State constrained reachability for stochastic hybrid systems
نویسندگان
چکیده
The stochastic hybrid systems constitute well established classes of realistic models of hybrid discrete/continuous dynamics subject to random perturbations, autonomous uncontrollable transitions, nondeterminism or uncertainty. Stochastic reachability analysis is a key factor in the verification and deployment of stochastic hybrid systems. The encouraging recent progress prompts us to refine the problem to cover more realistic situations. We extend the so called constrained reachability problem from the probabilistic discrete case to stochastic hybrid systems. Then we define mathematically this problem, and we obtain the reach probabilities as solutions of a boundary value problem. The last problem is well studied and numerical, even symbolic solutions exist. This characterization is useful in stochastic control, in probabilistic path planning and for nano-systems.
منابع مشابه
Generating Discrete Trace Transition System of a Polyhe-dral Invariant Hybrid Automaton
Supervisory control and fault diagnosis of hybrid systems need to have complete information about the discrete states transitions of the underling system. From this point of view, the hybrid system should be abstracted to a Discrete Trace Transition System (DTTS) and represented by a discrete mode transition graph. In this paper an effective method is proposed for generating discrete mode trans...
متن کاملComputational Techniques for Reachability Analysis of Partially Observable Discrete Time Stochastic Hybrid Systems
Reachability analysis of hybrid systems has been used as a safety verification tool to assess offline whether the state of a system is capable of remaining within a designated safe region for a given time horizon. Although it has been applied to stochastic hybrid systems, little work has been done on the equally important problem of reachability under incomplete or noisy measurements of the sta...
متن کاملFunctional Abstractions of Stochastic Hybrid Systems
The verification problem for stochastic hybrid systems is quite difficult. One method to verify these systems is stochastic reachability analysis. Concepts of abstractions for stochastic hybrid systems are needed to ease the stochastic reachability analysis. In this paper, we set up different ways to define abstractions for stochastic hybrid systems, which preserve the parameters of stochastic ...
متن کاملStochastic Reachability: From Markov Chains to Stochastic Hybrid Systems
Stochastic hybrid systems represent established classes of realistic models of hybrid dynamics subject to random perturbations, autonomous uncontrollable transitions, nondeterminism or uncertainty. Stochastic reachability analysis is a key factor in the verification and deployment of stochastic hybrid systems. In this paper, we tackle the stochastic reachability problem from a purely probabilis...
متن کاملProbabilistic reachability and safety for controlled discrete time stochastic hybrid systems
In this work, probabilistic reachability over a finite horizon is investigated for a class of discrete time stochastic hybrid systems with control inputs. A suitable embedding of the reachability problem in a stochastic control framework reveals that it is amenable to two complementary interpretations, leading to dual algorithms for reachability computations. In particular, the set of initial c...
متن کامل