Nonlinear Stochastic Model Predictive Control in the Circular Domain

In this paper, we present an open-loop Stochastic
Model Predictive Control (SMPC) method for discrete-time
nonlinear systems whose state is defined on the unit circle.
This modeling approach allows considering systems that include
periodicity in a more natural way than standard approaches
based on linear spaces. The main idea of this work is twofold:
(i) we model the quantities of the system, i.e., the state, the
measurements, and the noises, directly as circular quantities
described by circular probability densities, and (ii) we apply
deterministic sampling given in closed form to represent the
occurring densities. The latter allows us to make the prediction
required for solution of the SMPC problem tractable. We
evaluate the proposed control scheme by means of simulations.