Representing Structure in Linear Interconnected Dynamical Systems

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 ▲]

Constructive Synchronization of Networked Feedback Systems

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 ▲]

A Linear Programming Approach to Parameter Fitting for the Master Equation

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 ▲]

Control Theory and Systems Biology

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. ...

Network Structure Preserving Model Reduction: Results of a Simulation Study

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 ▲]

Minimal dynamical structure realisations with application to network reconstruction from data

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 ▲]

Necessary and sufficient conditions for dynamical structure reconstruction of LTI networks

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 ▲]

Global asymptotic stability of the limit cycle in piecewise linear versions of the Goodwin oscillator

in Proceedings of the 17th IFAC World Congress (2008)

Conditions in the form of linear matrix inequalities (LMIs) are used in this paper to guarantee the global asymptotic stability of a limit cycle oscillation for a class of piecewise linear (PWL) systems ... [more ▼]

Conditions in the form of linear matrix inequalities (LMIs) are used in this paper to guarantee the global asymptotic stability of a limit cycle oscillation for a class of piecewise linear (PWL) systems defined as the feedback interconnection of a saturation controller with a single input, single output (SISO) linear time-invariant (LTI) system. The proposed methodology extends previous results on impact maps and surface Lyapunov functions to the case when the sets of expected switching times are arbitrarily large. The results are illustrated on a PWL version of the Goodwin oscillator. [less ▲]

Dynamical structure analysis of sparsity and minimality heuristics for reconstruction of biochemical networks

in The proceedings of the 47th IEEE Conference on Decision and Control (2008)

Network reconstruction, i.e. obtaining network structure from input-output information, is a central theme in systems biology. A variety of approaches aim to obtaining structural information from ... [more ▼]

Network reconstruction, i.e. obtaining network structure from input-output information, is a central theme in systems biology. A variety of approaches aim to obtaining structural information from available data. Previous work has introduced dynamical structure functions as a tool for posing and solving the network reconstruction problem. Even for linear time invariant systems, reconstruction requires specific additional information not generated in the typical system identification process. This paper demonstrates that such extra information can be obtained through a limited sequence of system identification experiments on structurally modified systems, analogous to gene silencing and overexpression experiments. In the absence of such extra information, we discuss whether combined assumptions of network sparsity and minimality contribute to the recovery of the network dynamical structure. We provide sufficient conditions for a transfer function to have a completely decoupled minimal realization, and demonstrate that every transfer function is arbitrarily close to one that admits a perfectly decoupled minimal realization. This indicates that the assumptions of sparsity and minimality alone do not lend insight into the network structure. [less ▲]

Control theory methods for macro models with stochastic micro foundations

Scientific Conference (2008)