Near optimal interval observers bundle for uncertain bioreactors

Moisan, Marcelo; Bernard, Olivier; Gouzé, Jean‐Luc

doi:10.1016/j.automatica.2008.07.006

Cited by 192 publications

(176 citation statements)

References 10 publications

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“…Many works on the interval observer design [3], [12], [17], [16] deal with the case of a constant matrix A (or under some transformations the estimation error can be represented in the form with a constant matrix A, next an observer gain L can be found such that A − LC is Hurwitz and Metzler). In the present work, we are going to avoid such a restriction.…”

Section: Resultsmentioning

confidence: 99%

“…Under these assumptions, if we additionally assume that the matrix D is Metzler, then the following interval observer can be designed [3], [12], [17]:…”

Section: Resultsmentioning

confidence: 99%

“…There are several approaches to design interval observers [3], [7], [8], [12]. This paper continues the framework of interval observer design based on the monotone system theory [3], [12].…”

Section: Introductionmentioning

confidence: 99%

“…This paper continues the framework of interval observer design based on the monotone system theory [3], [12]. That approach has been recently extended in [17] to nonlinear systems using Linear-Parameter-Varying (LPV) representation with known minorant and majorant matrices, and in [16] for observable nonlinear systems.…”

Section: Introductionmentioning

confidence: 99%

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Interval state observer for nonlinear time varying systems

et al. 2013

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This paper is devoted to design of interval observers for Linear Time Varying (LTV) systems and a class of nonlinear time-varying systems in the output canonical form. An interval observer design is feasible if it is possible to calculate the observer gains making the estimation error dynamics cooperative and stable. It is shown that under some mild conditions the cooperativity of an LTV system can be ensured by a static linear transformation of coordinates. The efficiency of the proposed approach is demonstrated through numerical simulations.

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Section: Resultsmentioning

confidence: 99%

“…Under these assumptions, if we additionally assume that the matrix D is Metzler, then the following interval observer can be designed [3], [12], [17]:…”

Section: Resultsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Interval state observer for nonlinear time varying systems

et al. 2013

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“…The basic mathematical model for the chemostat was first derived in [40,41]. See [9,10,[18][19][20]28,39,46] for more recent discussions on the chemostat and its role in microbial ecology. For well-mixed chemostats, the competitive exclusion principle [2] specified conditions on the growth rates under which only one species can persist generically.…”

Section: Introductionmentioning

confidence: 99%

Stability and stabilization for models of chemostats with multiple limiting substrates

Mazenc

Malisoff

2012

Journal of Biological Dynamics

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We study chemostat models in which multiple species compete for two or more limiting nutrients. First, we consider the case where the nutrient flow and species removal rates and input nutrient concentrations are all given as positive constants. In that case, we use Brouwer degree theory to give conditions guaranteeing that the models admit globally asymptotically stable componentwise positive equilibrium points, from all componentwise positive initial states. Then we use the results to develop stabilization theory for a class of controlled chemostats with two or more limiting nutrients. For cases where the dilution rate and input nutrient concentrations can be selected as controls, we prove that many different componentwise positive equilibria can be made globally asymptotically stable. This extends the existing control results for chemostats with one limiting nutrient. We demonstrate our methods in simulations.

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Interval observer design based on nonlinear hybridization and practical stability analysis

Meslem

Ramdani

2010

Adaptive Control & Signal

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In this paper we design an interval observer for nonlinear uncertain continuous-time dynamical systems, in the unknown-but-bounded error framework. We show how to generate two coupled hybrid observers, which yield the best conservative upper and lower component-wise bounds for the state, provided bounds are available for initial conditions and uncertainties. The interval observer depends on a tuning gain, which is chosen to satisfy the practical stability of a given hybrid dynamical system. An example is studied to emphasize the performance of our method.

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Near optimal interval observers bundle for uncertain bioreactors

Cited by 192 publications

References 10 publications

Interval state observer for nonlinear time varying systems

Interval state observer for nonlinear time varying systems

Stability and stabilization for models of chemostats with multiple limiting substrates

Interval observer design based on nonlinear hybridization and practical stability analysis

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