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

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

Structural accessibility and structural observability of nonlinear networked systems

The classical notions of structural controllability and structural observability are receiving increasing attention in Network Science, since they provide a mathematical basis to answer how the network structure of a dynamic system affects its controllability and observability properties. However, these two notions are formulated assuming systems with linear dynamics, which significantly limit their applicability. To overcome this limitation, here we introduce and fully characterize the notions "structural accessibility" and "structural observability" for systems with nonlinear dynamics. We show how nonlinearities make easier the problem of controlling and observing networked systems, reducing the number of variables that are necessary to directly control and directly measure. Our results contribute to understanding better the role that the network structure and nonlinearities play in our ability to control and observe complex dynamic systems

A Polynomial Solution to the Model Matching Problem of Nonlinear Time-delay Systems

6 pagesInternational audienceIn this paper the model matching problem is considered for single input single output nonlinear systems with delays. A full characterization for its solvability is provided within a simple class of compensators. The approach is developed by means of the transfer functions of nonlinear time-delay systems. The state elimination problem for the systems given by their state-space representation is discussed as well

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

Modelling and Linear Control of a Buoyancy-Driven Airship

International audienceWe describe the modelling and control of a newkind airship which is propelled by buoyancy. Based on the Newton-Euler equations and Kirchhoff equations, and referred to the models of underwater gliders and aircraft, a 6DOF nonlinear mathematical model of a buoyancy-driven airship is derived, with features distributed internal mass, and no thrust, elevators and rudders. The attitudes are controlled by the motion of internal mass. The performances of the airship are studied in the vertical plane. A linear feedback controller is derived for the nonlinear model. The results of simulation display robustness properties of the controllers to disturbances

Nonlinear Control of a Buoyancy Driven Airship

International audienceThe control of a new kind of airship is presented. By restricting its flight to a vertical plane, the athematical model is reduced. The simplified model is proved to be minimum phase, and a nonlinear controller based on inputoutput linearization is designed. Since the performance of the controller is significantly impacted by the choice of parameters, simulations of three different pole placement strategies are presented. The nonlinear controller shows better performances than a linear LQR controller when the initial condition is significantly away from the desired equilibrium

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

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

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