Self‐triggered predictive control of nonlinear systems using approximation model

Abstract

Abstract This article studies discrete‐time model predictive control of continuous‐time nonlinear systems with measurement noises and exogenous disturbances. We consider the co‐design of discrete‐time finite horizon optimal control problem (FHOCP) and the associated self‐triggering schemes that schedule the time instants for sampling the state and computing the FHOCP. The state‐dependent nature of the self‐triggered scheduling can not only dynamically adjust the inter‐sampling period according to the system status, but dynamically discretize the model used in the FHOCP as well, in order to reduce the complexity of the FHOCP if designed appropriately. It is shown that the system can be stabilized with uniform ultimate boundedness, as long as the scheduling scheme matches the approximation model such that the one‐step approximation error between the predicted state and the actual state is below a threshold related to the cost function. These results can be applied to most existing model approximation methods with either fixed or time‐varying sampling rates.