A Framework for Predictive Control of Sampled-Data Systems Using Sporadic Model Approximation

This paper studies stability of sampled-data systems controlled by discrete-time model predictive control (MPC) algorithms. We consider a general framework for the co-design of discrete-time MPC law and the associated scheduling schemes, where the discrete-time model used in MPC approximates the behavior of the plant with state-dependent sampling periods. Sufficient conditions are derived to guarantee uniform ultimate boundedness of the resulting closed-loop system. The results can be applied to most existing model approximation methods with either fixed or time-varying sampling rates. It is shown that to stabilize the system, the model used in the FHOCP does not have to be very accurate as long as the associated scheduling scheme matches the model and the approximation error is below a threshold related to the running cost function.