This report presents the results of a friendly competition for formal verification and policy synthesis of stochastic models. The friendly competition took place as part of the workshop Applied Verification for Continuous and Hybrid Systems (ARCH) in 2018. In this first edition, we present five benchmarks with different levels of complexities and stochastic favours. We make use of six different tools and frameworks (in alphabetical order): Barrier Certificates, FAUST2, FIRM-GDTL, Modest, SDCPN modelling & MC simulation and SReachTools; and attempt to solve instances of the five different benchmark problems. Through these benchmarks, we capture a snapshot on the current state-of the art tools and frameworks within the stochastic modelling domain. We also present the challenges encountered within this domain and highlight future plans which will push forward the development of more tools and methodologies for performing formal verification and optimal policy synthesis of stochastic processes. @en

We present shrinking horizon model predictive control for discrete-time linear systems under stochastic disturbances with constraints encoded as signal temporal logic (STL) specification. The control objective is to satisfy a given STL specification with high probability against stochastic uncertainties while maximizing the robust satisfaction of an STL specification with minimum control effort. We formulate a general solution, which does not require precise knowledge of probability distributions of (possibly dependent) stochastic disturbances; only the bounded support of the density functions and moment intervals are used. For the specific case of disturbances that are normally distributed, we optimize the controllers by utilizing knowledge of the probability distribution of the disturbance. We show that in both cases, the control law can be obtained by solving optimization problems with linear constraints at each step. We experimentally demonstrate effectiveness of this approach by synthesizing a controller for a heating, ventilation, and air conditioning system.@en