This article has been accepted for inclusion in a future issue of this journal. Content is final as presented, with the exception of pagination. IEEE TRANSACTIONS ON SYSTEMS, MAN, AND CYBERNETICS: SYSTEMS 1 Fuzzy Tracking Control for a Class of Uncertain MIMO Nonlinear Systems With State Constraints Wei He, Senior Member, IEEE, Linghuan Kong, Yiting Dong, Student Member, IEEE, Yao Yu, Chenguang Yang, Senior Member, IEEE, and Changyin Sun Abstract—In this paper, an adaptive fuzzy neural network (FNN) control scheme is developed for a class of multiple- input and multiple-output (MIMO) nonlinear systems subject to unknown dynamics and state constraints. FNNs are used to approximate the unknown dynamics that comprises the effects of uncertain parameters and functions. Also, integral Lyapunov functions are introduced to address state constraints. A neural- network-based observer is designed to estimate the unmeasurable states. With state-feedback and output feedback tracking control, the stability of closed-loop system is guaranteed via Lyapunov’s stability theory. Two cases of simulations for MIMO systems with state constraints are conducted to verify the effectiveness of the proposed control. Index Terms—Adaptive control, fuzzy control, multiple-input and multiple-output (MIMO) nonlinear systems, state con- straints. I. I NTRODUCTION I N REAL life, multiple-input and multiple-output (MIMO) nonlinear systems widely exist in some fields such as Manuscript received December 31, 2016; revised March 26, 2017 and July 2, 2017; accepted August 18, 2017. This work was supported in part by the National Natural Science Foundation of China under Grant 61522302 and Grant 61761130080, in part by the National Basic Research Program of China (973 Program) under Grant 2014CB744206, in part by the Newton Advanced Fellowship from the Royal Society, U.K., under Grant NA160436, in part by the Beijing Natural Science Foundation under Grant 4172041, and in part by the Fundamental Research Funds for the China Central Universities of USTB under Grant FRF-BD-16-005A and Grant FRF-TP-15-005C1. This paper was recommended by Associate Editor Y.-J. Liu. (Corresponding author: Wei He.) W. He is with the School of Automation and Electrical Engineering, University of Science and Technology Beijing, Beijing 100083, China, and also with the Key Laboratory of Knowledge Automation for Industrial Processes, Ministry of Education, University of Science and Technology Beijing, Beijing 100083, China (e-mail: weihe@ieee.org). L. Kong is with the School of Automation Engineering and Center for Robotics, University of Electronic Science and Technology of China, Chengdu 611731, China. Y. Dong is with the Department of Mechanical Engineering, Texas Tech University, Lubbock, TX 79409 USA. Y. Yu is with the School of Automation and Electrical Engineering, University of Science and Technology Beijing, Beijing 100083, China. C. Yang is with the Key Laboratory of Autonomous Systems and Networked Control, College of Automation Science and Engineering, South China University of Technology, Guangzhou 510640, China. C. Sun is with the School of Automation, Southeast University, Nanjing 210096, China. Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TSMC.2017.2749124 robot [1], [85], thermography imaging system [2], [3] etc. The control design of MIMO systems is more complicated and complex than that of single-input and single-output sys- tems because of unknown parameters and functions. In order to make better use of MIMO systems, uncertain dynamic functions need to be worked out, otherwise it can seri- ously restrict system performances and perhaps result in instability. In recent years, to obtain the accurate control of MIMO systems such that considered systems can track reference trajectories, many researches have tried fuzzy con- trol [4]–[14], neural network (NN) control [15]–[19], adap- tive control [20]–[36], machine learning control [37]–[39], nonlinear model predictive control [40], boundary con- trol [41]–[44], vibration control [45], [46], and sliding mode control [47]. Another important issue about nonlinear system control is existing unmeasurable states and this challenge makes the model-based control impossible. Therefore, it is obviously important that a feasible observer is designed to estimate the unknown states [48], [49]. In [50], an output position feedback controller of the electro-hydraulic system is pro- posed based on an extended-state-observer with backstepping. In [51], a disturbance observer is designed for a nonlinear transport aircraft model. In [52] and [53], fault detection schemes are introduced to measure the unknown states more accurately. Due to the ability of approximating nonlinear functions, neural networks (NNs) are employed to approximate the unknown dynamics [54]–[62]. In [63], an adaptive NN scheme has been employed for teleoperation of a robot system. In [64], the NN approximation technique is employed to compensate for uncertainties. In [65], adaptive control using radial basis function NNs is developed to compensate for the effect caused by the internal and external uncertainties. In [66], adaptive neural control is proposed for nonlinear MIMO systems in interconnected form. In [67], adaptive impedance control is developed for an n-link robotic manipu- lator with input saturation by employing NNs. Qiao et al. [68] provided a theoretical foundation for applications includ- ing the high-precision manipulation with low-precision sys- tem. A new concept called nonlinear measure is intro- duced to quantify stability of nonlinear systems in the way similar to the matrix measure for stability of linear systems in [69]. 2168-2216 c  2017 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications_standards/publications/rights/index.html for more information.