Observation of bilinear systems with application to biological control

Williamson, D.

doi:10.1016/0005-1098(77)90051-6

Cited by 190 publications

(66 citation statements)

References 5 publications

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“…Williamson (1977) considers bilinear models for microbial cell growth and product synthesis in continuous cultures. He points out that some of the state-variables cannot be measured on-line because reliable and accurate sensors do not exist.…”

Section: Introductionmentioning

confidence: 99%

Observability of Boolean networks: A graph-theoretic approach

2013

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Boolean networks (BNs) are discrete-time dynamical systems with Boolean state-variables and outputs. BNs are recently attracting considerable interest as computational models for genetic and cellular networks. We consider the observability of BNs, that is, the possibility of uniquely determining the initial state given a time sequence of outputs. Our main result is that determining whether a BN is observable is NP-hard. This holds for both synchronous and asynchronous BNs. Thus, unless P=NP, there does not exist an algorithm with polynomial time complexity that solves the observability problem. We also give two simple algorithms, with exponential complexity, that solve this problem. Our results are based on combining the algebraic representation of BNs derived by D. Cheng with a graph-theoretic approach. Some of the theoretical results are applied to study the observability of a BN model of the mammalian cell cycle.

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Section: Introductionmentioning

confidence: 99%

Observability of Boolean networks: A graph-theoretic approach

2013

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“…this subject (see [18,46,41,11] and the references therein). We base our work on the definition given by S. Diop & M. Fliess in [11] of the observability for the class of algebraic systems.…”

Section: Introduction Notations and Main Resultsmentioning

confidence: 99%

A probabilistic algorithm to test local algebraic observability in polynomial time

Sedoglavic

2001

Proceedings of the 2001 International Symposium on Symbolic and Algebraic Computation

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The following questions are often encountered in system and control theory. Given an algebraic model of a physical process, which variables can be, in theory, deduced from the input-output behavior of an experiment? How many of the remaining variables should we assume to be known in order to determine all the others? These questions are parts of the local algebraic observability problem which is concerned with the existence of a non trivial Lie subalgebra of the symmetries of the model letting the inputs and the outputs invariant.We present a probabilistic seminumerical algorithm that proposes a solution to this problem in polynomial time. A bound for the necessary number of arithmetic operations on the rational field is presented. This bound is polynomial in the complexity of evaluation of the model and in the number of variables. Furthermore, we show that the size of the integers involved in the computations is polynomial in the number of variables and in the degree of the differential system. Last, we estimate the probability of success of our algorithm and we present some benchmarks from our Maple implementation.

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“…The studies of this kind of systems are generally based on timevariant linear systems theory (D 'Angelo [1970]) and matrix Lie groups (Sontag [1998], Mohler and Kolodziej [1980], Bruni et al [1974]). Among these studies, the state observability of bilinear systems has been widely tackled since the results of (Williamson [1977], Grasselli and Isidori [1977]). The necessary and sufficient conditions to achieve this property are now very well known.…”

Section: Introductionmentioning

confidence: 99%

State and input observability for structured bilinear systems: A graph-theoretic approach

Boukhobza

Hamelin

2008

IFAC Proceedings Volumes

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To cite this version:Abstract: This paper deals with the state and input observability analysis for structured bilinear systems with unknown inputs. More precisely, we provide two groups of conditions, the first ones are necessary and the second ones are sufficient, to check whether or not a structured bilinear system generically state and input observable. These conditions, which are far to be trivial, are expressed in quite simple graphicterms. Moreover,the proposed method assumes only the knowledge of the system's structure and all the given conditions are easy to check because they deal with finding paths in a digraph. This makes the suggested approach particularly well suited to study large scale systems or systems with unknown parameters, as it may be the case during a conception stage.

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Observation of bilinear systems with application to biological control

Cited by 190 publications

References 5 publications

Observability of Boolean networks: A graph-theoretic approach

Observability of Boolean networks: A graph-theoretic approach

A probabilistic algorithm to test local algebraic observability in polynomial time

State and input observability for structured bilinear systems: A graph-theoretic approach

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