Abstract
ABSTRACTIn this paper, in order to achieve the best tracking control of a class of multi-input multi-output (MIMO) nonlinear systems with unknown dynamics and unknown disturbances, a new robust adaptive interval type-2 fuzzy sliding mode control law (AIT2-FSMCL) has been proposed. Based on developing interval type-2 fuzzy local models for some operating points of the controlled system, an interval type-2 fuzzy logic system (IT2-FLS) has been designed to better estimate the unknown nonlinear dynamics of the studied system. Then, to enhance the tracking control performance and ensure the system robustness in the presence of approximation errors, parameter variations, un-modelled dynamics and external disturbances, a new AIT2-fuzzy sliding mode system (AIT2-FSMS), has been introduced. In order to avoid the chattering phenomenon while keeping the system performance, the AIT2-FSMS uses three AIT2-fuzzy logic systems (AIT2-FLSs) to estimate the optimal gains of the AIT2-FSMCL. The adaptation laws have been derived using the Lyapunov stability approach. The mathematical proof shows that the closed-loop system with the proposed control approach is globally asymptotically stable. Finally, the proposed design method is applied to a two-link robot arm to validate the effectiveness of the proposed control approach.
Highlights
Control algorithms can hardly deal with multi-input multi-output (MIMO) uncertain nonlinear systems
Compared to the existing works in the literature, the main contributions of the present study are listed as follows: (1) A new robust adaptive interval type-2 fuzzy sliding mode control law (AIT2-FSMCL) is proposed for a large class of MIMO nonlinear systems to deal with the tracking control problem, with the following considerations are taken into account:
Theorem 2: For the MIMO nonlinear system (7), with the interval type-2 fuzzy logic system (IT2-fuzzy logic systems (FLSs)) defined in (9), the AIT2-FLSs proposed in (20) and the adaptive laws expressed by Equation (23), the designed AIT2-FSMCL (22) is smooth and globally stable in closed-loop system with the tracking error converges asymptotically to zero, despite unknown dynamics and unknown disturbances that affect the system (7), including un-modeled dynamics, parametric variations and unknown external disturbances
Summary
Control algorithms can hardly deal with multi-input multi-output (MIMO) uncertain nonlinear systems To cope with this problem of control, several robust approaches have been proposed. For nonlinear perturbed complex systems with uncertainties, FLSs cannot guarantee the global stability of the closed-loop system [10] To overcome this problem, many researchers have tried to combine FLSs with other advanced robust methods to achieve good performance, such as SMC, adaptive control, H∞ technique and neural network [11,12,13,14,15,16]. (1) A new robust adaptive interval type-2 fuzzy sliding mode control law (AIT2-FSMCL) is proposed for a large class of MIMO nonlinear systems to deal with the tracking control problem, with the following considerations are taken into account: All dynamics are entirely unknown and suffer from time varying disturbances.
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