Robust, Optimal Predictive Control of Jump Markov Linear Systems Using Particles

Hybrid discrete-continuous models, such as Jump Markov Linear Systems, are convenient tools for representing many real-world systems; in the case of fault detection, discrete jumps in the continuous dynamics are used to model system failures. Stochastic uncertainty in hybrid systems arises in both the continuous dynamics, in the form of uncertain state estimation, disturbances or uncertain modeling, and in the discrete dynamics, which are themselves stochastic. In this paper we present a novel method for optimal predictive control of Jump Markov Linear Systems that is robust to both continuous and discrete uncertainty. The approach extends our previous 'particle control' approach, which approximates the predicted distribution of the system state using a finite number of particles. Here, we present a weighted particle control approach, which uses importance weighting to ensure that low probability events such as failures are considered. We demonstrate the method with a car braking scenario.