Abstract: Model-based approaches to the verification of non-terminating Cyber-Physical Systems (CPSs) usually rely on numerical simulation of the System Under Verification (SUV) model under input scenarios of possibly varying duration, chosen among those satisfying given constraints. Such constraints typically stem from requirements (or assumptions) on the SUV inputs and its operational environment as well as from the enforcement of additional conditions aiming at, e.g., prioritising the (often extremely long) verification activity, by, e.g., focusing on scenarios explicitly exercising selected requirements, or avoiding </i>vacuity</i> in their satisfaction. In this setting, the possibility to efficiently sample at random (with a known distribution, e.g., uniformly) within, or to efficiently enumerate (possibly in a uniformly random order) scenarios among those satisfying all the given constraints is a key enabler for the practical viability of the verification process, e.g., via simulation-based statistical model checking. Unfortunately, in case of non-trivial combinations of constraints, iterative approaches like Markovian random walks in the space of sequences of inputs in general fail in extracting scenarios according to a given distribution (e.g., uniformly), and can be very inefficient to produce at all scenarios that are both legal (with respect to SUV assumptions) and of interest (with respect to the additional constraints). For example, in our case studies, up to 91% of the scenarios generated using such iterative approaches would need to be neglected. In this article, we show how, given a set of constraints on the input scenarios succinctly defined by multiple finite memory monitors, a data structure (scenario generator) can be synthesised, from which any-horizon scenarios satisfying the input constraints can be efficiently extracted by (possibly uniform) random sampling or (randomised) enumeration. Our approach enables seamless support to virtually all simulation-based approaches to CPS verification, ranging from simple random testing to statistical model checking and formal (i.e., exhaustive) verification, when a suitable bound on the horizon or an iterative horizon enlargement strategy is defined, as in the spirit of bounded model checking.

Abstract: Many Control Systems are indeed Software Based Control Systems, i.e. control systems whose controller consists of control software running on a microcontroller device. This motivates investigation on Formal Model Based Design approaches for automatic synthesis of control software.
Available algorithms and tools (e.g., QKS) may require weeks or even months of computation to synthesize control software for large-size systems. This motivates search for parallel algorithms for control software synthesis.
In this paper, we present a map-reduce style parallel algorithm for control software synthesis when the controlled system (plant) is modeled as discrete time linear hybrid system. Furthermore we present an MPI-based implementation PQKS of our algorithm. To the best of our knowledge, this is the first parallel approach for control software synthesis.
We experimentally show effectiveness of PQKS on two classical control synthesis problems: the inverted pendulum and the multi-input buck DC/DC converter. Experiments show that PQKS efficiency is above 65%. As an example, PQKS requires about 16 hours to complete the synthesis of control software for the pendulum on a cluster with 60 processors, instead of the 25 days needed by the sequential algorithm in QKS.