On observability and design of observers in timed continuous Petri net systems

This paper is devoted both to the study of observability criteria and the design of observers in the continuous Petri net setting. The concept of structural observability, regarding the possibility of estimating the marking of places, i.e., the system state, for any speed of the transitions is introduced and studied for the subclass of join-free Petri nets (JF). For non-join-free Petri nets, conditions to compute suitable state estimates are established. The proposed observers are piecewise linear systems that assure the continuity of the estimate even when a switch occurs. The system simulation may allow us to estimate even the unobservable space of the net system during a given time period. Note to Practitioners - Petri nets represent a modeling formalism for discrete dynamical systems that offers a great modeling power. Among others, Petri nets have been successfully applied in the fields of manufacture, communication, logistics, and traffic. Continuous Petri nets came up to handle the state explosion problem inherent to highly populated discrete systems. The state of a plant modeled with a continuous Petri net is given by a set of real variables. This way, the initial load of the plant has no effect on the complexity of the analysis techniques to be applied. Obtaining an accurate knowledge of the state of the plant is a crucial task that can determine the feasibility and reliability of subsequent activities as control. The usual way to catch information about the dynamical system under consideration is through sensors located on the physical plant. Unfortunately, in many real situations some state variables cannot be measured through sensors due to either their inaccessible location, the lack of such sensors or the high cost involved in the installation of the sensors. The good news is that the value of those a priori nonmeasurable variables can be estimated if the plant fulfils some technical conditions. Usually, state estimates can be obtained by building a dynamical system called observer whose output is the estimate for the plant. The paper can be roughly divided into two parts. In the first part, the conditions required to compute estimates are studied. The second part presents a method to design observers whose state converges to the state of the plant.