Introducing Dynamic Programming and Persistently Exciting into Data-Driven Model Predictive Control

In this paper, one new data-driven model predictive control scheme is proposed to adjust the varying coupling conditions between different parts of the system; it means that each group of linked subsystems is grouped as data-driven scheme, and this group is independently controlled through a decentralized model predictive control scheme. After combing coalitional scheme and model predictive control, coalitional model predictive control is used to design each controller, respectively. As the dynamic programming is only used in optimization theory, to extend its advantage in control theory, the idea of dynamic programming is applied to analyze the minimum principle and stability for the data-driven model predictive control. Further, the goal of this short note is to bridge the dynamic programming with model predictive control. Through adding the inequality constraint to the constructed model predictive control, one persistently exciting data-driven model predictive control is obtained. The inequality constraint corresponds to the condition of persistent excitation, coming from the theory of system identification. According to the numerical optimization theory, the necessary optimality condition is applied to acquire the optimal control input. Finally, one simulation example is used to prove the efficiency of our proposed theory.