Fuzzy Sets and Systems 179 (2011) 34 – 49 www.elsevier.com/locate/fss Adaptive fuzzy terminal sliding mode control for a class of MIMO uncertain nonlinear systems V. Nekoukar, A. Erfanian ∗ Neuromuscular Control Systems Laboratory, Iran Neural Technology Research Centre, Department of Biomedical Engineering, Iran University of Science and Technology (IUST), Tehran, Iran Received 24 July 2010; received in revised form 27 February 2011; accepted 12 May 2011 Available online 23 May 2011 Abstract This paper presents a new adaptive terminal sliding mode tracking control design for a class of nonlinear systems using fuzzy logic system. The terminal sliding mode control (TSM) was developed to provide faster convergence and higher-precision control than the linear hyperplane-based sliding control. However, the original TSM encountered singularity problem with discontinuous control action. Moreover, a prior knowledge about the plant to be controlled is required. The proposed controller combines a continuous non-singular TSM with an adaptive learning algorithm and fuzzy logic system to estimate the dynamics of the controlled plant so that closed-loop stability and finite-time convergence of tracking errors can be guaranteed. The performance of the proposed control strategy is evaluated through the control of a two-link rigid robotic manipulator. Finally, the effectiveness of the proposed scheme is demonstrated through the control of the ankle and knee movements in paraplegic subjects using functional electrical stimulation. Simulation and experimental results verify that the proposed control strategy can achieve favorable control performance with regard to system parameter variations and external disturbances. © 2011 Elsevier B.V. All rights reserved. Keywords: Adaptive fuzzy control; Terminal sliding mode; Time-varying; Functional electrical stimulation; Fuzzy system models 1. Introduction A useful and effective control scheme to deal with uncertainties, time varying properties, nonlinearities and bounded externals disturbances is the sliding mode control (SMC) [1,2]. The first step in the sliding mode control design is to choose a switching manifold, so that the state variables restricted to the manifold have a desired dynamics. However, conventional switching manifolds are usually linear hyperplanes which guarantee the asymptotic stability; therefore, error dynamics cannot converge to zero in finite time. The sliding mode parameters can be adjusted to get faster error convergence, however, this will, in turn, increase the control gain, which may cause severe chattering on the sliding surface and, therefore, deteriorate the system performance. To tackle the problems of globally asymptotic stabilization, terminal sliding mode (TSM) control scheme has been developed [3–5] to achieve finite-time stabilization. Different aspects of the conventional TMS control design were investigated in the literature [3–11] including singularity and chattering problems and requirement of prior knowledge about the dynamics of the process to be controlled. In order to solve the singularity problem of the initial TSM controller, several methods have been proposed. Zhihong and Yu [4] ∗ Corresponding author. Tel.: +98 21 77240465; fax: +98 21 77240490. E-mail addresses: nekoukar@iust.ac.ir (V. Nekoukar), erfanian@iust.ac.ir (A. Erfanian). 0165-0114/$-see front matter © 2011 Elsevier B.V. All rights reserved. doi:10.1016/j.fss.2011.05.009