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.