A model-free predictive control method by ℓ1-minimization

We propose a new predictive control method utilizing a sparse solution of a minimization problem defined by both online and stored input/output data of the controlled system. The conventional predictive control methods generally require a mathematical model of the controlled system to predict an optimal future input to control the system. The mathematical model is usually obtained by applying a standard system identification method to the measured input/output data. The proposed method in this paper requires no mathematical model to predict future control input to achieve the desired output. This model-free control method, also called just-in-time predictive control, was originally proposed by Inoue and Yamamoto in 2004 and simplified by Yamamoto in 2014. In this paper, to develop another simplified method, we formulate an ℓ1-minimization problem.