When discrete-event systems are used to model systems with a large number of possible (reachable) states, many problems such as simulation, optimization, and control, may become computationally prohibitive because they require some enumeration of such states. A common way to effectively address this issue is fluidization. The goal of this paper is that of studying the effect of fluidization on fault diagnosis. In particular, we focus on the purely logic Petri net (PN) model that results in the untimed continuous PN model after fluidization. In accordance to most of the literature on discrete-event systems, we define three diagnosis states, namely N , U , and F , corresponding respectively to no fault, uncertain, and fault state. We prove that, given an observation, the resulting diagnosis state can be computed solving linear programming problems rather than integer programming problems as in the discrete case. The main advantage of fluidization is that it enables to deal with much more general PN structures. In particular, the unobservable subnet needs not be acyclic as in the discrete case. Moreover, the compact representation of the set of consistent markings using convex polytopes can be seen in some cases as an improvement in terms of computational complexity.

This research proposes a centralized method for planning and monitoring the motion of one or a few mobile robots in an environment where regions of interest appear and disappear based on exponential probability density functions. The motion task is given as a linear temporal logic formula over the set of regions of interest. The solution determines robotic trajectories and updates them whenever necessary, such that the task is most likely to be satisfied with respect to probabilistic information on regions. The robots' movement capabilities are abstracted to finite state descriptions, and operations as product automata and graph searches are used in the provided solution. The approach builds up on temporal logic control strategies for static environments by incorporating probabilistic information and by designing an execution monitoring strategy that reacts to actual region observations yielded by robots. Several simulations are included, and a software implementation of the solution is available. The computational complexity of our approach increases exponentially when more robots are considered, and we mention a possible solution to reduce the computational complexity by fusing regions with identical observations.

In this paper we propose an automated method for planning a team of mobile robots such that a Boolean-based mission is accomplished. The task consists of logical requirements over some regions of interest for the agents' trajectories and for their final states. In other words, we allow combinatorial specifications defining desired final states whose attainment includes visits to, avoidance of, and ending in certain regions. The path planning approach should select such final states that optimize a certain global cost function. In particular, we consider minimum expected traveling distance of the team and reduce congestions. A Petri net (PN) with outputs models the movement capabilities of the team and the regions of interest. The imposed specification is translated to a set of linear restrictions for some binary variables, the robot movement capabilities are formulated as linear constraints on PN markings, and the evaluations of the binary variables are linked with PN markings via linear inequalities. This allows us to solve an Integer Linear Programming problem whose solution yields robotic trajectories satisfying the task.

This paper proposes an online approach for fault diagnosis of timed discrete event systems modeled by Time Petri Net (TPN). The set of transitions is partitioned into two subsets containing observable and unobservable transitions, respectively. Faults correspond to a subset of unobservable transitions. In accordance with most of the literature on discrete event systems, we define three diagnosis states, namely normal, faulty and uncertain states, respectively. The proposed approach uses a fault diagnosis graph, which is incrementally computed using the state class graph of the unobservable TPN. After each observation, if the part of FDG necessary to compute the diagnosis states is not available, the state class graph of the unobservable TPN is computed starting from the consistent states. This graph is then optimized and added to the partial FDG keeping only the necessary information for computation of the diagnosis states. We provide algorithms to compute the FDG and the diagnosis states. The method is implemented as a software package and simulation results are included.