On a nonlinear multivariable servomechanism problem
Automatica (Journal of IFAC)
Accuracy and Stability of Numerical Algorithms
Accuracy and Stability of Numerical Algorithms
Neural network enhanced output regulation in nonlinear systems
Automatica (Journal of IFAC)
A neural network-based approximation method for discrete-time nonlinear servomechanism problem
IEEE Transactions on Neural Networks
ACC'09 Proceedings of the 2009 conference on American Control Conference
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A numerical method to solve the so-called regulator equation is presented here. This equation consists of partial differential equations combined with algebraic ones and arises when solving the output-regulation problem. Solving the regulator equation is becoming difficult especially for the nonminimum phase systems where reducing variables against algebraic part leads to a potentially unsolvable differential part. The proposed numerical method is based on the successive approximation of the differential part of the regulator equation by the finite-element method while trying to minimize a functional expressing the error of its algebraical part. The method is analyzed to obtain theoretical estimates of its convergence and it is tested on an example of the ''two-carts with an inverted pendulum'' system. Simulations are included to illustrate the suggested approach.