Runtime Monitors for Markov Decision Processes

We investigate the problem of monitoring partially observable systems with nondeterministic and probabilistic dynamics. In such systems, every state may be associated with a risk, e.g., the probability of an imminent crash. During runtime, we obtain partial information about the system state in form of observations. The monitor uses this information to estimate the risk of the (unobservable) current system state. Our results are threefold. First, we show that extensions of state estimation approaches do not scale due the combination of nondeterminism and probabilities. While exploiting a geometric interpretation of the state estimates improves the practical runtime, this cannot prevent an exponential memory blowup. Second, we present a tractable algorithm based on model checking conditional reachability probabilities. Third, we provide prototypical implementations and manifest the applicability of our algorithms to a range of benchmarks. The results highlight the possibilities and boundaries of our novel algorithms.

Filtering method for linear and non-linear stochastic optimal control of partially observable systems II

In this paper we studied stochastic optimal control problem based on partially observable systems (SOCPP) with a control factor on the diffusion term. A SOCPP has state and observation processes. This kind of problem has also a minimum payoff function. The payoff function should be minimized according to the partially observable systems consist of the state and observation processes. In this regard, the filtering method is used to evaluat this kind of problem and express full consideration of it. Finally, presented estimation methods are used to simulate the solution of a partially observable system corresponding to the control factor of this problem. These methods are numerically used to solve linear and nonlinear cases.