In recent years, Arenz et al. proposed the idea of reachable set characterization based on quantum speed limit (QSL); that is, target unitary gate in a closed qubit system can be characterized by considering QSL as necessary condition control setup must satisfy order to achieve goal. Inspired this idea, paper we characterize general Markovian open derived \cite{Kohei2}. Note bound is not only e...

In this note, we show that any distributive lattice is isomorphic to the set of reachable configurations of an Edge Firing Game. Together with the result of James Propp, saying that the set of reachable configurations of any Edge Firing Game is always a distributive lattice, this shows that the two concepts are equivalent.

In this work, switching systems are named endogenous when their switching pattern is controllable. Linear endogenous switching systems can be considered as a particular class of bilinear control systems. The key idea is that both types of systems are equivalent to polysystems i.e. to systems whose flow is piecewise smooth. The reachable set of a linear endogenous switching system can be studied...

This paper considers nonlinear perturbations of control systems with linear dynamics and seeks to analyze whether the approximately reachable set may be left unchanged by this perturbation. Under suitable conditions it is shown that this analysis may be reduced to the presumably simpler analysis of such invariance for a family of affine perturbations. Interest centers on the context of infinite...

The paper investigates the structure of the reachable set of linear switched systems. The structure of the reachable set is determined using techniques from classical nonlinear systems theory, namely, the theory of orbits developed by H. Sussman and the realization theory for nonlinear systems developed by B. Jakubczyk.

In this paper, the output reachable estimation and safety verification problems for multi-layer perceptron neural networks are addressed. First, a conception called maximum sensitivity in introduced and, for a class of multi-layer perceptrons whose activation functions are monotonic functions, the maximum sensitivity can be computed via solving convex optimization problems. Then, using a simula...