Neural network based modeling and control of elbow joint motion under functional electrical stimulation

Neurocomputing 340 (2019) 171–179

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Neurocomputing journal homepage: www.elsevier.com/locate/neucom

Neural network based modeling and control of elbow joint motion under functional electrical stimulation Yurong Li a,b,∗, Wenxin Chen a,b, Jun Chen a,b, Xin Chen c, Jie Liang c, Min Du b a

College of Electrical Engineering and Automation, Fuzhou University, Fuzhou, Fujian 350108, China Fujian Key Lab of Medical Instrumentation & Pharmaceutical Technology, Fuzhou University, Fuzhou, Fujian 350108, China c Fuzhou Second Hospital Affiliated to Xiamen University, Fuzhou, Fujian 350007, China b

a r t i c l e

i n f o

Article history: Received 5 December 2018 Revised 26 February 2019 Accepted 1 March 2019 Available online 6 March 2019 Communicated by Prof. Zidong Wang Keywords: Functional electrical stimulation Dynamic neural network model Iterative learning control Elbow joint motion model Neurorehabilitation

a b s t r a c t In patients with stroke and spinal cord injury, motor function is reduced or even lost because motor nerve signals cannot be transmitted due to nerve injury. Functional electrical stimulation (FES) is one of the most important rehabilitation techniques for the treatment of motor impairment in patients with stroke and spinal cord injury, which has been widely used in the recovery and reconstruction of limb motor function. In this paper, we propose a neural network based modeling method and control implementation of FES system for upper limb neurorehabilitation. A dynamic neural network model based on Hammerstein structure is proposed for modeling the elbow joint motion under functional electrical stimulation. A closed-loop control system for FES is realized using iterative learning control (ILC) and achieved an excellent tracking performance. Both simulation and experiment are carried out to demonstrate the results. Considering the 20 tests of the model, the average of average relative error (ARE) and root mean square error (RMSE) of the testing samples are 4.11% and 4.12◦ , respectively. The ability of ILC system to resist model disturbance is discussed, and the maximum error between the actual elbow joint trajectory and the desired trajectory for each motion cycle is analysed. As the number of iterations increases, the actual elbow motion can track the desired trajectory. The experiment verifies that the real-time system can realize the desired trajectory tracking. The results show that the established dynamic neural network model is suitable for studying the motion characteristics of elbow joint under electrical stimulation. It is feasible to train the network with the aid of genetic algorithm, and the iterative learning strategy can achieve excellent control effect in elbow joint FES system. © 2019 Elsevier B.V. All rights reserved.

1. Introduction As a result of the nerve system damage, the limbs of patients with hemiplegia cannot be controlled by nervous system to complete the desired movements, resulting in limb dysfunction, which brings not only serious physical and psychological damage to patients, but also gives rise to serious burden to families and society. The two major diseases that cause hemiplegia are cerebral apoplexy and spinal cord injury. Cerebral apoplexy, also known as stroke or cerebrovascular accident, is one of the most harmful diseases in the world. Its an acute cerebrovascular disease caused by sudden rupture of blood vessels in the brain or blood vessels that cannot flow into the brain due to occlusion of blood vessels. Spinal cord injury is usually caused by external or disease factors such as traffic accidents, high altitude falls, sports accidents, spinal ∗ Corresponding author at: College of Electrical Engineering and Automation, Fuzhou University, Fuzhou, Fujian 350108, China. E-mail address: [email protected] (Y. Li).

https://doi.org/10.1016/j.neucom.2019.03.003 0925-2312/© 2019 Elsevier B.V. All rights reserved.

tuberculosis, spinal degeneration, spinal or spinal cord tumours, etc. With the aging of the population and the development of transportation, the incidence of stroke and spinal cord injury is increasing. Three-quarters of the stroke patients who survive have various degrees of physical dysfunction [1]. Currently, there is no reliable estimate of global prevalence, but the annual global incidence is estimated to be 40 to 80 per million people [2]. For such a large group of patients with limb dysfunction, how to help them recover and rebuild their motor function is of great significance. Reconstruction of upper extremity motor function is important to help patients with limb dysfunction to achieve self-care. The elbow joint is critical to the recovery of the entire upper extremity motor function. Functional Electrical Stimulation (FES) is one of the important rehabilitation techniques for the treatment of limb dysfunction in patients with stroke or spinal cord injury. FES was first used in 1961 and it was originally referred to as Functional Electrotherapy by Liberson [3]. FES is an alternative therapy in the absence of central nervous system stimulation, which can be used as a temporary

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therapy for a rehabilitation purpose. Experiment and clinical treatment have verified that FES can effectively improve the motor function of patient and it has been widely used [4–6]. Designing the FES system for elbow joint rehabilitation training is of great significance for helping the upper limb motor function rehabilitation of patients with limb dysfunction. FES systems have evolved from open-loop system to closedloop system. Open loop control refers to the control of the system through an external manual switch, or the pressure, acceleration and other sensors to trigger the FES system to start or stop [7–9]. The stimulation current parameters, including the stimulation amplitude, frequency, and waveform, are set by experience. After being set, they are fixed throughout the stimulation process, and cannot be adjusted in real time according to the actual movement of the patient’s limb. This kind of fixed stimulation produces either excess stimulation resulting in muscle fatigue, or insufficient stimulation making it difficult for muscles to come out corresponding contractions, both of which are imposible to complete the specific function. In order to achieve the precise adjustment of stimulus intensity, the closed-loop control of FES system is generated. By measuring the motion trajectory, angle, angular velocity, joint torque and other parameters of patients in the rehabilitation process, the closed-loop control system is constituted to realize the precise control of stimulation parameters [10,11]. The application of the closed-loop control algorithm mostly adopts the traditional PID and the improved PID control algorithm, and focuses on the simulation research. However, the physical rehabilitation processes are often repetitive exercises. Compared with PID control algorithm, the ILC algorithm is more suitable for the control of repeated exercises. It exhibits superior self-learning ability and is more resistant to model parameter interference and external noise [12]. At the same time, in order to realize a precisely controlled FES output system, guarantee the safety of the rehabilitation process and improve the effect of elbow rehabilitation training, we need to study the motion characteristics of elbow joints. Many researches have benn carried out on the motion characteristics of human joints. Focusing on muscle force producing mechanism, some studies calculated the muscle force by analysing the muscle activation, muscle tension and muscle contraction speed based on the Hill model, combining with the rigid body mechanics to establish the model of the joints [13–15]. However, the mechanism of electrically stimulated elbow joint movement is complicated, greatly increasing the difficulty of mechanism model, and many physiological parameters are difficult to determine, leading to the unreliable result. Therefore, researches have combined mechanism and parameter identification to solve the problems of mechanism model in many applications. For example, the unscented Kalman filter, extended Kalman filter(EKF), switching particle swarm optimization and hybrid EKF switching particle swarm optimization algorithm has been used, and the effectiveness of the proposed method has been demonstrated [16–19]. By analysing the motion process of electrically stimulated ankle joint, Misgeld et al. established a mechanism model with unknown parameters which was identified by Kalman filter [20]. On the other hand, in order to avoid the complicated mechanism analysis, machine learning was successfully applied in biomedical fields [21,22]. A feedforward neural network was used to establish a joint model under electrical stimulation [23]. However, the joint motion under electrical stimulation is a dynamic nonlinear model with strong time-varying characteristics. A simple feedforward neural network cannot reflect its characteristics. The famous module-based dynamic nonlinear Hammerstein model, composed of static nonlinear modules and dynamic linear modules in series [24], has been applied to study the motion characteristics of muscles and joints under electrical stimulation [25,26]. Kurosawa designed a dynamic neural network based on the Ham-

merstein structure to model the wrist joint, establishing the relationship between the electrical stimulation and the wrist joint angle [25]. However, the designed model included only feedback, not considering the feedforward effect of the previous stimulation, which really existed in the stimulation effect. Also it adopted the error back propagation to train the network, which was not suitable for training the neural network with feedback connections. In this paper, by carrying out the electrical stimulation-induced elbow motion experiments, a dynamic neural network based on Hammerstein structure is constructed to reflect the relation between electric stimulation and elbow joint angle. In this model, the feedforward effect of the stimulus current input and the feedback of the angle output are considered comprehensively. Genetic algorithm is used to optimize the dynamic neural network. Based on the established model, the simulation and experiment of the closed-loop FES control system are implemented simultaneously using ILC algorithm. 2. Elbow joint motion model under electrical stimulation An accurate electrically stimulated elbow joint motion model is the basis for precise control of the elbow joint motion FES system. Firstly, the elbow joint motion experiment is carried out under electrical stimulation. Then, the Hammerstein based dynamic neural network of the electrically stimulated elbow joint motion is established. Finally, the genetic algorithm is used to optimize the dynamic neural network model. 2.1. Experimental set-up In this paper, a male subject(age: 26 years, height: 170 cm, weight: 60 kg) was recruited as a volunteer. The experiment requires the upper limb to be complete freedom and relaxed, without any voluntary effort during the electrical stimulation process which ensures that the movement is completely undertaken by electrically stimulated biceps. The experimental equipment contains the electrical stimulation device (MotionStim8, Medel GembH, Germany), goniometer (Goniometer sensor SG 150, Biometrics Ltd., England) and the wireless signal acquisition system (Trigno Wireless System, Delsys Inc., USA). The signal acquisition system transmits wirelessly the value of goniometer to the base station, and then to the computer. The stimulated electrode is with the size of 4 cm × 4 cm × 1 mm, and the maximum surface resistance is 3K ± 10%. The diagram of the elbow joint movement under electrical stimulation and the angular coordinate system are shown in Fig. 1. The forearm naturally drooping direction, the positive direction of the X axis and the positive direction of the Y axis are calibrated as 0◦ , 90◦ and 180◦ , respectively. In general, human elbow joint motion angle ranges from 0◦ to 135◦ . The subject stands upright so that the elbow joint can freely flex and extend in the sagittal plane of the human body. The two output electrodes A and B of the FES stimulation instrument are placed on the upper and lower ends of the biceps muscle. The goniometer is placed at the elbow joint with the sampling frequency of 37 Hz. The experimental environment is shown in Fig. 2. Once the electrical stimulation is delivered, the biceps will contract to flex elbow joint. Decreasing the stimulation intensity will decrease the contraction force. When the contraction force is less than the gravity, the elbow joint will be extended. In our experiment, the flexion and extension movements of elbow joint are in the sagittal plane. The stimulation current and elbow joint angle are recorded. In the experiment, the frequency and amplitude of the stimulation current are fixed at 20 Hz and 30 mA, respectively. The electrical stimulation device adjusts the stimulation current intensity by changing the pulse width, ranging from 40 to 110 μs. The

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which is a single-layer neural network with feedforward hysteresis and feedback hysteresis. In Fig. 4, u(k) represents an input signal, x(k) represents an intermediate signal, and y(k) represents an output signal. Z −1 represents the unit delay, the superscript N represents the delay order, and the subscript M represents the number of hidden nonlinear neurons in the static nonlinear part. L1 , L2 , and L3 are linear neurons, whose function is f(x ) = ωx + β . S1 , S2 , . . . , SM are S-type neurons whose function is g(x ) = (1 − e−x )/(1 + e−x ). Then we obtain the functional relationship of the static part as:

x (k ) =

M 

ωm g(ηm u(k ) + βm ) + β1

(1)

m=1

where ηm and β m , m = 1, 2, . . . , M are weights and thresholds for L1 neurons to hidden layer S-type neurons, ωm , m = 1, 2, . . . , M, and β 1 are weights and thresholds for hidden layer S-type neurons to L2 neurons, respectively. The dynamic partial function relationship is given as

Fig. 1. Elbow joint experiment diagram.

y (k ) =

N 

ωi x ( k − i ) +

i=1

N 

ω j x(k − j ) + β2

(2)

j=1

where ωi , i = 1, 2, . . . , N are weights from L2 layer neurons to L3 layer neurons, ωj , j = 1, 2, . . . , N are weights from y(k) to L3 layer neurons and β 2 is the threshold of L3 layer neurons, respectively. Substituting (1) into (2) to obtain the model function relationship:

y (k ) =

N  M 

ωi ωm g(ηm u(k − i ) + βm ) +

i=1 m=1

+

N 

ω j y(k − j ) + β2

N 

ωi β1

j=1

(3)

j=1

Fig. 2. Elbow joint electrical stimulation experimental environment.

experiment includes ten sessions. In order to fully excite the movement characteristics of the elbow joint under different electrical stimulation intensity, the pulse width (PW) is generated randomly, shown in Fig. 3(A). In each session, the stimulation is repeated three trials, and each trial lasts for 30 s. It takes more than 3 minutes to rest between trials, preventing the muscle fatigue. We take the average of the angular value of the three trials, and an angle curve is obtained as shown in Fig. 3(B). Ten sets of data are obtained after ten sessions for the subsequent modeling and analysis. 2.2. Neural network model Hammerstein model was firstly proposed by Narendra and Gallman in 1966 [27]. It’s a module-based nonlinear model, connecting serially by a static nonlinear module and a dynamic linear module. Muscle or joint motion under electrical stimulation is a nonlinear system with time-varying characteristics. For such an unknown time-varying nonlinear system, we use a neural network based on Hammerstein model and parameters optimization method to model the electrically stimulated elbow joint movement. The neurons are connected according to the characteristics of the Hammerstein model, and the neural network structure is shown in Fig. 4. The neural network consists of two parts. The first part is the static nonlinear section, which is a single hidden layer feedforward neural network. The second part is the dynamic linear section,

The unknown model parameters ηm , ωm , ωi , ωj , β m , β 1 , and β 2 , where m = 1, 2, . . . , M, i = 1, 2, . . . , N, j = 1, 2, . . . , N can be determined by training the neural network with 10 sets of experimental data. In the preliminary exploration of training the Hammerstein neural network, it showed that the back propagation algorithm was sensitive to the initial value and easy to fall into local optimum. For the neural network with feedback and feedforward links, it was difficult to calculate the updated error gradient information during training by using the method of backward error propagation, which made it difficult for the algorithm to converge [28]. The training of neural network can in fact be transformed into the optimization of weight and threshold. Therefore intelligent optimization algorithms can be used to deal with the network training problems [29–32]. In particular, Genetic Algorithm (GA) is a random search optimization method developed to simulate the genetic mechanism of nature and biological evolution [33,34]. In this paper, the GA is used to optimize the structure of the Hammerstein network weights and threshold parameters. 2.3. Modeling results and discussion Ten-fold cross validation is applied to train and test the neural network, that is, the samples are randomly divided into ten groups, nine of which are used as training data in turn, and the remaining one group is used as testing data, ensuring that all samples have been tested. The PW of stimulation currents data is randomly generated and updated every two seconds. The stimulation lasts for 30 s, hence there are 15 random PWs in each group of stimulation, and 135 kinds of random PWs in the nine groups of training data. The 135 kinds of random stimuli can fully excite all the motion characteristics of the joint.

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Fig. 3. Stimulation current pulse width and resulting angle, (a) is pulse width, (b) is elbow joint angle. Table 1 ARE and RMSE under different test samples. Test sample

1

2

3

4

5

6

7

8

9

10

Average

ARE/(%) RMSE/(◦ )

4.12 4.16

4.91 6.12

3.35 3.45

3.82 4.51

4.10 4.12

4.23 4.53

2.71 3.01

4.37 4.64

5.64 6.32

3.16 2.39

4.28 4.32

Table 2 Average ARE and RMSE of multiple tests

Fig. 4. Neural network topology.

In the following, we will calculate the average relative error (ARE) and the root mean square error (RMSE) of the test samples using the model output and experimental data. The corresponding formulas are expressed as in (4) and (5). ARE and RMSE are used to evaluate the pros and cons of the model.

ARE =

v 



|Xex,i − Xmo,i | Xex,i

i=1



RMSE =

v

i=1



/v

(Xex,i − Xmo,i )2 v

(4)

Index

Training sample

Test sample

Average ARE/(%) Standard deviation of ARE /(%) Average RMSE/(◦ ) Standard deviation of RMSE/(◦ )

3.12 0.03 3.45 0.01

4.11 0.02 4.12 0.02

the 10 test samples are 5.64% and 4.28%, respectively; the maximum and average RMSE value of the 10 test samples are 6.32◦ and 4.32◦ , respectively. The results clearly show that the neural network model is effective, and hence the method is feasible. For the purpose of demonstration, one of the results is selected randomly from the ten-fold cross validation to show the fitting effect of the measured data and test results. We provide representative results on proposed model in Fig. 5. It can be found that the model output fits the measured data well. In order to verify the reliability of the modeling algorithm, the above ten-fold cross process is performed 20 times to test whether the algorithm can achieve the satisfied fitting effect each time. The average and the corresponding standard deviations of ARE and RMSE of the 20 tests are calculated, as shown in Table 2, which clearly show that the algorithm is reliable and can achieve a precise model each time. 3. The iterative learning control of elbow joint FES system

(5)

The ARE and RMSE values of each group of testing data are calculated in the ten-fold cross validation, as listed in Table 1. It can be seen from Table 1, the maximum and average ARE value of

Iterative learning control (ILC) is usually applied to objects with repetitive characteristics. ILC is based on the notion that the performance of a system that executes the same task multiple times can be improved by learning from previous executions (trials,

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Fig. 5. Fitting curve of test results.

Fig. 6. Simulation model of ILC system in Simulink.

iterations, passes) [35]. According to the ILC law, there are many types of ILC algorithms, such as, P-type ILC, D-type ILC, PI-type ILC, PD-type ILC, and PID-type ILC. In addition, in terms of the different calculations of ILC, it can be divided into open-loop ILC system and closed-loop ILC system [36]. 3.1. Establishment of ILC simulation system The elbow joint simulation system for ILC is completed in the MATLAB Simulink toolbox. Firstly, we need to establish a neural network model in Simulink, and use the experimental data to train the network with the aid of GA optimization. Then the network structure is converted into Simulink simulation module, which can be used to build the Simulink ILC simulation system. The ILC controller is composed of two parts: the control output of last time and the PID correction amount. The control output of last time is saved by importing it into the workspace, and moved from the workspace to the Simulink at the next time. The calculation of the PID correction amount is realized by the S-function. The PID structure in this paper is incremental PID. The simulation model of the ILC system in Simulink is shown in Fig. 6, where S − F unction generates the desired trajectory, and

the error of the desired trajectory and the actual model output is calculated by the Add module. The PID correction amount is calculated by the ILC _Control l er module. The Controlquantity_k − 1 module reads the stored control output of last time in the workspace, adding the PID correction amount to produce the current control output.The control output is limited by the Saturation module from 40 to 110μs. Finally, the control quantity is feed to the neural network model, generating the actual angle of the elbow joint motion. The Controlquantity module and the Modeloutput module are used to store the control amount and the actual output of the model, respectively. After establishing such a simulation system, we set the desired trajectory, adjust the proportional integral differential parameters of the PID in the ILC, and simulate it. 3.2. Simulation result analysis We compare the ILC with the PID control system. Firstly, the desired trajectory is set as the angular change of the elbow joint flexion and extension with uniform velocity in the sagittal plane, which is shown in Fig. 1. Next, the ILC system is simulated. One period of the acquired desired trajectory is shown as the solid line in Fig. 7. The proportional, integral and differential coefficients of

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Y. Li, W. Chen and J. Chen et al. / Neurocomputing 340 (2019) 171–179 Table 3 Performance of two control systems under model parameter disturbance.

Fig. 7. The desired trajectory and actual trajectory of 10 iterations of ILC system.

the PID in the ILC system are set as 0.6, 0.3 and 2, respectively. The ILC FES system is performed 10 iterations. The actual trajectory from the first to the tenth iteration is shown from bottom to top as dashed line respectively in Fig. 7. At the same time, we examine the performance of the PIDcontrolled FES system. The proportional, integral, and differential coefficients in the PID control system are carefully adjusted as 11, 10, and 0.6, respectively. The desired and the actual trajectories of 10 cycles under PID control are shown in Fig. 8. It can be seen from Fig. 8 that unlike the ILC control system, the actual trajectory does not track more and more closely to the desired trajectory as the control period increases, and the error between them always maintains a certain value. The output of the desired trajectory, the actual trajectory for the 10th iteration of the ILC system, as well as the 10th cycle of the PID system are shown in Fig. 9, respectively. It can be seen that the trajectory of the ILC output substantially tracks the desired trajectory. However, there exists a large error between the output trajectory of the PID system and the desired trajectory. The maximum error, ARE and RMSE between the output trajectory of the 10th ILC iteration and the expected trajectory are 0.438◦ , 0.32% and 0.245◦ , respectively. However, between the output trajectory of the 10th cycle of the PID system and the desired trajectory, the values equal to 8.263◦ , 14.65% and 5.636◦ , respectively. From the

Percentage (%)

Maximum error /◦

ARE /%

5 10 15

PID 9.131 11.022 18.228

PID 15.96 17.75 19.51

ILC 0.551 0.601 0.856

RMSE /◦ ILC 0.41 0.52 0.69

PID 6.004 7.794 9.983

ILC 0.351 0.482 0.785

results, the performances of the ILC system are significantly better than the case of PID system. The results show that the ILC method is more suitable for the control of electrical stimulation of elbow joint motion than PID one. The resistance to model disturbance is an important factor of the control system performance. In the simulation experiment, the model disturbances such as muscle fatigue, or an unconscious willingness to participate in the electrical stimulation process are simulated by changing the parameters of the neural network model. The results of PID and ILC algorithms of the FES system are analysed and compared. The 10% weights of the neural network are randomly selected and varied by 5%, 10%, and 15%, respectively. The maximum error, ARE and RMSE between the desired and actual trajectories of these two control systems are shown in Table 3. We can find that compared with the PID-controlled system, the ILC system has a smaller error and expresses a better performance. The actual output trajectory of the 10th iteration of the ILC system and the 10th cycle of the PID system are shown in Fig. 10 when the model parameters are varied by 10%. The ILC system can still maintain small errors, but the error of the PID system becomes larger. It can be seen that compared with the PID control, the change of the model parameters has less influence on the ILC system, and the resistance to model disturbance of the ILC control is stronger. The ILC algorithm has a certain learning ability, which can adjust the control input in real time according to the actual output, therefore, the ILC FES system has stronger resistance to model disturbance. 4. Experimental verification of electrical stimulation system In this section, the actual elbow joint is used as the control object to build an iterative learning real-time FES control system to verify whether the FES system can control the elbow joint to track the desired trajectory.

Fig. 8. The desired trajectory and actual trajectory of the PID system for 10 cycles.

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Fig. 9. The output of PID and ILC control system.

Fig. 10. Output of PID and ILC control system when model parameters varied by 10%.

electrical stimulation device, whose stimulation frequency and amplitude are set to 20 Hz and 30 mA, respectively. The PW is adjusted in real time by the control system. The Matlab on the PC communicates with the Trigno Lab wireless signal acquisition system in TCP/IP mode. Matlabs simulink toolbox can control the PW in real time through serial communication. The PC transmits the calculated PW in real time to the electrical stimulation device. The elbow joint angle is transmitted to the PC in real time through the angle acquisition device. The Real-time FES control system experimental environment is shown in Fig. 2. The stimulating electrode is placed on both ends of the biceps muscle and the goniometer is worn at the elbow joint. 4.2. Experimental results and analyzes Fig. 11. Real-time FES control system signal connection block diagram.

4.1. Real-time FES control system The signal connection relationship of the real-time FES control system is shown in Fig. 11. The equipment of the experimental system contains the electrical stimulation device and angle acquisition equipment as stated in Section 2.1. The MotionStim8 is chosen as

The actual elbow joint angle and the desired trajectory in the iterative control of the FES system are shown in Fig. 12. The actual motion trajectory of the elbow joint gradually approaches the desired trajectory as the number of iterations increase. After the 6th iteration, the actual motion trajectory of the elbow joint basically tracks the desired trajectory. It can be seen that there is still a certain hysteresis characteristic in the actual movement process of the elbow joint. As the number of iterations increase, the

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References

Fig. 12. Actual elbow joint trajectory and expected trajectory.

control system adjusts the stimulation PW in real time to track the desired trajectory. However, as the stimulation time increased, the experimenter’s biceps gradually entered a state of fatigue, resulting in a slight increase in the later error, which did not appear in the simulation. 5. Conclusion As the population ages and traffic accidents increase, the incidence of stroke and spinal cord injury increases. Stroke and spinal cord injury often cause limb dysfunction in patients. FES technology has been widely used in the recovery and reconstruction of limb motor function. In this paper, a more effective limb rehabilitation training FES system has been designed. The elbow joint has been used as the object, and the ILC has been employed to complete the closed-loop FES system of the elbow joint angle. A model of elbow joint motion under electrical stimulation has been established, which is a dynamic neural network model based on Hammerstein model structure. Based on characteristics of the electrically stimulated elbow joint in the sagittal plane, we have designed and conducted the experiment of elbow joint motion under electrical stimulation. The experimental data are used to optimize the neural network using genetic algorithms to obtain network parameters. Finally, the simulation results of the model are presented to illustrate the effectiveness of the established model. In this paper, iterative learning is applied to the control of the FES system, which achieve excellent result. Experiments verify that the system can achieve tracking control of the desired trajectory. Furthermore, there are some directions for furture research. Firstly, we can try to integrate the voluntary effort and other optimization method into the system control. According to recently novel research, the application of combined optimization strategy and multi-objective optimization design both achieve remarkable effect [37,38]. Inspired by it, we will develop the research in the near future by putting these ideas into our optimization process. Secondly, the experiment were carried out on able-bodied subject. The future work will carry out on the stroke and spinal cord injury subjects for further research and clinical trials. Acknowledgment This work was supported in part by National Natural Science Foundation of China (Grant no. 61773124), National Key Research and Development Program of China (Grant no. 2016YFE0122700) and UK-China Industry-Academia Partnership Programme\276.

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Wenxin Chen received his B.E. degree in automation from the College of Electrical Engineering and Automation, Fuzhou University, Fuzhou, China, in 2018. He is currently pursuing the Master’s degree in control engineering at Fuzhou University, Fuzhou, China. His research interests include computational neuroscience and intelligent information processing.

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Jun Chen received his B.S. degree in electrical engineering and automation from the College of Electrical Engineering and Automation, Fuzhou University, Fuzhou, China, in 2016. He is currently pursuing the Master’s degree in control theory and control engineering at Fuzhou University, Fuzhou, China. His research interests include neurorehabilitation and computational neuroscience.

Xin Chen received his undergraduate degree in clinical medicine from Colleges of Traditional Chinese Medicine of Fujian in 1994. Now he is the deputy chief physician of Fuzhou Second Hospital Affiliated to Xiamen University.And since 2016, he is the Director of the Department of Rehabilitation Medicine. His research interests include rehabilitation of orthopaedic diseases.

Jie Liang received his master degree in clinical medicine from Fujian University of Traditional Chinese Medicine in 2010. Now he is the attending physician at Fuzhou Second Hospital Affiliated to Xiamen University. His research interests include rehabilitation of orthopaedic diseases.

Min Du received her Ph.D. in electrical engineering from Fuzhou University in 2005. Now she is a professor and doctorial supervisor at Fuzhou University. And since 2007, she is the associate director of Fujian Key Laboratory of Medical Instrumentation & Pharmaceutical Technology. Her research interests include smart instrument and photoelectrical system.