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Constructive Synchronization of Networked Feedback Systems ; ; Goncalves, Jorge in The proceedings of the 49th IEEE Conference on Decision and Control (CDC) (2010) This paper is concerned with global asymptotic output synchronization in networks of identical feedback systems. Using an operator theoretic approach based on an incremental small gain theorem, the method ... [more ▼] This paper is concerned with global asymptotic output synchronization in networks of identical feedback systems. Using an operator theoretic approach based on an incremental small gain theorem, the method reformulates the synchronization problem as one of achieving incremental stability using a coupling operator that plays the role of an incrementally stabilizing feedback. In this way, conditions on static or dynamic coupling operators that achieve output synchronization of nodes of arbitrary structure are derived. These conditions lead to a methodology for the construction of coupling architectures that ensure output synchronization of a wide range of systems. The result is illustrated for a network of biochemical oscillators. [less ▲] Detailed reference viewed: 71 (0 UL)Minimal-time network reconstruction for DTLTI systems ; Goncalves, Jorge in The proceedings of the 49th IEEE Conference on Decision and Control (CDC) (2010) This paper considers the problem of obtaining in minimal time the “dynamical network structure” (DNS) from partial state observations of a discrete-time linear time-invariant system. From the DNS, we can ... [more ▼] This paper considers the problem of obtaining in minimal time the “dynamical network structure” (DNS) from partial state observations of a discrete-time linear time-invariant system. From the DNS, we can not only obtain the network structure of the system at the measurement level, but also estimate the minimal number of hidden states which are not observed directly. First, we discuss when reconstruction of the DNS is and is not possible. Then, we give an algorithm to find the minimal number of successive outputs to find the DNS. Finally, we discuss extensions of the results to non-linear and noisy systems. These results can be directly applied to the decentralised network control problem of multi-agent systems to find network connections of the observed agents. [less ▲] Detailed reference viewed: 86 (0 UL)Minimal-time uncertain output final value of unknown DT-LTI systems with application to the decentralised network consensus problem ; ; et al Scientific Conference (2010) Detailed reference viewed: 32 (0 UL)Robust dynamical network structure reconstruction ; ; et al Scientific Conference (2010) Motivated by biological applications, this paper addresses the problem of network reconstruction from data. Previous work has shown necessary and sufficient conditions for network reconstruction of noise ... [more ▼] Motivated by biological applications, this paper addresses the problem of network reconstruction from data. Previous work has shown necessary and sufficient conditions for network reconstruction of noise-free LTI systems. 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). Algorithms are therefore proposed to reconstruct dynamical (Boolean) network structure from time-series (steady-state) data respectively in presence of noise and 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 Boolean structures. Information criteria and optimisation technique balancing such distance and model complexity are introduced to search for the true structure. We conclude with biologically-inspired network reconstruction examples which include noise and nonlinearities. [less ▲] Detailed reference viewed: 80 (0 UL)Representing Structure in Linear Interconnected Dynamical Systems ; Goncalves, Jorge ; et al in The proceedings of the 49th IEEE Conference on Decision and Control (CDC) (2010) Interconnected dynamical systems are a pervasive component in our modern world's infrastructure. One of the fundamental steps to understanding the complex behavior and dynamics of these systems is ... [more ▼] Interconnected dynamical systems are a pervasive component in our modern world's infrastructure. One of the fundamental steps to understanding the complex behavior and dynamics of these systems is determining how to appropriately represent their structure. In this work, we discuss different ways of representing a system's structure. We define and present, in particular, four representations of system structure-complete computational, subsystem, signal, and zero pattern structure-and discuss some of their fundamental properties. We illustrate their application with a numerical example and show how radically different representations of structure can be consistent with a single LTI input-output system. [less ▲] Detailed reference viewed: 78 (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: 80 (0 UL)Correct biological timing in Arabidopsis requires multiple light-signaling pathways. ; ; et al in Proceedings of the National Academy of Sciences of the United States of America (2010), 107(29), 13171-13176 Circadian oscillators provide rhythmic temporal cues for a range of biological processes in plants and animals, enabling anticipation of the day/night cycle and enhancing fitness-associated traits. We ... [more ▼] Circadian oscillators provide rhythmic temporal cues for a range of biological processes in plants and animals, enabling anticipation of the day/night cycle and enhancing fitness-associated traits. We have used engineering models to understand the control principles of a plant's response to seasonal variation. We show that the seasonal changes in the timing of circadian outputs require light regulation via feed-forward loops, combining rapid light-signaling pathways with entrained circadian oscillators. Linear time-invariant models of circadian rhythms were computed for 3,503 circadian-regulated genes and for the concentration of cytosolic-free calcium to quantify the magnitude and timing of regulation by circadian oscillators and light-signaling pathways. Bioinformatic and experimental analysis show that rapid light-induced regulation of circadian outputs is associated with seasonal rephasing of the output rhythm. We identify that external coincidence is required for rephasing of multiple output rhythms, and is therefore important in general phase control in addition to specific photoperiod-dependent processes such as flowering and hypocotyl elongation. Our findings uncover a fundamental design principle of circadian regulation, and identify the importance of rapid light-signaling pathways in temporal control. [less ▲] Detailed reference viewed: 92 (2 UL)Robust dynamical network reconstruction ; ; et al in The proceedings of the 49th IEEE Conference on Decision and Control (CDC) (2010) Motivated by biological applications, this paper addresses the problem of network reconstruction from data. Previous work has shown necessary and sufficient conditions for network reconstruction of noise ... [more ▼] Motivated by biological applications, this paper addresses the problem of network reconstruction from data. Previous work has shown necessary and sufficient conditions for network reconstruction of noise-free LTI systems. 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). Algorithms are therefore proposed to reconstruct dynamical (Boolean) network structure from time-series (steady-state) data respectively in presence of noise and 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 Boolean structures. Information criteria and optimisation technique balancing such distance and model complexity are introduced to search for the true structure. We conclude with biologically-inspired network reconstruction examples which include noise and nonlinearities. [less ▲] Detailed reference viewed: 81 (0 UL)A Linear Programming Approach to Parameter Fitting for the Master Equation ; Goncalves, Jorge in IEEE Transactions on Automatic Control (2009), 54(10), 2451-2455 This technical note proposes a new framework for the design of continuous time, finite state space Markov processes. In particular, we propose a paradigm for selecting an optimal matrix within a pre ... [more ▼] This technical note proposes a new framework for the design of continuous time, finite state space Markov processes. In particular, we propose a paradigm for selecting an optimal matrix within a pre-specified pencil of transition rate matrices. Given any transition rate matrix specifying the time-evolution of the Markov process, we propose a class of figures of merit that upper-bounds the long-term evolution of any statistical moment. We show that optimization with respect to the aforementioned class of cost functions is tractable via dualization and linear programming methods. In addition, we suggest how this approach can be used as a tool for the sub-optimal design of the master equation, with performance guarantees. Our results are applied to illustrative examples. [less ▲] Detailed reference viewed: 97 (1 UL)Network Structure Preserving Model Reduction: Results of a Simulation Study ; Goncalves, Jorge ; et al in The proceedings of the Third International Conference on Foundations of Systems Biology in Engineering (FOSBE 2009) (2009) Reconstructed models of biochemical networks often reflect the high level of complexity inherent in the biological system being modeled. The difficulties of predicting gene expression and analyzing the ... [more ▼] Reconstructed models of biochemical networks often reflect the high level of complexity inherent in the biological system being modeled. The difficulties of predicting gene expression and analyzing the effects of individual perturbations at a system-wide resolution are exacerbated by model complexity. This paper extends a state projection method for structure preserving model reduction to a particular model class of reconstructed networks known as dynamical structure functions. In contrast to traditional approaches where a priori knowledge of partitions on unmeasured species is required, dynamical structure functions require a weaker notion of system structure, specifying only the causal relationship between measured chemical species of the system. The resulting technique, like similar approaches, does not provide theoretical performance guarantees, so an extensive computational study is conducted, and it is observed to work fairly well in practice. Moreover, sufficient conditions, characterizing edge loss resulting from the reduction process, are presented. [less ▲] Detailed reference viewed: 46 (2 UL)Decentralized final value theorem for discrete-time LTI systems with application to minimal time distributed consensus ; ; et al in The proceedings of the Joint 48th IEEE Conference on Decision and Control and 28th Chinese Control Conference (2009) In this study, we consider an unknown discrete-time, linear time-invariant, autonomous system and characterise, the minimal number of discrete-time steps necessary to compute the asymptotic final value of ... [more ▼] In this study, we consider an unknown discrete-time, linear time-invariant, autonomous system and characterise, the minimal number of discrete-time steps necessary to compute the asymptotic final value of a state. The results presented in this paper have a direct link with the celebrated final value theorem. We apply these results to the design of an algorithm for minimal-time distributed consensus and illustrate the results on an example. [less ▲] Detailed reference viewed: 49 (0 UL)Control Theory and Systems Biology Goncalves, Jorge ; in Iglesias, P. A.; Ingalls, B. P. (Eds.) Dynamical structure Functions in Network Reconstruction (2009) Presenting a control-theoretic treatment of stoichiometric systems, ... local parametric sensitivity analysis, the two approaches yield identical results. ... Detailed reference viewed: 162 (4 UL)A Comparison of Network Reconstruction Methods for Chemical Reaction Networks ; ; et al in The proceedings of the Third International Conference on Foundations of Systems Biology in Engineering (FOSBE 2009) (2009) Chemical reaction networks model biological interactions that regulate the functional properties of a cell; these networks characterize the chemical pathways that result in a particular phenotype. One ... [more ▼] Chemical reaction networks model biological interactions that regulate the functional properties of a cell; these networks characterize the chemical pathways that result in a particular phenotype. One goal of systems biology is to understand the structure of these networks given concentration measurements of various species in the system. Previous work has shown that this network reconstruction problem is fundamentally impossible, even for simplified linear models, unless a particular experiment design is followed. Nevertheless, reconstruction algorithms have been developed that attempt to approximate a solution using sparsity or similar heuristics. This work compares, in silico, the results of three of these methods in situations where the necessary experiment design has been followed, and it illustrates the degradation of each method as increasing noise levels are added to the data. [less ▲] Detailed reference viewed: 53 (1 UL)Minimal dynamical structure realisations with application to network reconstruction from data ; ; et al in The proceedings of the Joint 48th IEEE Conference on Decision and Control and 28th Chinese Control Conference (2009) Network reconstruction, i.e., obtaining network structure from data, is a central theme in systems biology, economics, and engineering. Previous work introduced dynamical structure functions as a tool for ... [more ▼] Network reconstruction, i.e., obtaining network structure from data, is a central theme in systems biology, economics, and engineering. Previous work introduced dynamical structure functions as a tool for posing and solving the problem of network reconstruction between measured states. While recovering the network structure between hidden states is not possible since they are not measured, in many situations it is important to estimate the number of hidden states in order to understand the complexity of the network under investigation and help identify potential targets for measurements. Estimating the number of hidden states is also crucial to obtain the simplest state-space model that captures the network structure and is coherent with the measured data. This paper characterises minimal order state-space realisations that are consistent with a given dynamical structure function by exploring properties of dynamical structure functions and developing algorithms to explicitly obtain a minimal reconstruction. [less ▲] Detailed reference viewed: 74 (0 UL)Network structure preserving model reduction with weak a priori structural information ; Goncalves, Jorge ; et al in The proceedings of the Joint 48th IEEE Conference on Decision and Control and 28th Chinese Control Conference (2009) This paper extends a state projection method for structure preserving model reduction to situations where only a weaker notion of system structure is available. This weaker notion of structure ... [more ▼] This paper extends a state projection method for structure preserving model reduction to situations where only a weaker notion of system structure is available. This weaker notion of structure, identifying the causal relationship between manifest variables of the system, is especially relevant is settings such as systems biology, where a clear partition of state variables into distinct subsystems may be unknown, or not even exist. The resulting technique, like similar approaches, does not provide theoretical performance guarantees, so an extensive computational study is conducted, and it is observed to work fairly well in practice. Moreover, conditions characterizing structurally minimal realizations and sufficient conditions characterizing edge loss resulting from the reduction process, are presented. [less ▲] Detailed reference viewed: 77 (0 UL)Reachability analysis of continuous-time piecewise affine systems ; Goncalves, Jorge in Automatica (2008), 44(12), 3189-3194 This paper proposes an algorithm for the characterization of reachable sets of states for continuous-time piecewise affine systems. Given a model of the system and a bounded set of possible initial states ... [more ▼] This paper proposes an algorithm for the characterization of reachable sets of states for continuous-time piecewise affine systems. Given a model of the system and a bounded set of possible initial states, the algorithm employs an LMI approach to compute both upper and lower bounds on reachable regions. Rather than performing computations in the state-space, this method uses impact maps to find the reachable sets on the switching surfaces of the system. This tool can then be used to deduce safety and performance results about the system. [less ▲] Detailed reference viewed: 109 (1 UL)Necessary and sufficient conditions for dynamical structure reconstruction of LTI networks Goncalves, Jorge ; in IEEE Transactions on Automatic Control (2008), 53(7), 1670-1674 This paper formulates and solves the network reconstruction problem for linear time-invariant systems. The problem is motivated from a variety of disciplines, but it has recently received considerable ... [more ▼] This paper formulates and solves the network reconstruction problem for linear time-invariant systems. The problem is motivated from a variety of disciplines, but it has recently received considerable attention from the systems biology community in the study of chemical reaction networks. Here, we demonstrate that even when a transfer function can be identified perfectly from input–output data, not even Boolean reconstruction is possible, in general, without more information about the system.We then completely characterize this additional information that is essential for dynamical reconstruction without appeal to ad-hoc assumptions about the network, such as sparsity or minimality. [less ▲] Detailed reference viewed: 94 (1 UL)Bimodal and hysteretic expression in mammalian cells from a synthetic gene circuit ; ; et al in Public Library of Science ONE (2008), 3(6), In order to establish cells and organisms with predictable properties, synthetic biology makes use of controllable, synthetic genetic devices. These devices are used to replace or to interfere with ... [more ▼] In order to establish cells and organisms with predictable properties, synthetic biology makes use of controllable, synthetic genetic devices. These devices are used to replace or to interfere with natural pathways. Alternatively, they may be interlinked with endogenous pathways to create artificial networks of higher complexity. While these approaches have been already successful in prokaryotes and lower eukaryotes, the implementation of such synthetic cassettes in mammalian systems and even animals is still a major obstacle. This is mainly due to the lack of methods that reliably and efficiently transduce synthetic modules without compromising their regulation properties. To pave the way for implementation of synthetic regulation modules in mammalian systems we utilized lentiviral transduction of synthetic modules. A synthetic positive feedback loop, based on the Tetracycline regulation system was implemented in a lentiviral vector system and stably integrated in mammalian cells. This gene regulation circuit yields a bimodal expression response. Based on experimental data a mathematical model based on stochasticity was developed which matched and described the experimental findings. Modelling predicted a hysteretic expression responsewhich was verified experimentally. Thereby supporting the idea that the system is driven by stochasticity. The results presented here highlight that the combination of three independent tools/methodologies facilitate the reliable installation of synthetic gene circuits with predictable expression characteristics in mammalian cells and organisms. [less ▲] Detailed reference viewed: 93 (0 UL)Batch control of the master equation: a linear programming approach Goncalves, Jorge ; Scientific Conference (2008) Detailed reference viewed: 51 (0 UL)Robust synchronization in networks of cyclic feedback systems ; Goncalves, Jorge ; in The proceedings of the 47th IEEE Conference on Decision and Control (2008) This paper presents a result on the robust synchronization of outputs of statically interconnected non-identical cyclic feedback systems that are used to model, among other processes, gene expression. The ... [more ▼] This paper presents a result on the robust synchronization of outputs of statically interconnected non-identical cyclic feedback systems that are used to model, among other processes, gene expression. The result uses incremental versions of the small gain theorem and dissipativity theory to arrive at an upper bound on the norm of the synchronization error between corresponding states, giving a measure of the degree of convergence of the solutions. This error bound is shown to be a function of the difference between the parameters of the interconnected systems, and disappears in the case where the systems are identical, thus retrieving an earlier synchronization result. [less ▲] Detailed reference viewed: 81 (2 UL) |
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