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EN
In this paper, we are dealing with the problem of directly regulating unknown multivariable affine in the control nonlinear systems and its robustness analysis. The method employs a new Neuro-Fuzzy Dynamical System definition, which uses the concept of Fuzzy Systems (FS) operating in conjunction with High Order Neural Networks. In this way the unknown plant is modeled by a fuzzy - recurrent high order neural network structure (F-RHONN), which is of the known structure considering the neglected nonlinearities. The development is combined with a sensitivity analysis of the closed loop in the presence of modeling imperfections and provides a comprehensive and rigorous analysis showing that our adaptive regulator can guarantee the convergence of states to zero or at least uniform ultimate boundedness of all signals in the closed loop when a not-necessarily-known modeling error is applied. The existence and boundedness of the control signal is always assured by employing a method of parameter “Hopping” and “Modified Hopping”, which appears in the weight updating laws. Simulations illustrate the potency of the method showing that by following the proposed procedure one can obtain asymptotic regulation despite the presence of modeling errors. Comparisons are also made to simple recurrent high order neural network (RHONN) controllers, showing that our approach is superior to the case of simple RHONN’s.
EN
It is very common that manipulators are subject to structured and/or unstructured uncertainties. Structural uncertainty is characterised by having a correct dynamical model but with parameter uncertainty due to imprecision of the manipulator link properties, unknown loads, inaccuracies in the torque constants of the actuators, and so on. Unstructured uncertainty is characterised by unmodelled dynamics. Neural Network (NN) controllers are usually introduced to generate additional inputs to compensate for disturbances due to model uncertainties. It is clear that the higher the degree of nonlinearity exists in the uncertainties, the greater benefits neural networks (NNs) can contribute. In Cartesian space control, more robust control is required due to the following problems: (i) the inverse dynamic in Cartesian space is more complicated than that in joint space; (ii) the singularity of Jacobian (J) becomes problem at hand when positions in Cartesian space are calculated from joint measurements; - more uncertainties are present. In this paper, we examine some of these issues by studying the Cartesian space robot manipulator control problem. Although NN compensation for model uncertainties has been traditionally carried out by modifying the joint torque/force of the robot, it is also possible to achieve the same objective by using the NN to modify the reference Cartesian trajectory. We present four different NN controller designs to achieve disturbance rejection for an uncertain system.
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