Monotone control systems

Angeli, David; Sontag, Eduardo D.

doi:10.1109/tac.2003.817920

Cited by 590 publications

(710 citation statements)

References 35 publications

Supporting

Mentioning

702

Contrasting

Unclassified

Order By: Relevance

“…2) A monotone control system perspective: The second method now explored is an attempt to apply the results on monotone control systems, as worked out in particular by [23], see also [24], [25], [26], [27]. The principle of this approach consists in decomposing the system under study as a monotone input-output system with feedback.…”

Section: Global Stability Issuesmentioning

confidence: 99%

“…In such a case, the study of asymptotics of the system obtained when closing the loop by the unitary feedback (9b) can be done by introducing static characteristics [23], [27]. However, things become immediately complicated in Fig.…”

Section: Global Stability Issuesmentioning

confidence: 99%

“…While the key arguments are based on the theory of input-output monotone systems developed after [23], none of the posterior refinements to multivalued characteristics or quasi-characteristics allowed to establish formally the main convergence result, and adequate adaptation had to be achieved. Extensions in this direction are presently studied.…”

Section: Conclusion and Further Studiesmentioning

confidence: 99%

See 2 more Smart Citations

Global stabilizing feedback law for a problem of biological control of mosquito-borne diseases

Bliman

Aronna

Coelho

et al. 2015

2015 54th IEEE Conference on Decision and Control (CDC)

View full text Add to dashboard Cite

Abstract-The control of the spread of dengue fever by introduction of the intracellular parasitic bacterium Wolbachia in populations of the vector Aedes aegypti, is presently one of the most promising tools for eliminating dengue, in the absence of an efficient vaccine. The success of this operation requires locally careful planning to determine the adequate number of mosquitoes carrying the Wolbachia parasite that need to be introduced into the natural population. The latter are expected to eventually replace the Wolbachia-free population and guarantee permanent protection against the transmission of dengue to human.In this paper, we propose and analyze a model describing the fundamental aspects of the competition between mosquitoes carrying Wolbachia and mosquitoes free of the parasite. We then introduce a simple feedback control law to synthesize an introduction protocol, and prove that the population is guaranteed to converge to a stable equilibrium where the totality of mosquitoes carry Wolbachia. The techniques are based on the theory of monotone control systems, as developed after Angeli and Sontag. Due to bistability, the considered inputoutput system has multivalued static characteristics, but the existing results are unable to prove almost-global stabilization, and ad hoc analysis has to be conducted.

show abstract

Section: Global Stability Issuesmentioning

confidence: 99%

Section: Global Stability Issuesmentioning

confidence: 99%

Section: Conclusion and Further Studiesmentioning

confidence: 99%

See 1 more Smart Citation

Global stabilizing feedback law for a problem of biological control of mosquito-borne diseases

Bliman

Aronna

Coelho

et al. 2015

2015 54th IEEE Conference on Decision and Control (CDC)

View full text Add to dashboard Cite

show abstract

“…Monotone systems are a class of dynamical systems that preserve a closed order relation from the input space and initial state to their state space and output space [1]. They constitute one of the most important classes used in mathematical biology and chemical modelling.…”

Section: Introductionmentioning

confidence: 99%

Positive systems analysis via integral linear constraints

Khong

Briat

Rantzer

2015

2015 54th IEEE Conference on Decision and Control (CDC)

View full text Add to dashboard Cite

Abstract-Closed-loop positivity of feedback interconnections of positive monotone nonlinear systems is investigated. It is shown that an instantaneous gain condition on the open-loop systems which implies feedback well-posedness also guarantees feedback positivity. Furthermore, the notion of integral linear constraints (ILC) is utilised as a tool to characterise uncertainty in positive feedback systems. Robustness analysis of positive linear time-varying and nonlinear feedback systems is studied using ILC, paralleling the well-known results based on integral quadratic constraints.

show abstract

“…Here, we present a method for analyzing positive-feedback systems of arbitrary order for the presence of bistability or multistability (i.e., more than two alternative stable steady states), bifurcation, and associated hysteretic behavior, subject to two conditions that are frequently satisfied even in complicated, realistic models of cell signaling systems: monotonicity and existence of steady-state characteristics (28)(29)(30)(31)(32)(33)(34). The main ideas of this article can be illustrated through two examples drawn from recent experimental studies: the Cdc2-cyclin B͞Wee1 system, which can be considered to be a two-variable system, and the Mos͞MAPK kinase p42 MAPK cascade, a five-variable system.…”

mentioning

confidence: 99%

Detection of multistability, bifurcations, and hysteresis in a large class of biological positive-feedback systems

Angeli

Ferrell

Sontag

2004

Proc. Natl. Acad. Sci. U.S.A.

929

787

View full text Add to dashboard Cite

It is becoming increasingly clear that bistability (or, more generally, multistability) is an important recurring theme in cell signaling. Bistability may be of particular relevance to biological systems that switch between discrete states, generate oscillatory responses, or ''remember'' transitory stimuli. Standard mathematical methods allow the detection of bistability in some very simple feedback systems (systems with one or two proteins or genes that either activate each other or inhibit each other), but realistic depictions of signal transduction networks are invariably much more complex. Here, we show that for a class of feedback systems of arbitrary order the stability properties of the system can be deduced mathematically from how the system behaves when feedback is blocked. Provided that this open-loop, feedback-blocked system is monotone and possesses a sigmoidal characteristic, the system is guaranteed to be bistable for some range of feedback strengths. We present a simple graphical method for deducing the stability behavior and bifurcation diagrams for such systems and illustrate the method with two examples taken from recent experimental studies of bistable systems: a two-variable Cdc2͞Wee1 system and a more complicated five-variable mitogenactivated protein kinase cascade.O ne of the most important and formidable challenges facing biologists and mathematicians in the postgenomic era is to understand how the behaviors of living cells arise out of the properties of complex networks of signaling proteins. One interesting systems-level property that even relatively simple signaling networks have the potential to produce is bistability. A bistable system is one that toggles between two discrete, alternative stable steady states, in contrast to a monostable system, which slides along a continuum of steady states (1-9). Early biological examples of bistable systems included the lambda phage lysis-lysogeny switch and the hysteretic lac repressor system (10-12). More recent examples have included several mitogen-activated protein kinase (MAPK) cascades in animal cells (13-15), and cell cycle regulatory circuits in Xenopus and Saccharomyces cerevisiae (16)(17)(18). Bistable systems are thought to be involved in the generation of switch-like biochemical responses (13,14,19), the establishment of cell cycle oscillations and mutually exclusive cell cycle phases (17, 18), the production of self-sustaining biochemical ''memories'' of transient stimuli (20,21), and the rapid lateral propagation of receptor tyrosine kinase activation (22).Bistability arises in signaling systems that contain a positivefeedback loop (Fig. 1a) or a mutually inhibitory, doublenegative-feedback loop (which, in some regards, is equivalent to a positive-feedback loop) (Fig. 1b). Indeed, Thomas (23) conjectured that the existence of at least one positive-feedback loop is a necessary condition for the existence of multiple steady states; alternative proofs of this conjecture are given in refs. 24-27. However, the existence of positive loop...

show abstract

Monotone control systems

Cited by 590 publications

References 35 publications

Global stabilizing feedback law for a problem of biological control of mosquito-borne diseases

Global stabilizing feedback law for a problem of biological control of mosquito-borne diseases

Positive systems analysis via integral linear constraints

Detection of multistability, bifurcations, and hysteresis in a large class of biological positive-feedback systems

Contact Info

Product

Resources

About