Different Approaches on Stochastic Reachability as an Optimal Stopping Problem

Reachability analysis is the core of model checking of time systems. For stochastic hybrid systems, this safety verification method is very little supported mainly because of complexity and difficulty of the associated mathematical problems. In this paper, we develop two main directions of studying stochastic reachability as an optimal stopping problem. The first approach studies the hypotheses for the dynamic programming corresponding with the optimal stopping problem for stochastic hybrid systems. In the second approach, we investigate the reachability problem considering approximations of stochastic hybrid systems. The main difficulty arises when we have to prove the convergence of the value functions of the approximating processes to the value function of the initial process. An original proof is provided

Target control for hybrid systems with linear continuous dynamics

We consider the target control problem for hybrid systems with linear continuous dynamics. The system is modelled as a hybrid automaton. Control action is applied on the discrete level, while the continuous dynamics is subject to constant or set valued disturbance. The proposed controller ensures that the system can be transferred from any point of an initial set to a target set of the hybrid state space. A control design algorithm based on reachability analysis is proposed. For the implementation of the algorithm, approximate reachability analysis is employed. This involves under-approximation of reachable sets under linear continuous dynamics. The algorithm is applied to a batch control proble

Reachability analysis of linear hybrid systems via block decomposition

Reachability analysis aims at identifying states reachable by a system within a given time horizon. This task is known to be computationally expensive for linear hybrid systems. Reachability analysis works by iteratively applying continuous and discrete post operators to compute states reachable according to continuous and discrete dynamics, respectively. In this paper, we enhance both of these operators and make sure that most of the involved computations are performed in low-dimensional state space. In particular, we improve the continuous-post operator by performing computations in high-dimensional state space only for time intervals relevant for the subsequent application of the discrete-post operator. Furthermore, the new discrete-post operator performs low-dimensional computations by leveraging the structure of the guard and assignment of a considered transition. We illustrate the potential of our approach on a number of challenging benchmarks.Comment: Accepted at EMSOFT 202

Weak Singular Hybrid Automata

The framework of Hybrid automata, introduced by Alur, Courcourbetis, Henzinger, and Ho, provides a formal modeling and analysis environment to analyze the interaction between the discrete and the continuous parts of cyber-physical systems. Hybrid automata can be considered as generalizations of finite state automata augmented with a finite set of real-valued variables whose dynamics in each state is governed by a system of ordinary differential equations. Moreover, the discrete transitions of hybrid automata are guarded by constraints over the values of these real-valued variables, and enable discontinuous jumps in the evolution of these variables. Singular hybrid automata are a subclass of hybrid automata where dynamics is specified by state-dependent constant vectors. Henzinger, Kopke, Puri, and Varaiya showed that for even very restricted subclasses of singular hybrid automata, the fundamental verification questions, like reachability and schedulability, are undecidable. In this paper we present \emph{weak singular hybrid automata} (WSHA), a previously unexplored subclass of singular hybrid automata, and show the decidability (and the exact complexity) of various verification questions for this class including reachability (NP-Complete) and LTL model-checking (PSPACE-Complete). We further show that extending WSHA with a single unrestricted clock or extending WSHA with unrestricted variable updates lead to undecidability of reachability problem

Computation of the Reachability Graph of untimed Hybrid Petri nets

Untimed hybrid Petri nets are a formalism for the analysis of dynamical systems, which combines discrete and continuous behaviour. The study of its reachability is interesting for analysis purposes, such as the study of behavioural properties. A method to compute its reachability graph and reachability space is proposed here

Improving polygonal hybrid systems reachability analysis through the use of the phase portrait

Polygonal hybrid systems (SPDI) are a subclass of planar hybrid automata which can be represented by piecewise constant dierential inclusions. The computation of certain objects of the phase portrait of an SPDI, namely the viability, controllability, invariance kernels and semi-separatrix curves have been shown to be eciently decidable. On the other hand, although the reachability problem for SPDIs is known to be decidable, its complexity makes it unfeasible on large systems. We summarise our recent results on the use of the SPDI phase portraits for improving reachability analysis by (i) state-space reduction and (ii) decomposition techniques of the state space, enabling compositional parallelisation of the analysis. Both techniques contribute to increasing the feasability of reachability analysis on large SPDI systems.peer-reviewe