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Abstract: In this paper, an adaptive neural network algorithm is developed for a class of interconnected nonlinear systems. Neural networks (NNs) are used to approximate the unknown nonlinear functions and interconnections in the subsystems. A systematic approach is established to synthesize the adaptive NN learning control scheme that ensures the boundedness of all the signals in the closed-loop system. The effectiveness of the proposed scheme is demonstrated by computer simulations. [Copyright &y& Elsevier]

Abstract: In this article, an adaptive neural network algorithm is developed for control issue of rigid-link electrically-driven (RLED) robot systems. First, an virtual control algorithm is designed to deal with the mechanical dynamics. Next, an actual neural network controller is used to handle the uncertainty in the mechanical and electrical dynamics. The stability is guaranteed by using a rigid stability proof. Finally, a simulation is given to show the effectiveness of the proposed algorithm. [Copyright &y& Elsevier]

Abstract: This paper presents extended results for geometrical error compensation and control, addressing several issues beyond the approach in Tan, Huang, and Seet (2000) (IEEE Transactions on Instrumentation and Measurement, 49, 984–991). It is a key objective to attain more efficient compensation performance with less or comparable memory using this approach. Three new features are associated with this proposed approach. Firstly, the geometrical error of an industrial XY table is considered and modeled in the overall control structure. Secondly, multilayer NNs are used to approximate the components of geometrical errors, resulting in a significantly less number of neurons compared to the use of radial basis functions (RBFs). Thirdly, the direction of motion is considered in the compensator in details, i.e., a separate compensator is used when compensating for motion in the forward and reverse direction. This is important as the geometrical errors can be quite distinct depending on the direction of motion due to backlash and other nonlinearities in the servo systems. The overall geometrical error is computed from these NNs based on a kinetic equation for the machine in point. Finally, the stability issue when considering the overall control system with the geometrical error compensation is discussed. Full results on the application of the proposed method to an XY table are presented, and the evaluation tests show that the overall geometrical errors can be reduced to about from . [Copyright &y& Elsevier]

Abstract: This paper designs a decentralized neural network (NN) controller for a class of nonlinear large-scale systems, in which strong interconnections are involved. NNs are used to handle unknown functions. The proposed scheme is proved guaranteeing the boundedness of the closed-loop subsystems using only local feedback signals. [Copyright &y& Elsevier]

In this paper, we develop an algorithm (hereby referred to as the S-function generator: SFG) for the automatic generation of dynamic S-function blocks which can be used for geometrical error compensation of precision machines. The function block is composed of neural network approximations of the geometrical errors of the machines which will serve as the basis for error compensation. It is generated automatically based on only raw calibration data obtained from a laser interferometer and simple user specifications in terms of approximation accuracy requirements. No coding is necessary on the part of the user. This tremendously simplifies the use of the functional error compensation approach which has clear advantages over a traditional look-up table approach. The SFG has been applied to the compensation of two XY tables and the evaluation tests show that the overall geometrical errors can be significantly reduced. [Copyright &y& Elsevier]

Presents a decentralized neural-network controller for a class of large-scale nonlinear systems with the high-order interconnections. Investigation of the decentralized stabilization problem for interconnected systems; Class of large-scale nonlinear systems; Controller structure of local subsystems.

Develops an adaptive compensation technique for a friction model using neural network approximations. Utilization of PD control structure and friction force estimation; Incorporation of Radial Basis Function to compensate the effect of Stribeck parameter in friction model; Account on the Lyapunov theory of compensator stability.

Abstract: In Kim et al. [(1997) A dynamic recurrent neural-network-based adaptive observer for a class of nonlinear systems. Automatica 33(8), 1539–1543], authors present an excellent neural network (NN) observer for a class of nonlinear systems. However, the output error equation in their paper is strictly positive real (SPR) which is restrictive assumption for nonlinear systems. In this note, by introducing a vector and Lyapunov equation, the observer design is obtained without requiring the SPR condition. Thus, our observer can be applied to a wider class of systems. [Copyright &y& Elsevier]

Abstract: The convergence of Xu''s LMSER algorithm with a constant learning rate, which is in the one unit case, is interpreted by analyzing an associated deterministic discrete time (DDT) system. Some convergent results relating to the Xu''s DDT system are obtained. An invariant set and an ultimate bound are identified so that the non-divergence of the system can be guaranteed. It is rigorously proven that all trajectories of the system from points in this invariant set will converge exponentially to a unit eigenvector associated with the largest eigenvalue of the correlation matrix. By comparing Xu''s algorithm with Oja''s algorithm, it can be observed, on the whole, the Xu''s algorithm evolves faster at a cost of larger computational complexity. Extensive simulations will be carried out to illustrate the theory. [Copyright &y& Elsevier]