Controller Synthesis for Probabilistic Safety Specifications using Observers**This work is supported in part by the European Commission IAPP project AMBI 324432, and by the John Fell Oxford University Press(OUP) Research Fund.
Kendra Lesser, Alessandro Abate · IFAC-PapersOnLine · 2015
We present a method for the correct-by-design synthesis of controllers that maximize the safety probability of partially observable stochastic systems. Given a stochastic system with outputs that are corrupted by Gaussian measurement noise, we construct a stochastically contracting observer that produces estimates of the internal state of the system. The contractivity guarantees that the distance between the internal state and the estimate produced by the observer remains bounded, and we can treat the observer as a fully observable abstraction of the original system. For the bounded-horizon probabilistic safety objective, we can synthesize a control law for the observer using a modified safe region according to the bound on the distance above. The control law applied to the original system guarantees that the safety objective is met with some given probability. We showcase the approach on a temperature control problem using a Kalman filter as the observer for a linear stochastic model.