Guaranteed performance for an approximation method for discrete-time nonlinear servomechanism problem

The solvability of the discrete-time nonlinear servomechanism problem relies on the solution of a set of nonlinear functional equations known as the discrete regulator equations. The exact solution of the discrete regulator equations is usually unavailable due to the nonlinearity of the system. This paper considers the problem of approximate solution of the discrete regulator equation using a feedforward neural network. It is shown that the discrete regulator equations can be approximately solved up to an arbitrarily small error by the feedforward neural networks. As a result, it is possible to design a feedback controller based on the neural network solution of the discrete regulator equations that solves the discrete nonlinear servomechanism problem approximately.