To sidestep the curse of dimensionality when computing solutions to Hamilton-Jacobi-Bellman partial differential equations (HJB PDE), we propose an algorithm that leverages a neural network to approximate the value function. We show that our final approximation of the value function generates near optimal controls which are guaranteed to successfully drive the system to a target state. Our fram...

ing away all continuous dynamics. Applying model checking to the abstract model identifies behaviors (the counterexamples) for which the latter violates the safety property. In a validation step, it is analyzed for these particular behaviors if corresponding counterexamples exist also for the hybrid automaton. If this applies, the procedure terminates with the result that the hybrid automaton d...

The philosophy, architecture, and capabilities of the COntinuous Reachability Analyzer (CORA) are presented. CORA is a toolbox that integrates various vector and matrix set representations and operations on them as well as reachability algorithms of various dynamic system classes. The software is designed such that set representations can be exchanged without having to modify the code for reach...

This work is concerned with the problem of computing the set of reachable states for linear time-invariant systems with bounded inputs. Our main contribution is a novel algorithm which improves significantly the computational complexity of reachability analysis. Algorithms to compute over and under-approximations of the reachable sets are proposed as well. These algorithms are not subject to th...

This paper presents applications of polytopic approximation methods for reachable set computation using dynamic optimization. The problem of computing exact reachable sets can be formulated in terms of a Hamilton-Jacobi partial differential equation (PDE). Numerical solutions which provide convergent approximations of this PDE have computational complexity which is exponential in the continuous...

This paper presents applications of polytopic approximation methods for reachable set computation using dynamic optimization. The problem of computing exact reachable sets can be formulated in terms of a Hamilton-Jacobi partial differential equation (PDE). Numerical solutions which provide convergent approximations of this PDE have computational complexity which is exponential in the continuous...

We introduce an analysis method that checks for the absence of (Euler) paths or cycles in the set of graphs reachable from a start graph via graph transformation rules. This technique is based on the approximation of graph transformation systems by Petri nets and on semilinear sets of markings. An important application is deadlock analysis in distributed systems.

In earlier work, we showed that the set of states which can reach a target set of a continuous dynamic game is the zero sublevel set of the viscosity solution of a time dependent Hamilton-Jacobi-Isaacs (HJI) partial differential equation (PDE). We have developed a numerical tool—based on the level set methods of Osher and Sethian— for computing these sets, and we can accurately calculate them f...

Branching vector addition systems are an extension of vector addition systems where new reachable vectors may be obtained by summing two reachable vectors and adding an integral vector from a fixed finite set. The reachability problem for them is shown hard for doubly-exponential space. For an alternative extension of vector addition systems, where reachable vectors may be combined by subtracti...

Reachability analysis of hybrid system imposes restrictions on the continuous and discrete behavior. In this paper a method is proposed to approximate the reachable set of linear systems by linear inequalities. It allows to use the full continuous dynamics of hybrid systems for reachability analysis. This method is applied to an automotive control problem, which was presented by Stauner et al. ...