Automated Verification and Synthesis of Stochastic Hybrid Systems: A Survey

Abstract

Stochastic hybrid systems have received significant attentions as a relevant modelling framework describing many systems, from engineering to the life sciences: they enable the study of numerous applications, including transportation networks, biological systems and chemical reaction networks, smart energy and power grids, and beyond. Automated verification and policy synthesis for stochastic hybrid systems can be inherently challenging: this is due to the heterogeneity of their dynamics (presence of continuous and discrete components), the presence of uncertainty, and in some applications the large dimension of state and input sets. Over the past few years, a few hundred articles have investigated these models, and developed diverse and powerful approaches to mitigate difficulties encountered in the analysis and synthesis of such complex stochastic systems. In this survey, we overview the most recent results in the literature and discuss different approaches, including (in)finite abstractions, verification and synthesis for temporal logic specifications, stochastic similarity relations, (control) barrier certificates, compositional techniques, and a selection of results on continuous-time stochastic systems; we finally survey recently developed software tools that implement the discussed approaches. Throughout the manuscript we discuss a few open topics to be considered as potential future research directions: we hope that this survey will guide younger researchers through a comprehensive understanding of the various challenges, tools, and solutions in this enticing and rich scientific area.

Sampling-Based Robust Control of Autonomous Systems with Non-Gaussian Noise

“…Reachability analysis. Verification and controller synthesis for reachability in stochastic systems is an active field of research in safety-critical engineering (Abate et al 2008;Lavaei et al 2021). Most approaches are based on formal abstractions (Alur et al 2000;Lahijanian, Andersson, and Belta 2015;Soudjani and Abate 2013) or work in the continuous domain directly, e.g., using Hamilton-Jacobi reachability analysis (Bansal et al 2017;Herbert et al 2017) or optimization (Rosolia, Singletary, and Ames 2020).…”

Sampling-Based Robust Control of Autonomous Systems with Non-Gaussian Noise

“…Reachability analysis. Verification and controller synthesis for reachability in stochastic systems is an active field of research in safety-critical engineering (Abate et al 2008;Lavaei et al 2021). Most approaches are based on formal abstractions (Alur et al 2000;Lahijanian, Andersson, and Belta 2015;Soudjani and Abate 2013) or work in the continuous domain directly, e.g., using Hamilton-Jacobi reachability analysis (Bansal et al 2017;Herbert et al 2017) or optimization (Rosolia, Singletary, and Ames 2020).…”

Automata-based Controller Synthesis for Stochastic Systems: A Game Framework via Approximate Probabilistic Relations

“…Later, results in [10,11] propose Bellman operators for synthesizing controllers enforcing co-safe LTL F properties [12] based on this relation. In the context of constructing finite abstractions for largescale stochastic systems, compositional abstraction-based techniques have been introduced to alleviate the scalability issue due to discretizing the state sets; see for example [13][14][15][16][17][18][19][20][21][22].…”