# Data-Driven Model-Free Adaptive Sliding Mode Control Based on FFDL for Electric Multiple Units
###### Abstract
After years of development, MFAC has been successfully applied in many practical systems, such as network services [10;11], robotic systems [12;13], and aircraft systems [14;15]. The studies applied to the field of rail transportation include the following: [PERSON] [16] used the traditional MFAC in a single-particle model of train operation control and achieved better control performance than the traditional PID method. Based on this, Reference [17] combined predictive control to achieve energy-efficient train operation by solving the optimal control problem online for each sampling point of the train system, making full use of the advantages of MFAC and predictive control. In addition, it is difficult for the controller designed based on the dynamics model to guarantee the safety of the train, when the actuator has some failure problems. Hence, MFAC has been widely applied in train fault-tolerant control in recent years: Reference [18] converted the train input and output data into a compact form dynamic linearization (CFDL) model, and proposed a model-free adaptive fault-tolerant control method based on actuator failure under the speed and traction/braking force constraints; References [19;20] further improved based on Reference [18], and proposed the model-free adaptive fault-tolerant control based on a partial form dynamic linearization (PFDL) model for high-speed trains with traction/braking force constraints and actuator faults, using methods such as neural networks to approximate the nonlinear terms caused by faults. In the above studies, the dynamic linearization of the train system is performed by using the CFDL or PFDL method, which only considers the relationship between the amount of variation in the system output and the amount of variation in the current or multiple inputs. All possible complex behaviors in the system, such as nonlinearity, parametric time variation, and structural time variation, are compressed into time-varying parameters. As a result, when the above methods are used in practical systems, more complex time-varying parameter estimation algorithms need to be designed to obtain better control effects. Moreover, the existing studies on the application of MFAC to trains do not consider the multi-particle train as the controlled object, nor do they consider the impact of disturbances on the system. Based on the above analysis and to further improve the robustness of the system, a data-driven MFASMC scheme for high-speed EMUs is proposed in this paper. 1. Compared with the MFAC methods used in References [16; 18], this paper further incorporates a discrete sliding mode control algorithm to reduce the effect of measurement perturbations. To prevent the output from being too large, the parameter estimation error is introduced as a limiting term, which improves the robustness of the system;
2. Compared with the CFDL model used in References [16; 17; 18; 19; 20], the FFDL method used in this paper integrates the relationship between the output change at the next moment and the input and output within a fixed-length sliding time window. Although the dimensionality of the FFDL data model increases, the dynamic behavior of each component becomes simpler, and the design and selection of the parameter estimation algorithm become easier. It is not sensitive to the time-varying structure and parameters of the system. 3. Compared with the existing literature on the application of MFAC to trains, the controlled object of this paper is a multi-power unit train, which is more in line with the actual operational requirements. The control method in this paper can be extended to other types of train systems (Such as CRH380 AL with 14 motors and 2 trailers, CRH380B with 4 motors and 4 trailers, TR08 magley train with 3-5 sections, and so on). 4. Compared with References [4; 5], the algorithm in this paper does not depend on the dynamic model of the EMUs and is a data-driven control algorithm.