_applied_  
_sciences_  
_Article_  
**Model-Assisted Reduced-Order ESO Based Command Filtered Tracking Control of Flexible-Joint Manipulators with Matched and Mismatched Disturbances**  
[PERSON] 12,*\(\copyright\), [PERSON] 1, [PERSON] 3, [PERSON] 1, [PERSON] 1 and [PERSON] 1  
1 School of Information and Electrical Engineering, Hunan University of Science and Technology, Xiangtan 411201, China 2 School of Automation, Guangdong University of Petrochemical Technology, Maoming 525000, China 3 Department of Mathematics, Guangdong University of Petrochemical Technology, Maoming 525000, China Correspondence: [EMAIL_ADDRESS]  
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uncertainties with a high precision control has attracted great attentions in both control theory and engineering community. In the past decades, many effective control methods have been proposed for the control of FJMs, e.g., fuzzy control [9; 10], singular perturbation control [11; 12; 13], feedback linearization control [14; 15], backstepping control [16; 17; 18; 19], etc. Among them, the backstepping control is a Lyapunov function-based recursive design method, which constructs control Lyapunov functions step by step and designs intermediate virtual control laws recursively until the actual control law is reached. However, it suffers from the drawback of \"explosion of complexity\", that is, the derivatives of virtual control laws designed in the procedures need to be computed repeatedly. To solve this problem, a dynamic surface control (DSC) was proposed in Ref. [20], where a first-order low-pass filter was introduced in each step to obtain the derivative of the virtual control law instead of taking the derivative directly. Based on the DSC technique, several adaptive control schemes [21; 22; 23] were proposed for the single-link FJMs with unknown nonlinearities, and a DSC backstepping-based impedance controller was designed in Ref. [24] for a 5-DOF flexible joint robot. However, these results do not consider the potential errors caused by the filters. Furthermore, the derivatives of virtual control laws in DSC are actually approximated through numerical differentiations, which may amplify the noise and reduce the control accuracy. To avoid numerical differentiations, a second-order command filtered backstepping (SCFB) method was proposed in Refs. [25; 26]. It obtains the derivatives of the virtual control laws through integrations instead of differentiations, which can not only avoid the problem of \"explosion of complexity\", but also simplify the controller design. With the SCFB technique, an adaptive neural tracking controller was designed in Ref. [27] for uncertain robotic manipulators, and an adaptive fuzzy controller was proposed in Ref. [28] for a two-link robotic manipulator. Furthermore, regarding the filtering errors produced by command filters, two improved SCFB controllers were designed in Refs. [29; 30] for FJM systems, where two error compensation mechanisms were constructed to reduce the filtering errors. Unfortunately, most of the above mentioned methods do not consider the practical uncertainties that may exist in the control of FJMs. To cope with uncertainties, intelligent control methods including neural networks (NNs) and fuzzy logic systems (FLSs), which are well-known for their universal approximation abilities, have been widely utilized for uncertain FJMs. For example, the uncertain model of FJMs was approximated by a Radial Basis Function (RBF) neural network in Ref. [31], on the basis of which an adaptive observer and DSC controller were developed. Similarly, an FLS was employed in Ref. [32] to approximate the unknown functions, and an adaptive fuzzy tracking controller was designed. However, both the NNs and the FLSs require complex online learning mechanisms, which are computationally expensive. Sliding mode control, which is famous for its insensitivity to uncertainties, has also been applied in the control of FJMs [33; 34; 35; 36], but the phenomenon of chattering cannot be avoided.