Adaptive Model Predictive Control Scheme Based on Non-Minimal State Space Representation

Abstract

The model predictive control (MPC) technique is widely employed in process industries as a control scheme. The quality of the model used greatly influences the performance of the MPC. In time-varying systems, the plant model plays a critical role in determining the controller’s performance, as the controller’s control action relies on an adaptive model. Therefore, updating the system parameters rapidly and symmetrically in time-varying systems becomes necessary. To address this need, in the proposed work, a non-minimal state space model of a time-varying system is utilized for parameter estimation, and these parameters are updated at every sampling instant using a multi-innovation recursive least squares (MIRLS) scheme, which enables the timely updates of system parameters. We have explored various extensions of the recursive least square (RLS) scheme, such as the multi-innovation recursive least squares (MIRLS) method. This extension aims to achieve a higher convergence rate for parameter estimation. Furthermore, we have focused on the parameter estimation of a non-minimal state space time-varying system, where the system parameters change at each time interval. Additionally, we have incorporated a time-varying objective function into the MPC formulations, which enables adaptability to change the system dynamics. To demonstrate the applicability of our proposed approach, we have conducted simulation experiments using a benchmark time-varying model. These experiments showcase the effectiveness and benefits of our proposed methodology in dealing with time-varying systems.