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In this paper we present a multi-rate control architecture for safetycritical systems. We consider a high level planner and a low level controllerwhich operate at different frequencies. This multi-rate behavior is describedby a piecewise nonlinear model which evolves on a continuous and a discretelevel. First, we present sufficient conditions which guarantee recursiveconstraint satisfaction for the closed-loop system. Afterwards, we propose acontrol design methodology which leverages Control Barrier Functions (CBFs) forlow level control and Model Predictive Control (MPC) policies for high levelplanning. The control barrier function is designed using the full nonlineardynamical model and the MPC is based on a simplified planning model. When thenonlinear system is control affine and the high level planning model is linear,the control actions are computed by solving convex optimization problems ateach level of the hierarchy. Finally, we show the effectiveness of the proposedstrategy on a simulation example, where the low level control action is updatedat a higher frequency than the high level command.

Multi-Rate Control Design Leveraging Control Barrier Functions and Model Predictive Control Policies