StocHy: automated verification and synthesis of stochastic processes

StocHy is a software tool for the quantitative analysis of discrete-time stochastic hybrid systems (SHS). StocHy accepts a high-level description of stochastic models and constructs an equivalent SHS model. The tool allows to (i) simulate the SHS evolution over a given time horizon; and to automatically construct formal abstractions of the SHS. Abstractions are then employed for (ii) formal verification or (iii) control (policy, strategy) synthesis. StocHy allows for modular modelling, and has separate simulation, verification and synthesis engines, which are implemented as independent libraries. This allows for libraries to be easily used and for extensions to be easily built. The tool is implemented in C++ and employs manipulations based on vector calculus, the use of sparse matrices, the symbolic construction of probabilistic kernels, and multi-threading. Experiments show StocHy's markedly improved performance when compared to existing abstraction-based approaches: in particular, StocHy beats state-of-the-art tools in terms of precision (abstraction error) and computational effort, and finally attains scalability to large-sized models (12 continuous dimensions). StocHy is available at www.gitlab.com/natchi92/StocHy

Efficiency through Uncertainty: Scalable Formal Synthesis for Stochastic Hybrid Systems

This work targets the development of an efficient abstraction method for formal analysis and control synthesis of discrete-time stochastic hybrid systems (SHS) with linear dynamics. The focus is on temporal logic specifications, both over finite and infinite time horizons. The framework constructs a finite abstraction as a class of uncertain Markov models known as interval Markov decision process (IMDP). Then, a strategy that maximizes the satisfaction probability of the given specification is synthesized over the IMDP and mapped to the underlying SHS. In contrast to existing formal approaches, which are by and large limited to finite-time properties and rely on conservative over-approximations, we show that the exact abstraction error can be computed as a solution of convex optimization problems and can be embedded into the IMDP abstraction. This is later used in the synthesis step over both finite- and infinite-horizon specifications, mitigating the known state-space explosion problem. Our experimental validation of the new approach compared to existing abstraction-based approaches shows: (i) significant (orders of magnitude) reduction of the abstraction error; (ii) marked speed-ups; and (iii) boosted scalability, allowing in particular to verify models with more than 10 continuous variables

Formal Controller Synthesis for Markov Jump Linear Systems with Uncertain Dynamics

Automated synthesis of provably correct controllers for cyber-physical systems is crucial for deployment in safety-critical scenarios. However, hybrid features and stochastic or unknown behaviours make this problem challenging. We propose a method for synthesising controllers for Markov jump linear systems (MJLSs), a class of discrete-time models for cyber-physical systems, so that they certifiably satisfy probabilistic computation tree logic (PCTL) formulae. An MJLS consists of a finite set of stochastic linear dynamics and discrete jumps between these dynamics that are governed by a Markov decision process (MDP). We consider the cases where the transition probabilities of this MDP are either known up to an interval or completely unknown. Our approach is based on a finite-state abstraction that captures both the discrete (mode-jumping) and continuous (stochastic linear) behaviour of the MJLS. We formalise this abstraction as an interval MDP (iMDP) for which we compute intervals of transition probabilities using sampling techniques from the so-called 'scenario approach', resulting in a probabilistically sound approximation. We apply our method to multiple realistic benchmark problems, in particular, a temperature control and an aerial vehicle delivery problem.Comment: 14 pages, 6 figures, under review at QES

Towards Scalable Synthesis of Stochastic Control Systems

Formal control synthesis approaches over stochastic systems have received significant attention in the past few years, in view of their ability to provide provably correct controllers for complex logical specifications in an automated fashion. Examples of complex specifications of interest include properties expressed as formulae in linear temporal logic (LTL) or as automata on infinite strings. A general methodology to synthesize controllers for such properties resorts to symbolic abstractions of the given stochastic systems. Symbolic models are discrete abstractions of the given concrete systems with the property that a controller designed on the abstraction can be refined (or implemented) into a controller on the original system. Although the recent development of techniques for the construction of symbolic models has been quite encouraging, the general goal of formal synthesis over stochastic control systems is by no means solved. A fundamental issue with the existing techniques is the known "curse of dimensionality," which is due to the need to discretize state and input sets and that results in an exponential complexity over the number of state and input variables in the concrete system. In this work we propose a novel abstraction technique for incrementally stable stochastic control systems, which does not require state-space discretization but only input set discretization, and that can be potentially more efficient (and thus scalable) than existing approaches. We elucidate the effectiveness of the proposed approach by synthesizing a schedule for the coordination of two traffic lights under some safety and fairness requirements for a road traffic model. Further we argue that this 5-dimensional linear stochastic control system cannot be studied with existing approaches based on state-space discretization due to the very large number of generated discrete states.Comment: 22 pages, 3 figures. arXiv admin note: text overlap with arXiv:1407.273

Scalable Approach to Uncertainty Quantification and Robust Design of Interconnected Dynamical Systems

Development of robust dynamical systems and networks such as autonomous aircraft systems capable of accomplishing complex missions faces challenges due to the dynamically evolving uncertainties coming from model uncertainties, necessity to operate in a hostile cluttered urban environment, and the distributed and dynamic nature of the communication and computation resources. Model-based robust design is difficult because of the complexity of the hybrid dynamic models including continuous vehicle dynamics, the discrete models of computations and communications, and the size of the problem. We will overview recent advances in methodology and tools to model, analyze, and design robust autonomous aerospace systems operating in uncertain environment, with stress on efficient uncertainty quantification and robust design using the case studies of the mission including model-based target tracking and search, and trajectory planning in uncertain urban environment. To show that the methodology is generally applicable to uncertain dynamical systems, we will also show examples of application of the new methods to efficient uncertainty quantification of energy usage in buildings, and stability assessment of interconnected power networks

Symbolic Models for Stochastic Switched Systems: A Discretization and a Discretization-Free Approach

Stochastic switched systems are a relevant class of stochastic hybrid systems with probabilistic evolution over a continuous domain and control-dependent discrete dynamics over a finite set of modes. In the past few years several different techniques have been developed to assist in the stability analysis of stochastic switched systems. However, more complex and challenging objectives related to the verification of and the controller synthesis for logic specifications have not been formally investigated for this class of systems as of yet. With logic specifications we mean properties expressed as formulae in linear temporal logic or as automata on infinite strings. This paper addresses these complex objectives by constructively deriving approximately equivalent (bisimilar) symbolic models of stochastic switched systems. More precisely, this paper provides two different symbolic abstraction techniques: one requires state space discretization, but the other one does not require any space discretization which can be potentially more efficient than the first one when dealing with higher dimensional stochastic switched systems. Both techniques provide finite symbolic models that are approximately bisimilar to stochastic switched systems under some stability assumptions on the concrete model. This allows formally synthesizing controllers (switching signals) that are valid for the concrete system over the finite symbolic model, by means of mature automata-theoretic techniques in the literature. The effectiveness of the results are illustrated by synthesizing switching signals enforcing logic specifications for two case studies including temperature control of a six-room building.Comment: 25 pages, 4 figures. arXiv admin note: text overlap with arXiv:1302.386