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

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.