Approximation capabilities of multilayer feedforward networks
Neural Networks
Nonlinear control of underactuated mechanical systems with application to robotics and aerospace vehicles
Adaptive fuzzy control for a class of uncertain nonaffine nonlinear systems
Information Sciences: an International Journal
Brief paper: Decentralized control design of interconnected chains of integrators: A case study
Automatica (Journal of IFAC)
A DSC approach to robust adaptive NN tracking control for strict-feedback nonlinear systems
IEEE Transactions on Systems, Man, and Cybernetics, Part B: Cybernetics - Special issue on game theory
Adaptive fuzzy robust tracking controller design via small gain approach and its application
IEEE Transactions on Fuzzy Systems
Swinging up the spherical pendulum via stabilization of its first integrals
Automatica (Journal of IFAC)
A neural-network method for the nonlinear servomechanism problem
IEEE Transactions on Neural Networks
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The spherical inverted pendulum is a two-input, two-output non-minimum phase nonlinear system. Recently, the output regulation problem of the spherical inverted pendulum was studied in [21]. It is known that the solvability of the output regulation problem depends on the solvability of the regulator equations which are a set of nonlinear partial differential equations. Since the exact solution of the regulator equations associated with the spherical inverted pendulum is not available due to the complexity of the equations, the paper [21] tried a polynomial approximation of the solution of the regulator equations. In this paper, we first show that the solution of the regulator equations associated with the spherical inverted pendulum exist and then find an approximate solution to the output regulation problem of the spherical inverted pendulum via a neural network approximation approach. We also make some comparison between the method in this paper and the method in [21].