An Adaptive Model Predictive Control Strategy for Nonlinear Distributed Parameter Systems using the Type-2 Takagi–Sugeno Model

Abstract

This paper proposes an adaptive model predictive control (MPC) strategy for nonlinear distributed parameter systems (DPSs) based on the online-tuning interval Type-2 Takagi-Sugeno (IT2 T–S) model. First, the infinite dimension DPS is approximated in a finite dimensional space via the finite difference method, and from this model, training data are generated. Principal component analysis is then used to project the finite, but still high, dimensional spatiotemporal training data into a low-dimensional time series using spatial basis functions. Next, an online-tuning IT2 T–S fuzzy model is proposed to predict the low-dimensional time series with a high accuracy by computing an optimal time-varying weight parameter. Furthermore, a new method for simplifying controller design is presented by transforming the control objective from the high-dimensional spatial outputs reaching their set points to the lower dimensional time outputs reaching their set points. These novel contributions increase the accuracy of the prediction model (thus improving control performance) and reduce the computational cost of the underlying MPC optimization. Lastly, simulations are presented on a typical DPS to demonstrate the accuracy and effectiveness of the proposed methods.