Abstraction-based Probabilistic Stability Analysis of Polyhedral Probabilistic Hybrid Systems
In this paper, we consider the problem of probabilistic stability analysis of a subclass of Stochastic Hybrid Systems, namely, Polyhedral Probabilistic Hybrid Systems (PPHS), where the flow dynamics is given by a polyhedral inclusion, the discrete switching between modes happens probabilistically at the boundaries of their invariant regions and the continuous state is not reset during switching. We present an abstraction-based analysis framework that consists of constructing a finite Markov Decision Processes (MDP) such that verification of certain property on the finite MDP ensures the satisfaction of probabilistic stability on the PPHS. Further, we present a polynomial-time algorithm for verifying the corresponding property on the MDP. Our experimental analysis demonstrates the feasibility of the approach in successfully verifying probabilistic stability on PPHS of various dimensions and sizes.
Code (0)
등록된 구현이 없습니다.
Similar Papers 제목 키워드 기반
A Foundational Theory of Quantitative Abstraction: Adjunctions, Duality, and Logic for Probabilistic Systems
The analysis and control of stochastic dynamical systems rely on probabilistic models such as (continuous-space) Markov decision processes, but large or continuous state spaces make exact analysis intractable and call fo…
Representation LearningSound Abstraction and Decomposition of Probabilistic Programs
Probabilistic programming languages are a flexible tool for specifying statistical models, but this flexibility comes at the cost of efficient analysis. It is currently difficult to compactly represent the subtle in…
Probabilistic ProgrammingProbabilistic Program Abstractions
Abstraction is a fundamental tool for reasoning about complex systems. Program abstraction has been utilized to great effect for analyzing deterministic programs. At the heart of program abstraction is the relationship b…
Static Analysis for Probabilistic Programs
Probabilistic programming is a powerful abstraction for statistical machine learning. Applying static analysis methods to probabilistic programs could serve to optimize the learning process, automatically verify properti…
BIG-bench Machine LearningProbabilistic ProgrammingA Probabilistic Programming Approach To Probabilistic Data Analysis
Probabilistic techniques are central to data analysis, but different approaches can be challenging to apply, combine, and compare. This paper introduces composable generative population models (CGPMs), a computational ab…
BIG-bench Machine LearningClusteringProbabilistic Programming