Multilayer neural network controller for a class of nonlinear systems

A family of novel multilayer discrete-time neural net (NN) controller is presented for the control of a class of multi-input multi-output (MIMO) dynamical systems. The NN controller includes modified delta rule weight tuning and exhibits a learning-while-functioning-features instead of learning-then-control so that control action is immediate with no explicit learning phase needed. The structure of the neural net controller is derived using a filtered error/passivity approach. Linearity in the parameters is not required and certainty equivalence is not used, which overcomes several limitations in adaptive control. For guaranteed stability, the upper bound on the constant learning rate parameter for the developed weight tuning mechanisms is shown to decrease with the number of hidden-layer neurons so that learning must slow down; this a major draw back often documented in the literature. This major draw back is shown to be overcome easily by using a projection algorithm at each layer. The notion of persistency of excitation (PE) for multilayer NN is explored. An extension of these weight tuning updates to NN with an arbitrary number of hidden layers is discussed. The notions of discrete-time passive NN and dissipative NN is introduced. Though the original system may not have any sort of passivity properties or it may be extremely difficult to demonstrate the passivity properties, the NN makes the closed-loop system passive. Simulation results show the theoretical conclusions