A safety property restricts the set of reachable states. In this paper, we introduce a notion of relative safety which states that certain program states are reachable provided certain other states are. A key, but not exclusive, application of this method is in representing symmetry in a program. Here, we show that relative safety generalizes the programs that are presently accommodated by exis...

We consider an affine control system whose vector fields span a third-order nilpotent Lie algebra. We show that the reachable set at time T using measurable controls is equivalent to the reachable set at time T using piecewise-constant controls with no more than four switches. The bound on the number of switches is uniform over any final time T . As a corollary, we derive a new sufficient condi...

Tools for state space exploration, or reachability analysers, work by incrementally constructing a set of reachable states. The applicability of these tools is limited by the vast state space of real systems. One way to attack this problem are different reduction methods— another approach is to come up with techniques for representing the set of reachable states in a compact way. The state—or m...

Among the various critical systems that worth to be formally analyzed, a wide set consists of controllers for dynamical systems. Those programs typically execute an infinite loop in which simple computations update internal states and produce commands to update the system state. Those systems are yet hardly analyzable by available static analysis method, since, even if performing mainly linear ...

In order to check if the system behavior satisfies the requirement set, this paper uses a class of DEVS, called finite & deterministic DEVS (FD-DEVS). Since the infinite state behavior of FD-DEVS networks can be abstracted as a finite reachable graph, this paper utilizes the reachable graph structure to check the emptiness of illegal behavior detected by checkers, called rejectors, as well as t...

The properties of reachable sets for linear dynamical systems for specified control sets are discussed. Iterative procedures for determining numerical approximations of the reachable set are suggested and methods of obtaining an admissible control function which transfers an initial state to as near a prescribed target as possible is described. The problem of teachability with multiple control ...

1  Abstract—Linear constraint transformation is an essential step to solve the forbidden state problem in Petri nets that contain uncontrollable transitions. This work studies the equivalent transformation from a legal-marking set to its admissible-marking set given such a net. First, the concepts of an escaping-marking set and a transforming marking set are defined. Based on them, two algorit...

Control systems can be subject to outside inputs, environmental effects, disturbances, and sensor/actuator inaccuracy. To model such systems, linear differential equations with constrained inputs are often used, ẋ(t) = Ax(t) + Bu(t), where the input vector u(t) stays in some bound. Simulating these models is an important tool for detecting design issues. However, since there may be many possibl...

An analysis of stick-slip behavior and convergence trajectories in the feedback-controlled motion systems with discontinuous Coulomb friction is provided. A closed-form parameter-dependent stiction region, around an invariant equilibrium set, proved to be always reachable globally attractive. It shown that only asymptotic can achieved, at least one but mostly infinite number consecutive cycles,...