Further results on the linearization problem in discrete time: the uncontrollable case.

The paper deals with the linearization problem of non controllable discrete time submersive systems. Following the approach recently introduced in the literature for continuous time systems in Menini et al.(2012), necessary and sufficient conditions are given for the equivalence of a discrete time (not necessarily controllable) single input system to a linear one. Keywords: Linear equivalence, differential geometry, exponential representatio

Semiglobal leader-following consensus for generalized homogenous agents

In the present paper, the Leader-Following consensus problem is investigated and sufficient conditions are given for the solvability of the problem, assuming that the agents are described by a nonlinear dynamics incrementally homogeneous in the upper bound

Accessibility of Nonlinear Time-Delay Systems

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

On the geometric interpretation of the Polynomial Lie Bracket for nonlinear time-delay systems

Time-delay systems are infinite dimensional, thus standard differential geometric tools can not be applied in a straightforward way. Though, thanks to a suitable extended Lie Bracket - or Polynomial Lie Bracket - which has been introduced recently, it is still possible to build up a geometric framework to tackle the analysis and synthesis problems for nonlinear time delay systems. The major contribution herein is to show that those geometric generalizations are not just formal, but are interpreted in terms of successive forward and backward flows similarly to the Lie Bracket of delay free vector fields

Integrability for Nonlinear Time-Delay Systems

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

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

On the observer canonical form for Nonlinear Time-Delay Systems

6 pagesInternational audienceNecessary and sufficient geometric conditions for the equivalence of a nonlinear time-delay system with one output, under bicausal change of coordinates and output transformation, to a linear weakly observable time-delay system up to output injection are given. These conditions are derived through the use of the Extended Lie Bracket operator recently introduced in the literature for dealing with time-delay systems. The results presented show how this operator is useful in the analysis of this class of nonlinear systems

Extended Lie Brackets for Nonlinear Time-Delay Systems

International audienceThe Extended Lie bracket operator is introduced for the analysis and control of nonlinear time-delay systems. This tool is used to characterize the integrability conditions of a given submodule. The obtained results have two fundamental outcomes. First, they define the necessary and sufficient conditions under which a given set of nonlinear one-forms in the n-dimensional delayed variables x(t),..., x(t-sD) where D is constant, are integrable. Secondly, they set the basis for the extension to this context of the geometric approach used for delay-free systems

Stochastic Leader-Following for Heterogeneous Linear Agents with Communication Delays

We study the leader-following problem for linear stochastic multi-agent systems with uniform and constant communication delays on directed or undirected graphs. We consider both the state feedback and output feedback solutions. In the latter case, the agents can be a set of heterogeneous linear systems. By resorting to a new approach based on the scalar Lambert equation we obtain a constructive design with less conservative closed-form delay bounds. In particular, it is possible to compensate arbitrarily large delays if the agents are not unstable

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

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