Identification of a class of nonlinear dynamical systems using multilayer neural networks

A novel multilayer discrete-time neural net (NN) paradigm is presented for the identification of a class of multi-input multi-output (MIMO) nonlinear dynamical systems. The major novelty of this approach is a rigorous proof of identification error convergence that reveals a requirement for a new identifier structure and nonstandard weight tuning algorithms under the assumption that the states of the plant are available for measurement. The NN identifier includes delta rule weight tuning and exhibits a learning-while-functioning-features instead of learning-then-functioning so that the identification is immediate with no explicit off-line learning phase needed. The structure of the neural net identifier is derived using a passivity approach. Linearity in the parameters is not required and certainty equivalence is not used. This overcomes several limitations of standard adaptive control. The notion of persistency of excitation (PE) for multilayer NN is explored. The notions of discrete-time passive NN are introduced. This new NN passivity property is employed to demonstrate the boundedness of weight estimates. Simulation studies indicate that the theoretical claims are justified