Abdullah Hamadeh

Massachusetts Institute of Technology, Cambridge, Massachusetts, United States

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Publications (20)31.17 Total impact

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    ABSTRACT: A method to synchronize and control a system of parallel single-phase inverters without communication is presented. Inspired by the phenomenon of synchronization in networks of coupled oscillators, we propose that each inverter be controlled to emulate the dynamics of a nonlinear dead-zone oscillator. As a consequence of the electrical coupling between inverters, they synchronize and share the load in proportion to their ratings. We outline a sufficient condition for global asymptotic synchronization and formulate a methodology for controller design such that the inverter terminal voltages oscillate at the desired frequency, and the load voltage is maintained within prescribed bounds. We also introduce a technique to facilitate the seamless addition of inverters controlled with the proposed approach into an energized system. Experimental results for a system of three inverters demonstrate power sharing in proportion to power ratings for both linear and nonlinear loads.
    IEEE Transactions on Power Electronics 11/2014; 29(11):6124-6138. DOI:10.1109/TPEL.2013.2296292 · 5.73 Impact Factor
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    ABSTRACT: Sufficient conditions are derived for the global asymptotic synchronization of a class of identical nonlinear oscillators coupled through a linear time-invariant network. In particular, we focus on systems where oscillators are connected to a common node through identical branch impedances. For such networks, it is shown that the synchronization condition is independent of the number of oscillators and the value of the load impedance connected to the common node. Theoretical findings are then leveraged to control a system of parallel single-phase voltage source inverters serving an impedance load in an islanded microgrid application. The ensuing paradigm: i) does not necessitate communication between inverters, ii) is independent of system load, and iii) facilitates a modular design approach because the synchronization condition is independent of the number of oscillators. We present both simulation and experimental case studies to validate the analytical results and demonstrate the proposed application.
    Circuits and Systems I: Regular Papers, IEEE Transactions on 03/2014; 61(3):834-844. DOI:10.1109/TCSI.2013.2284180 · 2.30 Impact Factor
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    ABSTRACT: A control scheme is proposed for an islanded low-inertia three-phase inverter-based microgrid with a high penetration of photovoltaic (PV) generation resources. The output of each inverter is programmed to emulate the dynamics of a nonlinear oscillator. The virtual oscillators within each controller are implicitly coupled through the physical electrical network. The asymptotic synchronization of the oscillators can be guaranteed by design, and as a result, a stable power system emerges innately with no communication between the inverters. Time-domain switching-level simulation results for a 45-kW microgrid with 33% PV penetration demonstrate the merits of the proposed technique; in particular they show that the load voltage can be maintained between prescribed bounds in spite of variations in incident irradiance and step changes in the load.
    IEEE Journal of Photovoltaics 01/2014; 4(1):387-395. DOI:10.1109/JPHOTOV.2013.2280953 · 3.00 Impact Factor
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    Abdullah Hamadeh, Brian Ingalls, Eduardo Sontag
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    ABSTRACT: The chemotaxis pathway of the bacterium Rhodobacter sphaeroides shares many similarities with that of Escherichia coli. It exhibits robust adaptation and has several homologues of the latter's chemotaxis proteins. Recent theoretical results have correctly predicted that the E. coli output behaviour is unchanged under scaling of its ligand input signal; this property is known as fold-change detection (FCD). In the light of recent experimental results suggesting that R. sphaeroides may also show FCD, we present theoretical assumptions on the R. sphaeroides chemosensory dynamics that can be shown to yield FCD behaviour. Furthermore, it is shown that these assumptions make FCD a property of this system that is robust to structural and parametric variations in the chemotaxis pathway, in agreement with experimental results. We construct and examine models of the full chemotaxis pathway that satisfy these assumptions and reproduce experimental time-series data from earlier studies. We then propose experiments in which models satisfying our theoretical assumptions predict robust FCD behaviour where earlier models do not. In this way, we illustrate how transient dynamic phenotypes such as FCD can be used for the purposes of discriminating between models that reproduce the same experimental time-series data.
    Journal of The Royal Society Interface 12/2013; 10(80):20120935. DOI:10.1098/rsif.2012.0935 · 3.86 Impact Factor
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    ABSTRACT: Sufficient conditions are derived for global asymptotic synchronization in a system of identical nonlinear electrical circuits coupled through linear time-invariant (LTI) electrical networks. In particular, the conditions we derive apply to settings where: i) the nonlinear circuits are composed of a parallel combination of passive LTI circuit elements and a nonlinear voltage-dependent current source with finite gain; and ii) a collection of these circuits are coupled through either uniform or homogeneous LTI electrical networks. Uniform electrical networks have identical per-unit-length impedances. Homogeneous electrical networks are characterized by having the same effective impedance between any two terminals with the others open circuited. Synchronization in these networks is guaranteed by ensuring the stability of an equivalent coordinate-transformed differential system that emphasizes signal differences. The applicability of the synchronization conditions to this broad class of networks follows from leveraging recent results on structural and spectral properties of Kron reduction---a model-reduction procedure that isolates the interactions of the nonlinear circuits in the network. The validity of the analytical results is demonstrated with simulations in networks of coupled Chua's circuits.
    Circuits and Systems I: Regular Papers, IEEE Transactions on 10/2013; 61(9). DOI:10.1109/TCSI.2014.2332250 · 2.30 Impact Factor
  • Sairaj V. Dhople, Brian B. Johnson, Abdullah O. Hamadeh
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    ABSTRACT: This paper summarizes a suite of methods that have recently been proposed for the control and synchronization of parallel single- and three-phase voltage source power electronics inverters. Inspired by the phenomenon of synchronization in networks of coupled oscillators, the premise of the proposed Virtual Oscillator Control (VOC) is to control an inverter such that it mimics the dynamics of a nonlinear oscillator. Consequently, the inverters synchronize their voltage outputs and share the load power in proportion to their power ratings without any communication. The VOC design philosophy and sufficient conditions for global asymptotic synchronization are outlined. Simulations validate the analytical results for a parallel system of three-phase inverters serving a constant-power load.
    2013 51st Annual Allerton Conference on Communication, Control, and Computing (Allerton); 10/2013
  • Abdullah Hamadeh, Eduardo Sontag, Brian Ingalls
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    ABSTRACT: Systems biology has revealed numerous examples of networks whose dynamic behavior is robust to system perturbations and noise. In many cases, this behavior arises from simple yet fundamental features of the system architecture. A well-studied example is the chemotactic response of Escherichia coli. In various models of this system, it is shown that simple assumptions on the receptor methylation dynamics lead to robust perfect adaptation of chemotactic activity. Recent experimental work has also shown that the transient E. coli chemotactic response is unchanged by a scaling of its ligand input signal; this behavior is called fold change detection (FCD), and is in agreement with earlier mathematical predictions. However, this prediction was based on very particular assumptions on the structure of the chemotaxis pathway. In this work, we begin by showing that behavior similar to FCD can be obtained under weaker conditions on the system structure. Namely, we show that under relaxed conditions, a scaling of the chemotaxis system's inputs leads to a time scaling of the output response. We propose that this may be a contributing factor to the robustness of the experimentally observed FCD. We further show that FCD is a special case of this time scaling behavior for which the time scaling factor of unity. We then proceed to extend the conditions for output time scaling to more general adapting systems, and demonstrate this time scaling behavior on a published model of the chemotaxis pathway of the bacterium Rhodobacter sphaeroides. This work therefore provides examples of how robust biological behavior can arise from simple yet realistic conditions on the underlying system structure.
    American Control Conference (ACC), 2013; 06/2013
  • Andrew Dhawan, Abdullah Hamadeh, Brian Ingalls
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    ABSTRACT: This paper considers the problem of synchronizing the outputs of nodes in a network of N coupled dynamical systems in the presence of uncertainty. A computational approach is used to design coupling dynamics that ensure synchrony when nodes are subject to model uncertainty and that minimize nodal deviation from synchrony in the presence of input noise. The main result of this paper recasts the problem of designing the coupling a robust stability problem with a structured uncertainty element. A coupling satisfying the criteria of this robust stability problem can then be designed through an application of the small-gain theorem and μ-synthesis techniques.
    Proceedings of the American Control Conference 06/2012; DOI:10.1109/ACC.2012.6314720
  • Abdullah Hamadeh, Brian Ingalls, Eduardo Sontag
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    ABSTRACT: The chemotaxis pathway of the bacterium Rhodobacter sphaeroides has many similarities to the well-studied pathway in Escherichia coli. It exhibits robust adaptation and has several homologues of the latter's chemotaxis proteins. Recent theoretical results have been able to correctly predict that the chemotactic response of Escherichia coli exhibits the same output behavior in response to scaled ligand inputs, a dynamic property known as fold-change detection (FCD), or input-scale invariance. In this paper, we present theoretical assumptions on the R. sphaeroides chemotaxis sensing dynamics that can be analytically shown to yield FCD behavior in a specific ligand concentration range. Based on these assumptions, we construct two models of the full chemotaxis pathway that are able to reproduce experimental time-series data from earlier studies. To test the validity of our assumptions, we propose a series of experiments in which our models predict robust FCD behavior where earlier models do not. In this way, we illustrate how a dynamic phenotype such as FCD can be used for the purposes of discriminating between two models that reproduce the same experimental time-series data.
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    ABSTRACT: 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.
    IEEE Transactions on Automatic Control 02/2012; 57(2):478-483. DOI:10.1109/TAC.2011.2164015 · 3.17 Impact Factor
  • A. Hamadeh, B. Ingalls, E. Sontag
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    ABSTRACT: Fold-change detection (FCD) is the property that a dynamical system with an adapting output will exhibit identical transient output responses when its input signals are scaled. This feature was recently demonstrated in the chemotactic response of the bacterium Escherichia coli, confirming earlier theoretical predictions. The chemotaxis pathway of the bacterium Rhodobacter sphaeroides has the same modular structure as that in E. coli but is significantly more complex in that it has multiple homologues of the latter's chemotaxis proteins and features two, rather than one, chemosensory cluster. Recent experimental results suggest that R. sphaeroides may also exhibit FCD. In this paper, we present a set of theoretical assumptions on the dynamics of the R. sphaeroides chemosensory system, and use these to fit an integrated chemotaxis model to experimental data. We then show that the assumptions we place are sufficient to make FCD a robust property of this chemotaxis pathway, in agreement with preliminary experimental evidence. We argue that the fact that the model we present here is able to reproduce this transient dynamic property whilst earlier models cannot makes FCD a useful tool for model discrimination on the basis of transient dynamic response. This is in contrast to earlier model discrimination methods which tested the validity of models based on their ability to reproduce a finite set of experimental data. Further experiments that can provide additional validation of our theoretical assumptions are suggested.
    Decision and Control (CDC), 2012 IEEE 51st Annual Conference on; 01/2012
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    ABSTRACT: Bacteria move towards favourable and away from toxic environments by changing their swimming pattern. This response is regulated by the chemotaxis signalling pathway, which has an important feature: it uses feedback to 'reset' (adapt) the bacterial sensing ability, which allows the bacteria to sense a range of background environmental changes. The role of this feedback has been studied extensively in the simple chemotaxis pathway of Escherichia coli. However it has been recently found that the majority of bacteria have multiple chemotaxis homologues of the E. coli proteins, resulting in more complex pathways. In this paper we investigate the configuration and role of feedback in Rhodobacter sphaeroides, a bacterium containing multiple homologues of the chemotaxis proteins found in E. coli. Multiple proteins could produce different possible feedback configurations, each having different chemotactic performance qualities and levels of robustness to variations and uncertainties in biological parameters and to intracellular noise. We develop four models corresponding to different feedback configurations. Using a series of carefully designed experiments we discriminate between these models and invalidate three of them. When these models are examined in terms of robustness to noise and parametric uncertainties, we find that the non-invalidated model is superior to the others. Moreover, it has a 'cascade control' feedback architecture which is used extensively in engineering to improve system performance, including robustness. Given that the majority of bacteria are known to have multiple chemotaxis pathways, in this paper we show that some feedback architectures allow them to have better performance than others. In particular, cascade control may be an important feature in achieving robust functionality in more complex signalling pathways and in improving their performance.
    PLoS Computational Biology 05/2011; 7(5):e1001130. DOI:10.1371/journal.pcbi.1001130 · 4.83 Impact Factor
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    ABSTRACT: This paper investigates the chemotaxis behavior of the bacterium R. sphaeroides. We review the results of a recent study comparing different possible mathematical models of this bacterium's chemotaxis decision mechanisms. It was found that only one of the aforesaid models could explain the experimental chemotactic response data. From a control theoretic perspective, we show that, compared to the other models posed, this model exhibits better and more robust chemotactic performance. This decision mechanism parallels a feedback architecture that has been used extensively to improve performance in engineered systems. We suggest that this mechanism may play a role in maintaining the chemotactic performance of this and potentially other bacteria.
    01/2011; DOI:10.1109/CDC.2011.6161020
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    Abdullah Omar Hamadeh, Guy-Bart Stan, Jorge M. Goncalves
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    ABSTRACT: 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.
    Proceedings of the 49th IEEE Conference on Decision and Control, CDC 2010, December 15-17, 2010, Atlanta, Georgia, USA; 01/2010
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    ABSTRACT: Developing methods for understanding the connectivity of signalling pathways is a major challenge in biological research. For this purpose, mathematical models are routinely developed based on experimental observations, which also allow the prediction of the system behaviour under different experimental conditions. Often, however, the same experimental data can be represented by several competing network models. In this paper, we developed a novel mathematical model/experiment design cycle to help determine the probable network connectivity by iteratively invalidating models corresponding to competing signalling pathways. To do this, we systematically design experiments in silico that discriminate best between models of the competing signalling pathways. The method determines the inputs and parameter perturbations that will differentiate best between model outputs, corresponding to what can be measured/observed experimentally. We applied our method to the unknown connectivities in the chemotaxis pathway of the bacterium Rhodobacter sphaeroides. We first developed several models of R. sphaeroides chemotaxis corresponding to different signalling networks, all of which are biologically plausible. Parameters in these models were fitted so that they all represented wild type data equally well. The models were then compared to current mutant data and some were invalidated. To discriminate between the remaining models we used ideas from control systems theory to determine efficiently in silico an input profile that would result in the biggest difference in model outputs. However, when we applied this input to the models, we found it to be insufficient for discrimination in silico. Thus, to achieve better discrimination, we determined the best change in initial conditions (total protein concentrations) as well as the best change in the input profile. The designed experiments were then performed on live cells and the resulting data used to invalidate all but one of the remaining candidate models. We successfully applied our method to chemotaxis in R. sphaeroides and the results from the experiments designed using this methodology allowed us to invalidate all but one of the proposed network models. The methodology we present is general and can be applied to a range of other biological networks.
    BMC Systems Biology 10/2009; 3:105. DOI:10.1186/1752-0509-3-105 · 2.85 Impact Factor
  • Abdullah Omar Hamadeh, Jorge M. Goncalves
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    ABSTRACT: 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.
    Automatica 12/2008; 44(12):3189-3194. DOI:10.1016/j.automatica.2008.05.023 · 3.13 Impact Factor
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    Abdullah Omar Hamadeh, Guy-Bart Stan, Jorge M. Goncalves
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    ABSTRACT: 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.
    Proceedings of the 47th IEEE Conference on Decision and Control, CDC 2008, December 9-11, 2008, Cancún, México; 01/2008
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    ABSTRACT: This paper is concerned with the global analysis of asymptotic synchronization of outputs in networks of identical oscillators. The oscillator models are assumed to possess a cyclic feedback structure. Such networks of oscillators abound in biochemistry, and are exemplified by circadian rhythm and cardiac cell networks. The main result exploits an incremental output feedback passivity property of cyclic feedback systems to prove global asymptotic output synchronization in a network composed of identical cyclic feedback systems. This result is illustrated on a network of Goodwin oscillators.
    American Control Conference, 2007. ACC '07; 08/2007
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    A.O. Hamadeh, J.M. Goncalves
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    ABSTRACT: This paper presents a new approach to the reachability problem for a class of hybrid systems called Piecewise Linear Systems (PLS). The principal tool used is the impact map between switching surfaces. The method consists of specifying a ellipsoidal set on the initial switching surface and finding upper- and lower-bound estimates of the possible reach sets using tools such as the S-procedure to set up linear matrix inequalities, of which numerical solutions are then computed.
    Decision and Control, 2005 and 2005 European Control Conference. CDC-ECC '05. 44th IEEE Conference on; 01/2006
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    Abdullah Hamadeh, Hughes Hall

Publication Stats

103 Citations
31.17 Total Impact Points

Institutions

  • 2013–2014
    • Massachusetts Institute of Technology
      Cambridge, Massachusetts, United States
    • University of Waterloo
      • Department of Applied Mathematics
      Ватерлоо, Ontario, Canada
  • 2006–2012
    • University of Cambridge
      • Department of Engineering
      Cambridge, England, United Kingdom
  • 2009–2011
    • University of Oxford
      • • Department of Engineering Science
      • • Department of Biochemistry
      Oxford, England, United Kingdom