Controller Design for Time-Varying Sampling, Co-Regulated Systems

Xinkai Zhang, Justin M. Bradley

Abstract: Co-regulation” is a time-varying periodic sampling strategy wherein the sampling rate is dynamically adjusted in response to the performance of the controlled system. The controller for co-regulated system needs to adjust control outputs corresponding to the current (changing) sampling rate. This makes performance guarantees such as stability difficult to obtain. In this letter we develop two stability guaranteed control algorithms for co-regulated systems. First is a correct-by-construction stabilizing controller where the control gain matrices are pre-computed offline for a set of sampling rates. This method allows for arbitrary switching of the sampling rates but as a result can be overly conservative. Then a hybrid Model Predictive Control (MPC) algorithm is tailored for co-regulated systems where both the system state trajectory and the sampling rate (scheduling parameter) trajectory are predicted within the receding horizon. The performances of the proposed controllers are demonstrated and discussed for a co-regulated multicopter Unmanned Aircraft System (UAS). The results show co-regulation can efficiently reallocate computational resources based on control performance by varying the sampling rate at runtime, while the proposed control strategies can guarantee co-regulated system stability when working under a time-varying sampling rate.