Multiscale theory for linear dynamic processes. Part 2. Multiscale model predictive control (MS-MPC)

A multiscale framework, defined in a time-scale domain, offers significant advantages in designing and deploying model predictive control (MPC). The resulting multiscale MPC (MS-MPC) allows variable prediction and control horizons, which are adjusted in real-time in conjuction with the actual external disturbances that affect process behavior and the characteristics of model uncertainty generated in the course of feedback control, and can overcome the theoretical and practical hurdles of fixed-horizon classical MPC. In addition, MS-MPC can incorporate, naturally, richer descriptions of external disturbances and model uncertainties over several distinct temporal scales (ranges of frequencies) and can accommodate, naturally and optimally, measurements at multiple sampling intervals and control actions at multiple rates. MS-MPC is based on the multiscale framework of analysis established in Part 1 of this series. It employs a wavelet-based transformation of states, inputs and outputs from the time-domain to a time-scale domain, and multiscale process models on homogeneous binary trees, which define the time-scale domain. Finally, MS-MPC is better suited to handle input and output constraints over varying lengths of time. A series of numerical examples will illustrate the MS-MPC approach and its advantages in designing and deploying feedback process control systems.