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

Observability of nonlinear time–delay systems and its application to their state realization

In this paper, it is shown that the two notions of weak observability and strong observability may not be sufficient to describe the link between the input/output equation associated to the behaviour of a system and its state space realization. A new notion, called regular observability, is introduced, which is shown to capture essential features of nonlinear time delay systems and the existence of some realization

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

Occurrence of HIV eradication for preexposure prophylaxis treatment with a deterministic HIV model

The authors examine the human immunodeficiency virus (HIV) eradication in this study using a mathematical model and analyse the occurrence of virus eradication during the early stage of infection. To this end they use a deterministic HIV-infection model, modify it to describe the pharmacological dynamics of antiretroviral HIV drugs, and consider the clinical experimental results of preexposure prophylaxis HIV treatment. They also use numerical simulation to model the experimental scenario, thereby supporting the clinical results with a model-based explanation. The study results indicate that the protocol employed in the experiment can eradicate HIV in infected patients at the early stage of the infection

Integration of Cattle and Improved Pastures under Coconuts in Southern Luzon, Philippines

Results of two studies involving 1) grazing of Signalgrass (Brachiaria decumbens) pastures at different stocking and 2) cut-and-carry forages in smallholder farms for cattle under coconuts are presented. Grazing at 3 AU/ha and 2 AU/ha gave significantly higher LWG/ha (P 0.05) over 1 AU/ha but highest financial return was obtained from 2 AU/ha. Productivity of cattle on cut-and-carry forages in small farms varies among farmers with better animal performance directly related to quantity and quality of feeds offered and industriousness of individual farmers. Both studies showed the benefits derived from integration of cattle with improved pastures under coconuts

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

Stream Reaeration in Nonuniform Flow: Macroroughness Enhancement

The authors presented two papers that are a welcome addition to the topic of water quality and stream reaeration. The renewal theory and small eddy model provide interesting results for smooth and small-roughness channels. The discussers feel, however, that the second paper highlights some limits of the method, particularly when free-surface aeration takes place. The present discussion provides additional material on the problem of stream reaeration in the presence of 'whitewater' (i.e., air bubble entrainment). It complements the original paper, and some references are added, including large-scale data