87 research outputs found

    Accessibility of Nonlinear Time-Delay Systems

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    A full characterization of accessibility is provided for nonlinear time-delay systems. It generalizes the rank condition which is known for weak controllability of linear time-delay systems, as well as the celebrated geometric approach for delay-free nonlinear systems and the characterization of their accessibility. Besides, fundamental results are derived on integrability and basis completion which are of major importance for a number of general control problems for nonlinear time-delay systems. They are shown to impact preconceived ideas about canonical forms for nonlinear time-delay systems

    Integrability for Nonlinear Time-Delay Systems

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    In this note, the notion of integrability is defined for 1-forms defined in the time-delay context. While in the delay-free case, a set of 1-forms defines a vector space, it is shown that 1-forms computed for time-delay systems have to be viewed as elements of a module over a certain non-commutative polynomial ring. Two notions of integrability are defined, strong and weak integrability, which coincide in the delay-free case. Necessary and sufficient conditions are given to check if a set of 1-forms is strongly or weakly integrable. To show the importance of the topic, integrability of 1-forms is used to characterize the accessibility property for nonlinear time-delay systems. The possibility of transforming a system into a certain normal form is also considered

    The observer error linearization problem via dynamic compensation

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    Linearization by output injection has played a key role in the observer design for nonlinear control systems for almost three decades. In this technical note, following some recent works, geometric necessary and sufficient conditions are derived for the existence of a dynamic compensator solving the problem under regular output transformation. An algorithm which computes a compensator of minimal order is given. © 2014 IEEE

    From the hospital scale to nationwide: observability and identification of models for the COVID-19 epidemic waves

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    Two mathematical models of the COVID-19 dynamics are considered as the health system in some country consists in a network of regional hospital centers. The first macroscopic model for the virus dynamics at the level of the general population of the country is derived from a standard SIR model. The second local model refers to a single node of the health system network, i.e. it models the flows of patients with a smaller granularity at the level of a regional hospital care center for COVID-19 infected patients. Daily (low cost) data are easily collected at this level, and are worked out for a fast evaluation of the local health status thanks to control systems methods. Precisely, the identifiability of the parameters of the hospital model is proven and thanks to the availability of clinical data, essential characteristics of the local health status are identified. Those parameters are meaningful not only to alert on some increase of the infection, but also to assess the efficiency of the therapy and health polic

    Disturbance Decoupling in Nonlinear Impulsive Systems

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    International audienceThis work deals with the problem of structural disturbance decoupling by state feedback for nonlinear impulsive systems. The dynamical systems addressed exhibit a hybrid behavior characterized by a nonlinear continuous-time state evolution interrupted by abrupt discontinuities at isolated time instants. The problem considered consists in finding a state feedback such that the system output is rendered totally insensitive to the disturbance. Both the case of static state feedback and that of dynamic state feedback are considered. A necessary and sufficient condition for the existence of a static state feedback that solves the problem in the multivariable case is proven by defining suitable tools in the context of the differential geometric approach. The situation concerning solvability by a dynamic state feedback is examined in the framework of the differntial algeraic approach. A necessary and sufficient solvaility condition is conjectured and discussed

    Practical identification of a glucose-insulin dynamics model

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    Glycemia regulation algorithms which are designed to be implemented in several artificial pancreas projects are often model based control algorithms. However, actual diabetes monitoring is based throughout the world on the so-called Flexible Insulin Therapy (FIT) which does not always cope with current mathematical models. In this paper, we initiate an identification methodology of those FIT parameters from some standard ambulatory clinical data. This issue has an interest per se, or for a further use in any closed-loop regulation system

    Infinitesimal Brunovsky form for nonlinear systems, with applications to dynamic linearization

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    International audienceWe define, in an infinite-dimensional differential geometric framework, the "infinitesimal Brunovsky form" which we previously introduced in another framework and link it with equivalence via diffeomorphism to a linear system, which is the same as linearizability by "endogenous dynamic feedback".NB: this paper follows "A differential geometric setting for dynamic equivalence and dynamic linearization", by J.-B. Pomet, published in the same 1995 volume, which is its natural intrduction.This is a corrected version of the reports http://hal.inria.fr/inria-00074360 and http://hal.inria.fr/inria-0007436

    Infinitesimal Brunovsky Form for Nonlinear Systems with Applications to Dynamic Linearization

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    We define the ``infinitesimal Brunovsky form'' for nonlinear systems in the infinite-dimensionnal differential geometric framework devellopped in ``A Differential Geometric Setting for Dynamic Equivalence and Dynamic Linearization'' (Rapport INRIA No XXXX, needed to understand the present note), and link it with endogenous dynamic linearizability, i.e. conjugation of the system to a linear one by a (infinite dimensional) diffeomorphism

    Analysis of nonlinear time-delay systems using modules over non-commutative rings,

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    Abstract The theory of non-commutative rings is introduced to provide a basis for the study of nonlinear control systems with time delays. The left Ore ring of non-commutative polynomials deÿned over the ÿeld of meromorphic function is suggested as the framework for such a study. This approach is then generalized to a broader class of nonlinear systems with delays that are called generalized Roesser systems. Finally, the theory is applied to analyze nonlinear time-delay systems. A weak observability is deÿned and characterized, generalizing the well-known linear result. Properties of closed submodules are then developed to obtain a result on the accessibility of such systems.
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