Fast model predictive control based on multiscale system theory

Owing to its ability to deal with hard constraints, model predictive control (MPC) can meet the good control performance requirements of modern complex industrial control systems. But the large computational load limits its application to more fields such as fast dynamic systems. In order to apply MPC to millisecond timescale systems, this paper studies the fast MPC based on multiscale system theory. By using the discrete wavelet transform, the state-space model, prediction model, constrains and objective function of classical MPC algorithm can be transformed from time domain to time-scale domain. The multiscale MPC (MSMPC) can share many theoretical properties (such as stability, observability and etc.) with the classical MPC. Besides, MSMPC has a new property that it allows variable length horizon, which could enhance the real-time performance of the MPC, and promote its potential applications. Finally, we apply the MSMPC to two case studies with millisecond timescales, and compare the computational performance between the MSMPC and the classical MPC.