Simultaneous model prediction and data-driven control with relaxed assumption on the model

Roozbeh Abolpour; Alireza Khayatian; Maryam Dehghani

doi:10.1016/j.isatra.2023.11.023

Simultaneous model prediction and data-driven control with relaxed assumption on the model

ISA Trans. 2024 Feb:145:225-238. doi: 10.1016/j.isatra.2023.11.023. Epub 2023 Dec 2.

Authors

Roozbeh Abolpour¹, Alireza Khayatian², Maryam Dehghani³

Affiliations

¹ School of Electrical and Computer Engineering, Shiraz University, Shiraz, Iran. Electronic address: r.abolpour@shirazu.ac.ir.
² School of Electrical and Computer Engineering, Shiraz University, Shiraz, Iran. Electronic address: khayatia@shirazu.ac.ir.
³ School of Electrical and Computer Engineering, Shiraz University, Shiraz, Iran. Electronic address: mdehghani@shirazu.ac.ir.

PMID: 38245466
DOI: 10.1016/j.isatra.2023.11.023

Abstract

This paper aims to design a Model Predictive Control (MPC) law based on the time series data gathered from the input and output of a system. An Auto-Regressive Integrated Moving Average (ARIMA) model with unknown parameters and an unknown sequence of controller signal are considered for the system. Based on a window of data, an optimization problem is formulated which can find the optimal unknown model parameters and controller sequence, simultaneously. This problem is a non-convex optimization problem with many non-convex constraints and difficult to solve. Therefore, a transformation is developed which can transfer the optimization problem to an equivalent problem with convex constraints and a non-convex objective function. This new problem is much easier to solve with the present solvers. The effectiveness of the overall approach is proved via several examples that reveal satisfaction and convincingness.

Keywords: Convex optimization; Data-driven model predictive control (DD-MPC); Linear matrix inequality (LMI); Simultaneous model prediction and control.