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Harib et al. Intell Robot 2022;2(1):37-71  https://dx.doi.org/10.20517/ir.2021.19       Page 51

               Table 3. Different adaptive NN-based controls in the recent years
                Research                 Method/approach            Solved problem
                1. Nonaffine nonlinear systems
                     [73]
                Dai et al.  Obtaining the implicit desired control input (IDCI), and use of   Learning from adaptive NN-based control for a class of
                            NNs to approximate it                   nonaffine nonlinear systems in uncertain dynamic
                                                                    environments
                      [74]
                Chen et al.  The unknown functions are approximated by using the   Adaptive fuzzy-NN (FNN) for a class of nonlinear
                            property of the fuzzy-neural control    stochastic systems with unknown functions and a nonaffine
                                                                    pure-feedback form
                2. Tracking control
                     [75]
                Dai et al.  Radial basis function NNs (RBF-NNs) to learn the unknown   Stabilization of the tracking control problem of a marine
                            dynamics, and adaptive neural control to guarantee the   surface vessel with unknown dynamics
                            ultimate boundedness (UB)
                Li et al. [76]  NNs to approximate the unknown functions, and Barrier   Adaptive tracking control for a category of SISO stochastic
                            Lyapunov function (BLF) for nonstrict-feedback stochastic   nonlinear systems with dead zone and output constraint
                            nonlinear system
                       [77]
                Cheng et al.  Use of NN-based inversion-free controller, and construction of  Displacement tracking control of piezo-electric actuators
                            dynamic model using feedforward MLNs    (PEAs)
                Ren et al. [78]  Use of adaptive neural control, and inclusion of σ-modification  Tracking control problem of unknown nonlinear systems in
                            to the adaptation law to establish stability  pure-feedback form with the generalized P-I hysteresis
                                                                    input
                3. Unknown model/direction
                Luo et al. [79]  Implementing three NNs to approximate the value function,   Date-driven H  control for nonlinear distributed parameter
                                                                             ∞
                            control and disturbance policies, respectively  systems with a completely unknown model
                Liu et al. [80]  Two types of BLFs are used to design the controller and   Stabilize a class of nonlinear systems with the full state
                            analyze the stability                   constraints and the unknown control direction
                4. Backstepping design
                    [81]
                Li et al.   Adaptive backstepping control and RBF-NNs.  Overcoming the robustness issues of backstepping design
                                                                    and its uncertainty.
                5. Discrete-time systems
                       [82]
                Zhang et al.  Iterative adaptive dynamic programming algorithm, with two   Solving the optimal control problem for discrete-time
                            NNs to approximate the costate function and the   systems with control constraints
                            corresponding control law
               NNs: Neural Networks.


               In 1991, Lin and Kim integrated the CMAC into the self-learning control scheme that was based on the
               work of Lin and Kim . The CMAC model was originally proposed by Albus [89-92]  and it was based on
                                  [88]
               models of human memory and neuromuscular control. The CMAC-based technique in the work of Lin and
                   [88]
               Kim  is tested using the inverted pendulum problem, and the results are compared to those of
               Barto et al.  and Anderson . The technique has the highest learning speed due to its capability of
                        [83]
                                       [87]
               generalization and good learning behavior. Furthermore, the memory size can be reduced compared to the
               box-based system. A summarized timeline of the above literature, where NN-based control was
               implemented to balance the inverted pendulum, is presented in Figure 5.


               Many control laws for inverted pendulums have been presented in those research work [93-95] , including
               classical, robust, and adaptive control laws, but they all take structured parametric uncertainty into account.
               In 2009, Chaoui et al.  proposed an ANN based adaptive control strategy for inverted pendulums that
                                  [96]
               accomplishes asymptotic motion tracking and posture control with unknown dynamics. Two neural
               networks ANN  and ANN  are designed to control the motion along the x axis and the pendulum posture
                            x
                                      θ
               with unknown dynamics. Figure 6 shows the block diagram of the proposed system.

               Three experiments are carried out to evaluate the performance of the proposed controller. The velocity and
               posture of the pendulum progressively decrease to zero in the first experiment. The proposed adaptive
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