This work deals with finite time observability of switched linear systems (SLS) when they are represented by a family of nonautonomous linear systems (LS) and an interpreted Petri net (IPN). Based on this SLS representation, new detection of the commutation time and LS distinguishability characterizations in SLS extended to the non autonomous case are presented. Using these results, the novel concept of distinguishability between LS sequences is presented and characterized. This concept together with the IPN input-output information is used to determine the IPN marking sequence. From the knowledge of this sequence, the conditions for the computation of the continuous state are presented. Also necessary and sufficient conditions for the observability in infinitesimal time are provided.

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This paper proposes to use machine learning techniques with ultrasonic sensors to predict the behavior and status of a person when they live solely inside their house. The proposed system is tested on a single room. A grid of ultrasonic sensors is placed in the ceiling of a room to monitor the position and the status of a person (standing, sitting, lying down). The sensors readings are wirelessly communicated through a microcontroller to a cloud. An intelligent system will read the sensors values from the cloud and analyses them using machine learning algorithms to predict the person behavior and status and decide whether it is a normal situation or abnormal. If an abnormal situation is concluded, then an alert with be risen on a dashboard, where a care giver can take an immediate action. The proposed system managed to give results with accuracy exceeding 90%. Results out of this project will help people with supported needed, for example elderly people, to live their life as independent as possible, without too much interference from the caregivers. This will also free the care givers and allows them to monitors more units at the same time.