Particle Model Predictive Control: Tractable Stochastic Nonlinear Output-Feedback MPC

We combine conditional state density construction with an extension of the Scenario Approach for stochastic Model Predictive Control to nonlinear systems to yield a novel particle-based formulation of stochastic nonlinear output-feedback Model Predictive Control. Conditional densities given noisy measurement data are propagated via the Particle Filter as an approximate implementation of the Bayesian Filter. This enables a particle-based representation of the conditional state density, or information state, which naturally merges with scenario generation from the current system state. This approach attempts to address the computational tractability questions of general nonlinear stochastic optimal control. The Particle Filter and the Scenario Approach are shown to be fully compatible and -- based on the time- and measurement-update stages of the Particle Filter -- incorporated into the optimization over future control sequences. A numerical example is presented and examined for the dependence of solution and computational burden on the sampling configurations of the densities, scenario generation and the optimization horizon.