Mohsenian Rad","doi":"10.23919/ACC.2017.7963476","DOIUrl":"https://doi.org/10.23919/ACC.2017.7963476","url":null,"abstract":"In a destabilizing attack against a power system, the adversary hacks into generators or load control mechanisms to insert positive feedback into the power system dynamics. The implementation of destabilizing attacks, both on the generation and load sides, have recently been studied. There are also recent advances on how to detect, i.e., realize the presence of, destabilizing attacks in power systems. However, identifying the location(s) of the compromised buses is still an open problem. This is particularly challenging if, as in practice, one does not even know the number of compromised buses. Another challenge is to keep the computational complexity low to allow fast attack identification with high accuracy. To address these various issues, we observe in this paper that destabilizing attacks can be modeled as a reparameterization of the power system's dynamical model. Therefore, we propose an attack detection method that uses the unscented Kalman filter to jointly estimate both the system states and parameters of the attack. We also propose a low-rank modification to the Kalman filter that improves computational efficiency while maintaining the detection accuracy. We show empirically that this method successfully identifies complex attacks involving many buses.","PeriodicalId":422926,"journal":{"name":"2017 American Control Conference (ACC)","volume":"3 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2017-05-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131411511","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 : 2017-05-24DOI: 10.23919/ACC.2017.7963205
Saied Mehdian, Zhengyuan Zhou, N. Bambos
Scheduling in queueing networks concerns a scenario where a scheduler, using system backlog information, decides to which processor to route arriving jobs to achieve various objectives. However, in such scenarios, a significant yet inevitable challenge facing the scheduler in practice is its delayed access to such system configuration information. In this paper, we incorporate this crucial delay element by considering the join-the-shortest-queue scheduling scheme and studying the effects on the system stability and performance arising from random delay in terms of the scheduler's access to system updates information. We characterize the interesting phenomenon observed that is of practical value: the join-the-shortest-queue is robust in the presence of such information delays.
{"title":"Join-the-shortest-queue scheduling with delay","authors":"Saied Mehdian, Zhengyuan Zhou, N. Bambos","doi":"10.23919/ACC.2017.7963205","DOIUrl":"https://doi.org/10.23919/ACC.2017.7963205","url":null,"abstract":"Scheduling in queueing networks concerns a scenario where a scheduler, using system backlog information, decides to which processor to route arriving jobs to achieve various objectives. However, in such scenarios, a significant yet inevitable challenge facing the scheduler in practice is its delayed access to such system configuration information. In this paper, we incorporate this crucial delay element by considering the join-the-shortest-queue scheduling scheme and studying the effects on the system stability and performance arising from random delay in terms of the scheduler's access to system updates information. We characterize the interesting phenomenon observed that is of practical value: the join-the-shortest-queue is robust in the presence of such information delays.","PeriodicalId":422926,"journal":{"name":"2017 American Control Conference (ACC)","volume":"133 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2017-05-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131425580","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 : 2017-05-24DOI: 10.23919/ACC.2017.7963478
M. Alizadeh, Hoi-To Wai, A. Goldsmith, A. Scaglione
We consider the coupling introduced between power and transportation systems through Electric Vehicles (EVs). We envision that a number of charging network operators track the mobility of EVs to better estimate their battery charging needs. They use this information to make better-informed decisions on how to participate in the wholesale market of electricity and also to design marginal retail prices that reduce wait times and electricity costs at charging stations. To formulate these decision-making and price design problems, we introduce a network flow model that can capture the temporally-variable travel and charge patterns of an EV population through expanding the transportation network with virtual arcs.
{"title":"Marginal charging station pricing in an intelligent electric transportation system","authors":"M. Alizadeh, Hoi-To Wai, A. Goldsmith, A. Scaglione","doi":"10.23919/ACC.2017.7963478","DOIUrl":"https://doi.org/10.23919/ACC.2017.7963478","url":null,"abstract":"We consider the coupling introduced between power and transportation systems through Electric Vehicles (EVs). We envision that a number of charging network operators track the mobility of EVs to better estimate their battery charging needs. They use this information to make better-informed decisions on how to participate in the wholesale market of electricity and also to design marginal retail prices that reduce wait times and electricity costs at charging stations. To formulate these decision-making and price design problems, we introduce a network flow model that can capture the temporally-variable travel and charge patterns of an EV population through expanding the transportation network with virtual arcs.","PeriodicalId":422926,"journal":{"name":"2017 American Control Conference (ACC)","volume":"115 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2017-05-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134198377","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 : 2017-05-24DOI: 10.23919/ACC.2017.7963375
C. Favaretto, D. Bassett, A. Cenedese, F. Pasqualetti
In this paper we study cluster synchronization in a network of Kuramoto oscillators, where groups of oscillators evolve cohesively and at different frequencies from the neighboring oscillators. Synchronization is critical in a variety of systems, where it enables complex functionalities and behaviors. Synchronization over networks depends on the oscillators' dynamics, the interaction topology, and coupling strengths, and the relationship between these different factors can be quite intricate. In this work we formally show that three network properties enable the emergence of cluster synchronization. Specifically, weak inter-cluster connections, strong intra-cluster connections, and sufficiently diverse natural frequencies among oscillators belonging to different groups. Our approach relies on system-theoretic tools, and is validated with numerical studies.
{"title":"Bode meets Kuramoto: Synchronized clusters in oscillatory networks","authors":"C. Favaretto, D. Bassett, A. Cenedese, F. Pasqualetti","doi":"10.23919/ACC.2017.7963375","DOIUrl":"https://doi.org/10.23919/ACC.2017.7963375","url":null,"abstract":"In this paper we study cluster synchronization in a network of Kuramoto oscillators, where groups of oscillators evolve cohesively and at different frequencies from the neighboring oscillators. Synchronization is critical in a variety of systems, where it enables complex functionalities and behaviors. Synchronization over networks depends on the oscillators' dynamics, the interaction topology, and coupling strengths, and the relationship between these different factors can be quite intricate. In this work we formally show that three network properties enable the emergence of cluster synchronization. Specifically, weak inter-cluster connections, strong intra-cluster connections, and sufficiently diverse natural frequencies among oscillators belonging to different groups. Our approach relies on system-theoretic tools, and is validated with numerical studies.","PeriodicalId":422926,"journal":{"name":"2017 American Control Conference (ACC)","volume":"82 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2017-05-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115726274","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 : 2017-05-24DOI: 10.23919/ACC.2017.7963075
Ji Liu, Dan Wang, Wei Chen, T. Başar
This paper considers a discrete-time modulus consensus model in which the interaction among a group of agents is described by a time-dependent, complex-valued, weighted digraph. It is shown that for any sequence of repeatedly jointly strongly connected digraphs, without any assumption on the structure of the complex-valued weights, the system asymptotically reaches modulus consensus. Sufficient conditions for exponential convergence to each possible type of limit states are provided. Specifically, it is shown that (1) if the sequence of complex-valued weighted digraphs is repeatedly jointly balanced with respect to the same type, the corresponding type of modulus consensus will be reached exponentially fast for almost all initial conditions; (2) if the sequence of complex-valued weighted digraphs is repeatedly jointly unbalanced, the system will converge to zero exponentially fast for all initial conditions.
{"title":"Modulus consensus over time-varying digraphs","authors":"Ji Liu, Dan Wang, Wei Chen, T. Başar","doi":"10.23919/ACC.2017.7963075","DOIUrl":"https://doi.org/10.23919/ACC.2017.7963075","url":null,"abstract":"This paper considers a discrete-time modulus consensus model in which the interaction among a group of agents is described by a time-dependent, complex-valued, weighted digraph. It is shown that for any sequence of repeatedly jointly strongly connected digraphs, without any assumption on the structure of the complex-valued weights, the system asymptotically reaches modulus consensus. Sufficient conditions for exponential convergence to each possible type of limit states are provided. Specifically, it is shown that (1) if the sequence of complex-valued weighted digraphs is repeatedly jointly balanced with respect to the same type, the corresponding type of modulus consensus will be reached exponentially fast for almost all initial conditions; (2) if the sequence of complex-valued weighted digraphs is repeatedly jointly unbalanced, the system will converge to zero exponentially fast for all initial conditions.","PeriodicalId":422926,"journal":{"name":"2017 American Control Conference (ACC)","volume":"35 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2017-05-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115298851","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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