The topic of this paper is the (partial) minimal realization problem in the max algebra, which is one of the modeling frameworks that can be used to model discrete event systems. We use the fact that a system of multivariate max-algebraic polynomial equalities can be transformed into an Extended Linear Complementarity Problem to find all equivalent minimal state space realizations of a multiple...

We propose an algorithm to find a counterexample to some property in a finite state program. This algorithm is derived from SPIN’s one, but it finds a counterexample faster than SPIN does. In particular it still works in linear time. Compared with SPIN’s algorithm, it requires only one additional bit per state stored. We further propose another algorithm to compute a counterexample of minimal s...

The topic of this paper is the (partial) minimal realization problem in the max algebra, which is one of the modeling frameworks that can be used to model discrete event systems. We use the fact that a system of multi-variate max-algebraic polynomial equalities can be transformed into an Extended Linear Complementarity Problem to nd all equivalent minimal state space realizations of a multiple ...

The state of turbulent, minimal-channel flow is estimated from spatio-temporal sparse observations the velocity, using both a physics-informed neural network (PINN) and adjoint-variational data assimilation (4DVar). performance PINN assessed against benchmark results 4DVar. efficient to implement, takes advantage automatic differentiation evaluate governing equations, does not require developme...

In this paper we estimate the minimal controllability time for a class of non-linear control systems with bounded convex state constraint. An explicit expression is given if image matrix co-dimension one. A lower bound in general case. The technique based on finding dimension system similar properties as original system. controls corresponding to time, or close one, are discussed and computed a...