On the structural controllability of compartmental systems

Hayakawa, Yoshikazu; Hosoe, Shigeyuki; Hayashi, Momoko; Ito, Masaaki

doi:10.1109/tac.1984.1103363

Cited by 22 publications

(15 citation statements)

References 12 publications

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“…Definition A. 1 The system (19) is said to be state-controllable on Ω if for any a, b ∈ Ω there exist a time T ≥ 0, and a control u ∈ U such that x(T, u, a) = b.…”

Section: Appendix Appendix A: Review Of Controllabilitymentioning

confidence: 99%

“…Definition A. 2 The system (19) is said to be output-controllable on some set Ψ ⊆ R k if for any p, q ∈ Ψ there exist a time T ≥ 0, and a control u ∈ U that steers the output from y(0) = p to y(T ) = q.…”

Section: Appendix Appendix A: Review Of Controllabilitymentioning

confidence: 99%

“…The system (19) is said to be accessible from a if the set RS(a) has a non empty interior. In other words, the control is powerful enough to allow steering the trajectories emanating from a to a "full set" of directions.…”

Section: Appendix Appendix A: Review Of Controllabilitymentioning

confidence: 99%

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Controllability Analysis and Control Synthesis for the Ribosome Flow Model

Zarai

Margaliot

Sontag

et al. 2018

IEEE/ACM Trans. Comput. Biol. and Bioinf.

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The ribosomal density along different parts of the coding regions of the mRNA molecule affect various fundamental intracellular phenomena including: protein production rates, global ribosome allocation and organismal fitness, ribosomal drop off, co-translational protein folding, mRNA degradation, and more. Thus, regulating translation in order to obtain a desired ribosomal profile along the mRNA molecule is an important biological problem. We study this problem using a dynamical model for mRNA translation, called the ribosome flow model (RFM). In the RFM, the mRNA molecule is modeled as chain of n sites. The n state-variables describe the ribosomal density profile along the mRNA molecule, whereas the transition rates from each site to the next are controlled by n + 1 positive constants. To study the problem of controlling the density profile, we consider some or all of the transition rates as time-varying controls. We consider the following problem: given an initial and a desired ribosomal density profile in the RFM, determine the time-varying values of the transition rates that steer the system to this density profile, if they exist. More specifically, we consider two control problems. In the first, all transition rates can be regulated and the goal is to steer the ribosomal density profile and the protein production rate from a given initial value to a desired value. In the second, a single transition rate is controlled and the goal is to steer the production rate to a desired value. In the first case, we show that the system is controllable, i.e. the control is powerful enough to steer the system to any desired value, and we provide simple closed-form expressions for constant control functions (or transition rates) that asymptotically steer the system to the desired value. In the second case, we show that we can steer the production rate to any desired value in a feasible region determined by the other constant transition rates. We discuss some of the biological implications of these results.

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“…Definition A. 1 The system (19) is said to be state-controllable on Ω if for any a, b ∈ Ω there exist a time T ≥ 0, and a control u ∈ U such that x(T, u, a) = b.…”

Section: Appendix Appendix A: Review Of Controllabilitymentioning

confidence: 99%

Section: Appendix Appendix A: Review Of Controllabilitymentioning

confidence: 99%

See 1 more Smart Citation

Controllability Analysis and Control Synthesis for the Ribosome Flow Model

Zarai

Margaliot

Sontag

et al. 2018

IEEE/ACM Trans. Comput. Biol. and Bioinf.

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show abstract

“…In particular, the notion of a "linearly parameterized" matrix pair was introduced in [52] which allowed parameters to appear in multiple locations in the pair (A, B). The engineering motivation for linear parameterization came from physical systems with unknown but dependent design parameters involving the imprecise values of their physical components [56] or measurements [53]. For example, the transfer function of the voltage divider circuit in Figure 1 is…”

Section: Introductionmentioning

confidence: 99%

A Graphical Characterization of Structurally Controllable Linear Systems With Dependent Parameters

Liu

Morse

2019

IEEE Trans. Automat. Contr.

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One version of the concept of structural controllability defined for single-input systems by Lin and subsequently generalized to multi-input systems by others, states that a parameterized matrix pair (A, B) whose nonzero entries are distinct parameters, is structurally controllable if values can be assigned to the parameters which cause the resulting matrix pair to be controllable. In this paper the concept of structural controllability is broadened to allow for the possibility that a parameter may appear in more than one location in the pair (A, B). Subject to a certain condition on the parameterization called the "binary assumption", an explicit graph-theoretic characterization of such matrix pairs is derived.

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“…Such systems are referred to as positive system, which means that their states and outputs are nonnegative whenever the initial conditions and inputs are nonnegative. In view of widespread applications of positive systems, many researchers have paid more attention to this kind of systems and many fundamental results about positive systems have been reported [1]- [10]. It is well mentioned that a lot of well-established results for general linear system cannot be easily applied to positive system, which due to the fact that the positive systems are defined on cones rather than linear space.…”

Section: Introductionmentioning

confidence: 99%

Positive observer for positive continuous systems with interval uncertainties and multiple time-delay

Wang

Sheng

2012

2012 24th Chinese Control and Decision Conference (CCDC)

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This paper addresses the design of positive observer for positive linear continuous system with interval uncertainties and multiple time-delay. Firstly, the sufficient and necessary condition for the existence of positive observers is established by using the vertical matrices of the uncertain domain which system matrices belong to. Then the desired observer matrices are given by solving a set of matrix inequalities. Finally, a numerical example is given to demonstrate the effectiveness of the proposed methods.Index Terms-ositive observer, time-delay, interval systems, linear matrix inequalities (LMIs), positive systemositive observer, time-delay, interval systems, linear matrix inequalities (LMIs), positive systemp

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On the structural controllability of compartmental systems

Cited by 22 publications

References 12 publications

Controllability Analysis and Control Synthesis for the Ribosome Flow Model

Controllability Analysis and Control Synthesis for the Ribosome Flow Model

A Graphical Characterization of Structurally Controllable Linear Systems With Dependent Parameters

Positive observer for positive continuous systems with interval uncertainties and multiple time-delay

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