Verification and Control of Turn-Based Probabilistic Real-Time Games

Quantitative verification techniques have been developed for the formal analysis of a variety of probabilistic models, such as Markov chains, Markov decision process and their variants. They can be used to produce guarantees on quantitative aspects of system behaviour, for example safety, reliability and performance, or to help synthesise controllers that ensure such guarantees are met. We propose the model of turn-based probabilistic timed multi-player games, which incorporates probabilistic choice, real-time clocks and nondeterministic behaviour across multiple players. Building on the digital clocks approach for the simpler model of probabilistic timed automata, we show how to compute the key measures that underlie quantitative verification, namely the probability and expected cumulative price to reach a target. We illustrate this on case studies from computer security and task scheduling

Control Synthesis for Cyber-Physical Systems to Satisfy Metric Interval Temporal Logic Objectives under Timing and Actuator Attacks

This paper studies the synthesis of controllers for cyber-physical systems (CPSs) that are required to carry out complex tasks that are time-sensitive, in the presence of an adversary. The task is specified as a formula in metric interval temporal logic (MITL). The adversary is assumed to have the ability to tamper with the control input to the CPS and also manipulate timing information perceived by the CPS. In order to model the interaction between the CPS and the adversary, and also the effect of these two classes of attacks, we define an entity called a durational stochastic game (DSG). DSGs probabilistically capture transitions between states in the environment, and also the time taken for these transitions. With the policy of the defender represented as a finite state controller (FSC), we present a value-iteration based algorithm that computes an FSC that maximizes the probability of satisfying the MITL specification under the two classes of attacks. A numerical case-study on a signalized traffic network is presented to illustrate our results

Optimizing Performance of Continuous-Time Stochastic Systems using Timeout Synthesis

We consider parametric version of fixed-delay continuous-time Markov chains (or equivalently deterministic and stochastic Petri nets, DSPN) where fixed-delay transitions are specified by parameters, rather than concrete values. Our goal is to synthesize values of these parameters that, for a given cost function, minimise expected total cost incurred before reaching a given set of target states. We show that under mild assumptions, optimal values of parameters can be effectively approximated using translation to a Markov decision process (MDP) whose actions correspond to discretized values of these parameters