1. F. Dörfler and F. Bullo. Synchronization and Transient Stability in Power Networks and Non-Uniform Kuramoto Oscillators. SIAM Journal on Control and Optimization, 50(3):1616-1642, 2012. Keyword(s): Power Networks, Complex Oscillator Networks. Abstract:

   Motivated by recent interest for multiagent systems and smart grid architectures, we discuss the synchronization problem for the network-reduced model of a power system with nontrivial transfer conductances. Our key insight is to exploit the relationship between the power network model and a first-order model of coupled oscillators. Assuming overdamped generators (possibly due to local excitation controllers), a singular perturbation analysis shows the equivalence between the classic swing equations and a nonuniform Kuramoto model. Here, nonuniform Kuramoto oscillators are characterized by multiple time constants, nonhomogeneous coupling, and nonuniform phase shifts. Extending methods from transient stability, synchronization theory, and consensus protocols, we establish sufficient conditions for synchronization of nonuniform Kuramoto oscillators. These conditions reduce to necessary and sufficient tests for the standard Kuramoto model. Combining our singular perturbation and Kuramoto analyses, we derive concise and purely algebraic conditions that relate synchronization in a power network to the underlying network parameters.

   
   

   @article{FD-FB:09z,
   abstract = {Motivated by recent interest for multiagent systems and smart grid architectures, we discuss the synchronization problem for the network-reduced model of a power system with nontrivial transfer conductances. Our key insight is to exploit the relationship between the power network model and a first-order model of coupled oscillators. Assuming overdamped generators (possibly due to local excitation controllers), a singular perturbation analysis shows the equivalence between the classic swing equations and a nonuniform Kuramoto model. Here, nonuniform Kuramoto oscillators are characterized by multiple time constants, nonhomogeneous coupling, and nonuniform phase shifts. Extending methods from transient stability, synchronization theory, and consensus protocols, we establish sufficient conditions for synchronization of nonuniform Kuramoto oscillators. These conditions reduce to necessary and sufficient tests for the standard Kuramoto model. Combining our singular perturbation and Kuramoto analyses, we derive concise and purely algebraic conditions that relate synchronization in a power network to the underlying network parameters. },
   author = {F. D{ö}rfler and F. Bullo},
   date-added = {2012-11-10 20:13:02 +0000},
   date-modified = {2013-10-01 04:25:28 +0000},
   funding = {IIS-0904501, CPS-1135819},
   journal = {SIAM Journal on Control and Optimization},
   keywords = {Power Networks, Complex Oscillator Networks},
   number = 3,
   pages = {1616-1642},
   pdf = {http://epubs.siam.org/doi/pdf/10.1137/110851584},
   title = {Synchronization and Transient Stability in Power Networks and Non-Uniform {K}uramoto Oscillators},
   url = {http://epubs.siam.org/doi/abs/10.1137/110851584},
   volume = 50,
   year = 2012,
   bdsk-url-1 = {http://epubs.siam.org/doi/abs/10.1137/110851584} 
   }
   

1. F. Dörfler and F. Bullo. Exploring synchronization in complex oscillator networks. In IEEE Conf. on Decision and Control, Maui, HI, USA, pages 7157-7170, December 2012. Keyword(s): Power Networks, Complex Oscillator Networks.
   

   @inproceedings{FD-FB:12i,
   address = {Maui, HI, USA},
   author = {F. D{ö}rfler and F. Bullo},
   booktitle = {{IEEE} Conf.\ on Decision and Control},
   date-added = {2012-07-02 15:34:10 -0600},
   date-modified = {2013-10-01 05:27:19 +0000},
   funding = {NSF-IIS-0904501 NSF-CPS-1135819},
   keywords = {Power Networks, Complex Oscillator Networks},
   month = dec,
   pages = {7157-7170},
   pdf = {http://motion.me.ucsb.edu/pdf/2012i-db.pdf},
   title = {Exploring synchronization in complex oscillator networks},
   url = {http://ieeexplore.ieee.org/xpl/articleDetails.jsp?tp=&arnumber=6425823&contentType=Conference+Publications&searchWithin%3Dp_Authors%3A.QT.Dorfler%2C+F..QT.%26searchField%3DSearch_All},
   year = 2012,
   bdsk-url-1 = {http://ieeexplore.ieee.org/xpl/articleDetails.jsp?tp=&arnumber=6425823&contentType=Conference+Publications&searchWithin%3Dp_Authors%3A.QT.Dorfler%2C+F..QT.%26searchField%3DSearch_All} 
   }
   




2. F. Dörfler, M. Chertkov, and F. Bullo. Synchronization Assessment in Power Networks and Coupled Oscillators. In IEEE Conf. on Decision and Control, Maui, HI, USA, pages 4998-5003, December 2012. Keyword(s): Power Networks, Complex Oscillator Networks.
   

   @inproceedings{FD-MC-FB:12d,
   address = {Maui, HI, USA},
   author = {F. D{ö}rfler and M. Chertkov and F. Bullo},
   booktitle = {{IEEE} Conf.\ on Decision and Control},
   date-added = {2012-11-17 06:50:25 +0000},
   date-modified = {2013-10-01 05:36:54 +0000},
   keywords = {Power Networks, Complex Oscillator Networks},
   month = {December},
   pages = {4998--5003},
   pdf = {http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=6426586},
   title = {Synchronization Assessment in Power Networks and Coupled Oscillators},
   url = {http://ieeexplore.ieee.org/xpls/abs_all.jsp?arnumber=6426586},
   year = {2012},
   bdsk-url-1 = {http://ieeexplore.ieee.org/xpls/abs_all.jsp?arnumber=6426586} 
   }
   




3. F. Pasqualetti, F. Dörfler, and F. Bullo. Cyber-physical security via geometric control: Distributed monitoring and malicious attacks. In IEEE Conf. on Decision and Control, Maui, HI, USA, pages 3418-3425, December 2012. Keyword(s): Secure Control Systems, Linear Control Design, Distributed Control Algorithms, Power Networks.
   

   @inproceedings{FP-FD-FB:12c,
   address = {Maui, HI, USA},
   author = {F. Pasqualetti and F. D{ö}rfler and F. Bullo},
   booktitle = {{IEEE} Conf.\ on Decision and Control},
   date-added = {2012-07-02 15:33:15 -0600},
   date-modified = {2013-10-01 05:25:24 +0000},
   funding = {NSF-IIS-0904501 NSF-CPS-1135819},
   keywords = {Secure Control Systems, Linear Control Design, Distributed Control Algorithms, Power Networks},
   month = dec,
   pages = {3418-3425},
   pdf = {http://motion.me.ucsb.edu/pdf/2012c-pdb.pdf},
   title = {Cyber-physical security via geometric control: {D}istributed monitoring and malicious attacks},
   url = {http://ieeexplore.ieee.org/xpl/articleDetails.jsp?tp=&arnumber=6426257&contentType=Conference+Publications&searchWithin%3Dp_Authors%3A.QT.Dorfler%2C+F..QT.%26searchField%3DSearch_All},
   year = 2012,
   bdsk-url-1 = {http://ieeexplore.ieee.org/xpl/articleDetails.jsp?tp=&arnumber=6426257&contentType=Conference+Publications&searchWithin%3Dp_Authors%3A.QT.Dorfler%2C+F..QT.%26searchField%3DSearch_All} 
   }
   




4. J. W. Simpson-Porco, F. Dörfler, and F. Bullo. Droop-controlled inverters are Kuramoto oscillators. In IFAC Workshop on Distributed Estimation and Control in Networked Systems, Santa Barbara, CA, USA, pages 264-269, September 2012. Keyword(s): Microgrids, Complex Oscillator Networks.
   

   @inproceedings{JWSP-FD-FB:12j,
   address = {Santa Barbara, CA, USA},
   author = {J. W. Simpson-Porco and F. D{ö}rfler and F. Bullo},
   booktitle = {IFAC Workshop on Distributed Estimation and Control in Networked Systems},
   date-added = {2012-10-17 18:15:38 +0000},
   date-modified = {2013-10-01 05:27:00 +0000},
   funding = {NSF-CPS-1135819},
   keywords = {Microgrids, Complex Oscillator Networks},
   month = sep,
   pages = {264-269},
   pdf = {http://motion.me.ucsb.edu/pdf/2012j-sdb.pdf},
   title = {Droop-controlled inverters are {Kuramoto} oscillators},
   url = {http://www.ifac-papersonline.net/Detailed/56785.html},
   year = 2012,
   bdsk-url-1 = {http://www.ifac-papersonline.net/Detailed/56785.html} 
   }
   

1. F. Dörfler and F. Bullo. Exploring Synchronization in Complex Oscillator Networks, September 2012. Note: Extended version including proofs. Available at http://arxiv.org/abs/1209.1335. Keyword(s): Power Networks, Complex Oscillator Networks.
   

   @misc{FD-FB:12i-arxiv,
   author = {F. D{ö}rfler and F. Bullo},
   date-added = {2012-10-17 18:24:08 +0000},
   date-modified = {2013-10-01 05:22:09 +0000},
   funding = {NSF-IIS-0904501 NSF-CPS-1135819},
   keywords = {Power Networks, Complex Oscillator Networks},
   month = sep,
   note = {{E}xtended version including proofs. Available at {http://arxiv.org/abs/1209.1335}},
   pdf = {http://arxiv.org/pdf/1209.1335},
   title = {Exploring Synchronization in Complex Oscillator Networks},
   year = 2012 
   }
   




2. F. Dörfler, M. Chertkov, and F. Bullo. Synchronization in Complex Oscillator Networks and Smart Grids, July 2012. Note: Available at http://arxiv.org/abs/1208.0045. Keyword(s): Complex Oscillator Networks, Power Networks.
   

   @misc{FD-MC-FB:11v-arxiv,
   author = {F. D{ö}rfler and M. Chertkov and F. Bullo},
   date-added = {2013-07-19 16:43:21 +0000},
   date-modified = {2013-10-01 05:00:43 +0000},
   keywords = {Complex Oscillator Networks, Power Networks},
   month = jul,
   note = {Available at {http://arxiv.org/abs/1208.0045}},
   pdf = {http://arxiv.org/pdf/1208.0045},
   title = {Synchronization in Complex Oscillator Networks and Smart Grids},
   year = 2012 
   }
   




3. F. Pasqualetti, F. Dörfler, and F. Bullo. Attack Detection and Identification in Cyber-Physical Systems -- Part I: Models and Fundamental Limitations, February 2012. Note: Available at http://arxiv.org/abs/1202.6144. Keyword(s): Secure Control Systems, Power Networks, Power Networks, Distributed Control Algorithms, Secure Control Systems, Linear Control Design. Abstract:

   Cyber-physical systems integrate computation, communication, and physical capabilities to interact with the physical world and humans. Besides failures of components, cyber-physical systems are prone to malignant attacks, and specific analysis tools as well as monitoring mechanisms need to be developed to enforce system security and reliability. This paper proposes a unified framework to analyze the resilience of cyber-physical systems against attacks cast by an omniscient adversary. We model cyber-physical systems as linear descriptor systems, and attacks as exogenous unknown inputs. Despite its simplicity, our model captures various real-world cyber-physical systems, and it includes and generalizes many prototypical attacks, including stealth, (dynamic) false-data injection and replay attacks. First, we characterize fundamental limitations of static, dynamic, and active monitors for attack detection and identification. Second, we provide constructive algebraic conditions to cast undetectable and unidentifiable attacks. Third, by using the system interconnection structure, we describe graph-theoretic conditions for the existence of undetectable and unidentifiable attacks. Finally, we validate our findings through some illustrative examples with different cyber-physical systems, such as a municipal water supply network and two electrical power grids.

   
   

   @misc{FP-FD-FB:10ya,
   abstract = {Cyber-physical systems integrate computation, communication, and physical capabilities to interact with the physical world and humans. Besides failures of components, cyber-physical systems are prone to malignant attacks, and specific analysis tools as well as monitoring mechanisms need to be developed to enforce system security and reliability. This paper proposes a unified framework to analyze the resilience of cyber-physical systems against attacks cast by an omniscient adversary. We model cyber-physical systems as linear descriptor systems, and attacks as exogenous unknown inputs. Despite its simplicity, our model captures various real-world cyber-physical systems, and it includes and generalizes many prototypical attacks, including stealth, (dynamic) false-data injection and replay attacks. First, we characterize fundamental limitations of static, dynamic, and active monitors for attack detection and identification. Second, we provide constructive algebraic conditions to cast undetectable and unidentifiable attacks. Third, by using the system interconnection structure, we describe graph-theoretic conditions for the existence of undetectable and unidentifiable attacks. Finally, we validate our findings through some illustrative examples with different cyber-physical systems, such as a municipal water supply network and two electrical power grids. },
   author = {F. Pasqualetti and F. D{ö}rfler and F. Bullo},
   date-added = {2012-11-21 18:27:48 +0000},
   date-modified = {2013-10-01 05:06:24 +0000},
   funding = {CNS-1135819, W911NF-09-0001},
   keyword = {Secure Control Systems, Power Networks},
   keywords = {Power Networks, Distributed Control Algorithms, Secure Control Systems, Linear Control Design},
   month = feb,
   note = {{Available at {http://arxiv.org/abs/1202.6144}}},
   pdf = {http://arxiv.org/pdf/1202.6144v2.pdf},
   title = {Attack Detection and Identification in Cyber-Physical Systems -- {P}art {I}: {M}odels and Fundamental Limitations},
   year = 2012,
   bdsk-url-1 = {http://arxiv.org/pdf/1202.6144v2.pdf} 
   }
   




4. F. Pasqualetti, F. Dörfler, and F. Bullo. Attack Detection and Identification in Cyber-Physical Systems -- Part II: Centralized and Distributed Monitor Design, February 2012. Note: Available at http://arxiv.org/abs/1202.6049. Keyword(s): Secure Control Systems, Power Networks, Power Networks, Distributed Control Algorithms, Secure Control Systems, Linear Control Design. Abstract:

   Cyber-physical systems integrate computation, communication, and physical capabilities to interact with the physical world and humans. Besides failures of components, cyber-physical systems are prone to malicious attacks so that specific analysis tools and monitoring mechanisms need to be developed to enforce system security and reliability. This paper builds upon the results presented in our companion paper \cite{FP-FD-FB:12a} and proposes centralized and decentralized monitors for attack detection and identification. First, we design optimal centralized attack detection and identification monitors. Optimality refers to the ability of detecting (respectively identifying) \emph{every} detectable (respectively identifiable) attack. Second, we design an optimal distributed attack detection filter based upon a waveform relaxation technique. Third, we show that the attack identification problem is computationally hard, and we design a sub-optimal distributed attack identification procedure with performance guarantees. Finally, we illustrate the robustness of our monitors to system noise and unmodeled dynamics through a simulation study.

   
   

   @misc{FP-FD-FB:10yb,
   abstract = {Cyber-physical systems integrate computation, communication, and physical capabilities to interact with the physical world and humans. Besides failures of components, cyber-physical systems are prone to malicious attacks so that specific analysis tools and monitoring mechanisms need to be developed to enforce system security and reliability. This paper builds upon the results presented in our companion paper \cite{FP-FD-FB:12a} and proposes centralized and decentralized monitors for attack detection and identification. First, we design optimal centralized attack detection and identification monitors. Optimality refers to the ability of detecting (respectively identifying) \emph{every} detectable (respectively identifiable) attack. Second, we design an optimal distributed attack detection filter based upon a waveform relaxation technique. Third, we show that the attack identification problem is computationally hard, and we design a sub-optimal distributed attack identification procedure with performance guarantees. Finally, we illustrate the robustness of our monitors to system noise and unmodeled dynamics through a simulation study.},
   author = {F. Pasqualetti and F. D{ö}rfler and F. Bullo},
   date-added = {2012-11-21 18:27:48 +0000},
   date-modified = {2013-10-01 05:00:12 +0000},
   funding = {CNS-1135819, W911NF-09-0001},
   keyword = {Secure Control Systems, Power Networks},
   keywords = {Power Networks, Distributed Control Algorithms, Secure Control Systems, Linear Control Design},
   month = feb,
   note = {{Available at {http://arxiv.org/abs/1202.6049}}},
   pdf = {http://arxiv.org/pdf/1202.6049v1.pdf},
   title = {Attack Detection and Identification in Cyber-Physical Systems -- {P}art {II}: {C}entralized and Distributed Monitor Design},
   year = 2012 
   }
   




5. J. W. Simpson-Porco, F. Dörfler, and F. Bullo. Droop-controlled inverters are Kuramoto oscillators, June 2012. Note: Available at http://arxiv.org/pdf/1206.5033v1.pdf. Keyword(s): Complex Oscillator Networks, Microgrids.
   

   @misc{JWSP-FD-FB:12j-arxiv,
   author = {J. W. Simpson-Porco and F. D{ö}rfler and F. Bullo},
   date-added = {2012-10-17 18:24:08 +0000},
   date-modified = {2013-10-01 05:00:26 +0000},
   keywords = {Complex Oscillator Networks, Microgrids},
   month = jun,
   note = {Available at {http://arxiv.org/pdf/1206.5033v1.pdf}},
   pdf = {http://arxiv.org/pdf/1206.5033},
   title = {Droop-controlled inverters are {Kuramoto} oscillators},
   year = 2012 
   }
   




6. J. W. Simpson-Porco, F. Dörfler, and F. Bullo. Synchronization and Power Sharing for Droop-Controlled Inverters in Islanded Microgrids, November 2012. Note: Available at http://arxiv.org/abs/1206.5033. Keyword(s): Microgrids, Complex Oscillator Networks, Distributed Control Algorithms, Frequency Control, Power Networks.
   

   @misc{JWSP-FD-FB:12u-arxiv,
   author = {J. W. Simpson-Porco and F. D{ö}rfler and F. Bullo},
   date-added = {2012-11-21 18:40:10 +0000},
   date-modified = {2018-05-01 12:24:01 +0000},
   funding = {CPS-1135819},
   keywords = {Microgrids, Complex Oscillator Networks, Distributed Control Algorithms, Frequency Control, Power Networks},
   month = nov,
   note = {{Available at {http://arxiv.org/abs/1206.5033}}},
   pdf = {http://arxiv.org/pdf/1206.5033v3.pdf},
   title = {Synchronization and Power Sharing for Droop-Controlled Inverters in Islanded Microgrids},
   year = 2012 
   }
   

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