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Decentralised minimum-time consensus ; ; et al in Automatica (2013), 49(5), 1227-1235 We consider the discrete-time dynamics of a network of agents that exchange information according to a nearest-neighbour protocol under which all agents are guaranteed to reach consensus asymptotically ... [more ▼] We consider the discrete-time dynamics of a network of agents that exchange information according to a nearest-neighbour protocol under which all agents are guaranteed to reach consensus asymptotically. We present a fully decentralised algorithm that allows any agent to compute the final consensus value of the whole network in finite time using the minimum number of successive values of its own state history. We show that the minimum number of steps is related to a Jordan block decomposition of the network dynamics, and present an algorithm to compute the final consensus value in the minimum number of steps by checking a rank condition of a Hankel matrix of local observations. Furthermore, we prove that the minimum number of steps is related to graph theoretical notions that can be directly computed from the Laplacian matrix of the graph and from the minimum external equitable partition. [less ▲] Detailed reference viewed: 147 (4 UL)Distributed Kalman Filter with minimum-time covariance computation ; ; et al in The proceedings of the IEEE 52nd Annual Conference on Decision and Control (2013) This paper considerably improves the well-known Distributed Kalman Filter (DKF) algorithm by Olfati-Saber (2007) by introducing a novel decentralised consensus value computation scheme, using only local ... [more ▼] This paper considerably improves the well-known Distributed Kalman Filter (DKF) algorithm by Olfati-Saber (2007) by introducing a novel decentralised consensus value computation scheme, using only local observations of sensors. It has been shown that the state estimates obtained in [8] and [9] approaches those of the Central Kalman Filter (CKF) asymptotically. However, the convergence to the CKF can sometimes be too slow. This paper proposes an algorithm that enables every node in a sensor network to compute the global average consensus matrix of measurement noise covariance in minimum time without accessing global information. Compared with the algorithm in [8], our theoretical analysis and simulation results show that the new algorithm can offer improved performance in terms of time taken for the state estimates to converge to that of the CKF. [less ▲] Detailed reference viewed: 92 (0 UL)Robust Signal-Structure Reconstruction ; ; Goncalves, Jorge et al in The proceedings of the IEEE 52nd Annual Conference on Decision and Control (2013) This paper focuses on the reconstruction of the signal structure of a system in the presence of noise and nonlinearities. Previous results on polynomial time reconstruction in this area were restricted to ... [more ▼] This paper focuses on the reconstruction of the signal structure of a system in the presence of noise and nonlinearities. Previous results on polynomial time reconstruction in this area were restricted to systems where target specificity was part of the inherent structure, [5]. This work extends these results to all reconstructible systems and proposes a faster reconstruction algorithm along with an improved model selection procedure. Finally, a simulation study then details the performance of this new algorithm on reconstructible systems. [less ▲] Detailed reference viewed: 87 (0 UL)Real-time Fault Diagnosis for Large-Scale Nonlinear Power Networks Pan, Wei ; ; et al in The proceedings of the IEEE 52nd Annual Conference on Decision and Control (2013) In this paper, automatic fault diagnosis in large scale power networks described by second-order nonlinear swing equations is studied. This work focuses on a class of faults that occur in the transmission ... [more ▼] In this paper, automatic fault diagnosis in large scale power networks described by second-order nonlinear swing equations is studied. This work focuses on a class of faults that occur in the transmission lines. Transmission line protection is an important issue in power system engineering because a large portion of power system faults is occurring in transmission lines. This paper presents a novel technique to detect, isolate and identify the faults on transmissions using only a small number of observations. We formulate the problem of fault diagnosis of nonlinear power network into a compressive sensing framework and derive an optimisation-based formulation of the fault identification problem. An iterative reweighted ℓ1-minimisation algorithm is finally derived to solve the detection problem efficiently. Under the proposed framework, a real-time fault monitoring scheme can be built using only measurements of phase angles of nonlinear power networks. [less ▲] Detailed reference viewed: 88 (0 UL)Network reconstruction using knock-out and over-expression data ; ; Goncalves, Jorge in The proceedings of the 2013 European Control Conference (ECC) (2013) This paper outlines necessary and sufficient conditions for network reconstruction of linear, time-invariant systems using data from either knock-out or over-expression experiments. These structural ... [more ▼] This paper outlines necessary and sufficient conditions for network reconstruction of linear, time-invariant systems using data from either knock-out or over-expression experiments. These structural system perturbations, which are common in biological experiments, can be formulated as unknown system inputs, allowing the network topology and dynamics to be found. We assume that only partial state measurements are available and propose an algorithm that can reconstruct the network at the level of the measured states using either time-series or steady-state data. A simulated example illustrates how the algorithm successfully reconstructs a network from data. [less ▲] Detailed reference viewed: 92 (0 UL)Dynamical structure function identifiability conditions enabling signal structure reconstruction ; ; et al in The proceedings of the 51st IEEE Conference on Decision and Control (CDC) (2012, December) Networks of controlled dynamical systems exhibit a variety of interconnection patterns that could be interpreted as the structure of the system. One such interpretation of system structure is a system's ... [more ▼] Networks of controlled dynamical systems exhibit a variety of interconnection patterns that could be interpreted as the structure of the system. One such interpretation of system structure is a system's signal structure, characterized as the open-loop causal dependencies among manifest variables and represented by its dynamical structure function. Although this notion of structure is among the weakest available, previous work has shown that if no a priori structural information is known about the system, not even the Boolean structure of the dynamical structure function is identifiable. Consequently, one method previously suggested for obtaining the necessary a priori structural information is to leverage knowledge about target specificity of the controlled inputs. This work extends these results to demonstrate precisely the a priori structural information that is both necessary and sufficient to reconstruct the network from input-output data. This extension is important because it significantly broadens the applicability of the identifiability conditions, enabling the design of network reconstruction experiments that were previously impossible due to practical constraints on the types of actuation mechanisms available to the engineer or scientist. The work is motivated by the proteomics problem of reconstructing the Per-Arnt-Sim Kinase pathway used in the metabolism of sugars. [less ▲] Detailed reference viewed: 90 (0 UL)In-silico Robust Reconstruction of the Per-Arnt-Sim Kinase Pathway using Dynamical Structure Functions ; ; et al Scientific Conference (2012, October) Detailed reference viewed: 56 (1 UL)EARLY FLOWERING4 Recruitment of EARLY FLOWERING3 in the Nucleus Sustains the Arabidopsis Circadian Clock ; ; et al in Plant Cell (2012), 24(2), 428-443 The plant circadian clock is proposed to be a network of several interconnected feedback loops, and loss of any component leads to changes in oscillator speed. We previously reported that Arabidopsis ... [more ▼] The plant circadian clock is proposed to be a network of several interconnected feedback loops, and loss of any component leads to changes in oscillator speed. We previously reported that Arabidopsis thaliana EARLY FLOWERING4 (ELF4) is required to sustain this oscillator and that the elf4 mutant is arrhythmic. This phenotype is shared with both elf3 and lux. Here, we show that overexpression of either ELF3 or LUX ARRHYTHMO (LUX) complements the elf4 mutant phenotype. Furthermore, ELF4 causes ELF3 to form foci in the nucleus. We used expression data to direct a mathematical position of ELF3 in the clock network. This revealed direct effects on the morning clock gene PRR9, and we determined association of ELF3 to a conserved region of the PRR9 promoter. A cis-element in this region was suggestive of ELF3 recruitment by the transcription factor LUX, consistent with both ELF3 and LUX acting genetically downstream of ELF4. Taken together, using integrated approaches, we identified ELF4/ELF3 together with LUX to be pivotal for sustenance of plant circadian rhythms. [less ▲] Detailed reference viewed: 107 (0 UL)Global State Synchronization in Networks of Cyclic Feedback Systems ; ; et al in IEEE Transactions on Automatic Control (2012), 57(2), 478-483 This technical note studies global asymptotic state synchronization in networks of identical systems. Conditions on the coupling strength required for the synchronization of nodes having a cyclic feedback ... [more ▼] This technical note studies global asymptotic state synchronization in networks of identical systems. Conditions on the coupling strength required for the synchronization of nodes having a cyclic feedback structure are deduced using incremental dissipativity theory. The method takes advantage of the incremental passivity properties of the constituent subsystems of the network nodes to reformulate the synchronization problem as one of achieving incremental passivity by coupling. The method can be used in the framework of contraction theory to constructively build a contracting metric for the incremental system. The result is illustrated for a network of biochemical oscillators. [less ▲] Detailed reference viewed: 90 (0 UL)Robust network reconstruction in polynomial time ; ; Goncalves, Jorge in The proceedings of the 51st IEEE Conference on Decision and Control (2012) This paper presents an efficient algorithm for robust network reconstruction of Linear Time-Invariant (LTI) systems in the presence of noise, estimation errors and unmodelled nonlinearities. The method ... [more ▼] This paper presents an efficient algorithm for robust network reconstruction of Linear Time-Invariant (LTI) systems in the presence of noise, estimation errors and unmodelled nonlinearities. The method here builds on previous work [1] on robust reconstruction to provide a practical implementation with polynomial computational complexity. Following the same experimental protocol, the algorithm obtains a set of structurally-related candidate solutions spanning every level of sparsity. We prove the existence of a magnitude bound on the noise, which if satisfied, guarantees that one of these structures is the correct solution. A problem-specific model-selection procedure then selects a single solution from this set and provides a measure of confidence in that solution. Extensive simulations quantify the expected performance for different levels of noise and show that significantly more noise can be tolerated in comparison to the original method. [less ▲] Detailed reference viewed: 94 (0 UL)Decentralised minimal-time dynamic consensus ; ; et al in The proceedings of the 2012 American Control Conference (ACC) (2012) This paper considers a group of agents that aim to reach an agreement on individually measured time-varying signals by local communication. In contrast to static network averaging problem, the consensus ... [more ▼] This paper considers a group of agents that aim to reach an agreement on individually measured time-varying signals by local communication. In contrast to static network averaging problem, the consensus we mean in this paper is reached in a dynamic sense. A discrete-time dynamic average consensus protocol can be designed to allow all the agents tracking the average of their reference inputs asymptotically. We propose a minimal-time dynamic consensus algorithm, which only utilises minimal number of local observations of randomly picked node in a network to compute the final consensus signal. Our results illustrate that with memory and computational ability, the running time of distributed averaging algorithms can be indeed improved dramatically using local information as suggested by Olshevsky and Tsitsiklis. [less ▲] Detailed reference viewed: 79 (1 UL)Reconstruction of arbitrary biochemical reaction networks: A compressive sensing approach Pan, Wei ; ; Goncalves, Jorge et al in The proceedings of the 51st IEEE Conference on Decision and Control (2012) Reconstruction of biochemical reaction networks (BRN) and genetic regulatory networks (GRN) in particular is a central topic in systems biology which raises crucial theoretical challenges in system ... [more ▼] Reconstruction of biochemical reaction networks (BRN) and genetic regulatory networks (GRN) in particular is a central topic in systems biology which raises crucial theoretical challenges in system identification. Nonlinear Ordinary Differential Equations (ODEs) that involve polynomial and rational functions are typically used to model biochemical reaction networks. Such nonlinear models make the problem of determining the connectivity of biochemical networks from time-series experimental data quite difficult. In this paper, we present a network reconstruction algorithm that can deal with ODE model descriptions containing polynomial and rational functions. Rather than identifying the parameters of linear or nonlinear ODEs characterised by pre-defined equation structures, our methodology allows us to determine the nonlinear ODEs structure together with their associated parameters. To solve the network reconstruction problem, we cast it as a compressive sensing (CS) problem and use sparse Bayesian learning (SBL) algorithms as a computationally efficient and robust way to obtain its solution. [less ▲] Detailed reference viewed: 361 (0 UL)Quantifying crosstalk in biochemical systems ; ; et al in The proceedings of the 51st IEEE Conference on Decision and Control (2012) Recent work has introduced biocircuit architectures that exhibit robust oscillatory behavior in organisms ranging from cyanobacteria to mammals. Complementary research in synthetic biology has introduced ... [more ▼] Recent work has introduced biocircuit architectures that exhibit robust oscillatory behavior in organisms ranging from cyanobacteria to mammals. Complementary research in synthetic biology has introduced oscillators in vivo and in vitro suggesting that robust oscillation can be recapitulated using a small number of biochemical components. In this work, we introduce signaling crosstalk in biocircuits as a consequence of enzyme-mediated biochemical reactions. As a motivating example, we consider an in vitro oscillator with two types of crosstalk: crosstalk in production and degradation of RNA signals. We then propose a framework for quantifying crosstalk and use it to derive several dynamical constraints and suggest design techniques for ameliorating crosstalk in vitro biochemical systems. We demonstrate that the effects of crosstalk can be attenuated through the effective tuning of two key parameters in order to recover desired system dynamics. As an example, we show that by changing the balance between production and degradation crosstalk, we can tune a system to be stable or exhibit oscillatory behavior. [less ▲] Detailed reference viewed: 100 (0 UL)Robust dynamical network structure reconstruction ; ; et al in Automatica (2011), 47(6), This paper addresses the problem of network reconstruction from data. Previous work identified necessary and sufficient conditions for network reconstruction of LTI systems, assuming perfect measurements ... [more ▼] This paper addresses the problem of network reconstruction from data. Previous work identified necessary and sufficient conditions for network reconstruction of LTI systems, assuming perfect measurements (no noise) and perfect system identification. This paper assumes that the conditions for network reconstruction have been met but here we additionally take into account noise and unmodelled dynamics (including nonlinearities). In order to identify the network structure that generated the data, we compute the smallest distances between the measured data and the data that would have been generated by particular network structures. We conclude with biologically inspired network reconstruction examples which include noise and nonlinearities. [less ▲] Detailed reference viewed: 109 (0 UL)The circadian oscillator gene GIGANTEA mediates a long-term response of the Arabidopsis thaliana circadian clock to sucrose ; ; et al in PNAS (2011), 108(12), 51045109 Circadian clocks are 24-h timing devices that phase cellular responses; coordinate growth, physiology, and metabolism; and anticipate the day–night cycle. Here we report sensitivity of the Arabidopsis ... [more ▼] Circadian clocks are 24-h timing devices that phase cellular responses; coordinate growth, physiology, and metabolism; and anticipate the day–night cycle. Here we report sensitivity of the Arabidopsis thaliana circadian oscillator to sucrose, providing evidence that plant metabolism can regulate circadian function. We found that the Arabidopsis circadian system is particularly sensitive to sucrose in the dark. These data suggest that there is a feedback between the molecular components that comprise the circadian oscillator and plant metabolism, with the circadian clock both regulating and being regulated by metabolism. We used also simulations within a three-loop mathematical model of the Arabidopsis circadian oscillator to identify components of the circadian clock sensitive to sucrose. The mathematical studies identified GIGANTEA (GI) as being associatedwith sucrose sensing. Experimental validation of this prediction demonstrated that GI is required for the full response of the circadian clock to sucrose. We demonstrate that GI acts as part of the sucrose-signaling network and propose this role permits metabolic input into circadian timing in Arabidopsis. [less ▲] Detailed reference viewed: 111 (2 UL)Mathematical relationships between representations of structure in linear interconnected dynamical systems ; Goncalves, Jorge ; et al in The proceedings of the 2011 American Control Conference (ACC) (2011) A dynamical system can exhibit structure on multiple levels. Different system representations can capture different elements of a dynamical system's structure. We consider LTI input-output dynamical ... [more ▼] A dynamical system can exhibit structure on multiple levels. Different system representations can capture different elements of a dynamical system's structure. We consider LTI input-output dynamical systems and present four representations of structure: complete computational structure, subsystem structure, signal structure, and input output sparsity structure. We then explore some of the mathematical relation ships that relate these different representations of structure. In particular, we show that signal and subsystem structure are fundamentally different ways of representing system structure. A signal structure does not always specify a unique subsystem structure nor does subsystem structure always specify a unique signal structure. We illustrate these concepts with a numerical example. [less ▲] Detailed reference viewed: 96 (2 UL)Decentralised minimal-time consensus ; ; et al in The proceedings of the 2011 50th IEEE Conference on Decision and Control and European Control Conference (CDC-ECC) (2011) This study considers the discrete-time dynamics of a network of agents that exchange information according to the nearest-neighbour protocol under which all agents are guaranteed to reach consensus ... [more ▼] This study considers the discrete-time dynamics of a network of agents that exchange information according to the nearest-neighbour protocol under which all agents are guaranteed to reach consensus asymptotically. We present a fully decentralised algorithm that allows any agent to compute the consensus value of the whole network in finite time using only the minimal number of successive values of its own history. We show that this minimal number of steps is related to a Jordan block decomposition of the network dynamics and present an algorithm to obtain the minimal number of steps in question by checking a rank condition on a Hankel matrix of the local observations. Furthermore, we prove that the minimal number of steps is related to other algebraic and graph theoretical notions that can be directly computed from the Laplacian matrix of the graph and from the underlying graph topology. [less ▲] Detailed reference viewed: 89 (0 UL)Understanding uctuations and limitations in a multi-sector model of the economy with delays and intrinsic noise Goncalves, Jorge ; ; et al in American Control Conference (2010, July) Detailed reference viewed: 42 (0 UL)A cost-effective atomic force microscope for undergraduate control laboratories ; Goncalves, Jorge in IEEE Transactions on Education (2010), 53(2), 328-334 This paper presents a simple, cost-effective and robust atomic force microscope (AFM), which has been purposely designed and built for use as a teaching aid in undergraduate controls labs. The guiding ... [more ▼] This paper presents a simple, cost-effective and robust atomic force microscope (AFM), which has been purposely designed and built for use as a teaching aid in undergraduate controls labs. The guiding design principle is to have all components be open and visible to the students, so the inner functioning of the microscope has been made clear to see. All of the parts but one are off the shelf, and assembly time is generally less than two days, which makes the microscope a robust instrument that is readily handled by the students with little chance of damage. While the scanning resolution is nowhere near that of a commercial instrument, it is more than sufficient to take interesting scans of micrometer-scale objects. A survey of students after their having used the AFM resulted in a generally good response, with 80% agreeing that they had a positive learning experience. [less ▲] Detailed reference viewed: 136 (0 UL)Fluctuations and Limitations of a Multi-Sector Economic Model with Delays ; ; Goncalves, Jorge et al in The proceedings of the 2010 American Control Conference (ACC) (2010) A general multi-sector model of the economy is investigated. A sector's input to production, labor, evolves according to a jump Markov process. Labor jumps between sectors to balance supply and demand ... [more ▼] A general multi-sector model of the economy is investigated. A sector's input to production, labor, evolves according to a jump Markov process. Labor jumps between sectors to balance supply and demand, where each sector differs by its productivity. The jump model captures the intrinsic noise of the micro agents on the macro level, which is represented by the random timing of labor jumps. Quantifying this noise is a central theme of this paper. An operator theoretic approach is utilized to capture the fluctuations of a linearized jump system exactly. As an illustrative example two sector and three sector economies are studied. In each case the optimal aggressiveness, gain, of a sector is determined for minimal variance. Delays are then introduced into the model. It is shown that the presence of a delay creates a limit on the minimum variance achievable and that high gain is destabilizing. For both the two and three sector models the nonlinear jump systems are simulated. It is shown that the operator theoretic approach is an appropriate method for quantifying the second moments. [less ▲] Detailed reference viewed: 77 (0 UL) |
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