With the development of information science and technology, practical processes such as those relevant to the chemical industry, metallurgy, machinery, electronics, electricity, transportation, and logistics, have undergone significant changes. These industries have production technologies and equipments in a large scale, and production processes have become more complex. Modeling processes using first principles or identification has become more difficult. For this reason, traditional MBC theory has become impractical for control issues in these kinds of enterprises. Furthermore, many industrial processes generate and store huge amounts of process data at every time instant of every day, containing all the valuable state information of process operations and equipments. Using these data, both on-line and off-line, to directly design controllers, predict and assess system states, evaluate performance, make decisions, or even diagnose faults, would be very significant, especially under the lack of accurate process models. For this reason, the establishment and development of data-driven control theory (DDC) are urgent issues both in theory and application.

Data-driven controls are the control theories and methods in which the controller is designed directly using on-line or off-line I/O data of the controlled system or knowledge from the data processing without using explicit or implicit information of the mathematical model of the controlled process, and whose stability, convergence, and robustness can be guaranteed by rigorous mathematical analysis under certain reasonable assumptions.

The control system includes two main parts: the controller and the controlled object, and the controlled object can generally be divided into the following four categories:

(1) The mechanism model or identification model can be accurately obtained;

(2) The mechanism model or identification model is inaccurate and contains uncertain factors;

(3) Although the mechanism model or identification model is available, it is very complicated, with high order and strong nonlinearity;

(4) The mechanism model or identification model is difficult to establish or not available.

Among them, the last three categories are the main content of data-driven control methods that need to be studied. It should be pointed out that a complete control theory system should be able to deal with all the above-mentioned controlled objects. Therefore, from this perspective, a complete control theory system should include MBC theory and DDC theory. Both MBC and DDC are not mutually replaceable, they should be coexist and co-work with complementary advantages.

So far, more than 10 different DDC methods can be found in the literature, which can be summarized into the following three categories:

(1) DDC methods based on online data: including SPSA (simultaneous perturbation stochastic approximation), model-free adaptive control (MFAC), Unfalsified control (UC), etc..

(2) DDC method based on offline data: including PID control, iterative feedback tuning (IFT), correlation-based tuning (CbT), virtual reference feedback tuning (VRFT), etc.

(3) DDC method based on online/offline data: including iterative learning control (ILC), lazy learning, etc..

Take the model free adaptive control (MFAC) as an example: the MFAC method was proposed by Hou Zhongsheng in 1994.  The essential idea is that, using an equivalent dynamic linearization data model with a novel concept called pseudo partial derivative at every current operation point to replace the general discrete time nonlinear system, then estimate the pseudo partial derivative on-line solely using the input and output data from the controlled plant, finally design the model-free adaptive control strategy for a class of nonlinear discrete-time systems.

Note: For detailed introduction, please refer to the attached summary paper.