Synthesis of model predictive control based on data-driven learning. Sci China Inf Sci, for reviewDear editor, Model predictive control (MPC) is a practically effective and attractive approach in the field of industrial processes [1] owing to its excellent ability to handle constraints, nonlinearity, and performance/cost trade-offs. The core of all model-based predictive algorithms is to use "open-loop optimal control" instead of "closed-loop optimal control" within a moving horizon [2]. It is assumed in this letter that the reader is familiar with MPC as a control design methodology.Because the dynamic model of a system predicting its evolution is usually inaccurate, the actual behaviors may deviate significantly from the predicted ones. Thus, acquiring accurate knowledge of the physical model is essential to ensure satisfactory performance of MPC controllers. Owing to the well-developed information technology, copious amounts of measurable process data can be easily collected, and such data can then be employed to predict and assess system behaviors and make control decisions, especially for the establishment and development of learning MPC.For the application of MPC design in on-line regulation or tracking control problems, several studies have attempted to develop an accurate model, and realize adequate uncertainty description of linear or non-linear plants of the processes [3][4][5]. In this work, we employ the datadriven learning technique specified in [6] to it-eratively approximate the dynamical parameters, without requiring a priori knowledge of system matrices. The proposed MPC approach can predict and optimize the future behaviors using multiorder derivatives of control input as decision variables. Because the proposed algorithm can obtain a linear system model at each sampling, it can adapt to the actual dynamics of time-varying or nonlinear plants. This methodology can serve as a data-driven identification tool to study adaptive optimal control problems for unknown complex systems.Problem Formulation. In this work, we consider a continuous-time industrial process given bẏwhere t t 0 , x ∈ R n , and u ∈ R m are the system states and input, respectively. H(·, ·) :where ⊗ denotes the Kronecker product. Θ denotes the vector of the system parameters given by Θ △ = vec(A) T vec(B) T T ∈ R n 2 +nm , where A ∈ R n×n is the system matrix, B ∈ R n×m is the input matrix, and vec(·) denotes the vectorization operator, that is, vec(P ) = p T 1 , . . . , p T m T , where p i ∈ R n is the ith column of a matrix P ∈ R n×m . We assume that (A, B) is controllable and (A, C) is observable.