Related papers: On Recurrent Reachability for Continuous Linear Dy…
Markov decision processes model systems subject to nondeterministic and probabilistic uncertainty. A plethora of verification techniques addresses variations of reachability properties, such as: Is there a scheduler resolving the…
In the context of Markov decision processes running in continuous time, one of the most intriguing challenges is the efficient approximation of finite horizon reachability objectives. A multitude of sophisticated model checking algorithms…
We provide an algorithm to find the value and an optimal strategy of the solitaire variant of the Ten Thousand dice game in the framework of Markov Control Processes. Once an optimal critical threshold is found, the set of non-stopping…
In this paper a novel computational technique for finite discrete approximation of continuous dynamical systems suitable for a significant class of biochemical dynamical systems is introduced. The method is parameterized in order to affect…
Interval approaches for the reachability analysis of initial value problems for sets of classical ordinary differential equations have been investigated and implemented by many researchers during the last decades. However, there exist…
Verification of infinite-state Markov chains is still a challenge despite several fruitful numerical or statistical approaches. For decisive Markov chains, there is a simple numerical algorithm that frames the reachability probability as…
We consider small nonlinear perturbations of linear systems on a time scale with the phase space being finite or infinite-dimensional. For $\Delta$-differential operators, corresponding to linear dynamic systems we consider their…
We consider the time-bounded reachability problem for continuous-time Markov decision processes. We show that the problem is decidable subject to Schanuel's conjecture. Our decision procedure relies on the structure of optimal policies and…
We study several decision problems for counter systems with guards defined by convex polyhedra and updates defined by affine transformations. In general, the reachability problem is undecidable for such systems. Decidability can be achieved…
We study the problem of detecting zeros of continuous functions that are known only up to an error bound, extending the earlier theoretical work with explicit algorithms and experiments with an implementation. More formally, the robustness…
Linear Dynamical Systems, both discrete and continuous, are invaluable mathematical models in a plethora of applications such the verification of probabilistic systems, model checking, computational biology, cyber-physical systems, and…
We propose a method to outer bound forward reachable sets on finite horizons for uncertain nonlinear systems with polynomial dynamics. This method makes use of time-dependent polynomial storage functions that satisfy appropriate dissipation…
In real world applications, uncertain parameters are the rule rather than the exception. We present a reachability algorithm for linear systems with uncertain parameters and inputs using set propagation of polynomial zonotopes. In contrast…
This paper studies the set of terminal state covariances that are reachable over a finite time horizon from a given initial state covariance for a linear stochastic system with additive noise. For discrete-time systems, a complete…
There are many physical processes that have inherent discontinuities in their mathematical formulations. This paper is motivated by the specific case of collisions between two rigid or deformable bodies and the intrinsic nature of that…
The problem of computing the reachable set for a given system is a quintessential question in nonlinear control theory. While previous work has yielded a plethora of approximate and analytical methods for determining such a set, these…
We study a discrete time queueing system where deterministic arrivals have i.i.d. exponential delays $\xi_{i}$. The standard deviation $\sigma$ of the delay is finite, but its value is much larger than the deterministic unit service time.…
A fast convergence in a fixed-time of solutions of nonlinear dynamical systems, for which special requirements are satisfied on the derivative of a quadratic function calculated along the solutions of the system, is proposed. The conditions…
We consider linear programming (LP) problems in infinite dimensional spaces that are in general computationally intractable. Under suitable assumptions, we develop an approximation bridge from the infinite-dimensional LP to tractable finite…
We consider the problem of proving that each point in a given set of states ("target set") can indeed be reached by a given nondeterministic continuous-time dynamical system from some initial state. We consider this problem for abstract…