Orthonormal activation function-based neural networks for adaptive control of nonlinear systems

An orthonormal activation function based neural network (OAFNN) architecture is developed with the objective of its application in direct adaptive control of unknown, nonlinear dynamic systems. The activation function for the proposed OAFNNs can be any orthonormal function, permitting flexibility in their choice. The orthonormal activation functions have attractive properties for adaptive control of non-linear systems, as shown in this research. These properties include absence of local minima and fast parameter convergence. The single epoch learning capability of the Harmonic and Legendre Polynomial based OAFNNs is demonstrated.; Five direct adaptive control schemes were developed using proposed OAFNNs, for trajectory tracking control of a class of nonlinear systems. The OAFNNs were employed in these controllers for feed-forward compensation of unknown system dynamics. The network weights were tuned on-line, in real time. The weight adaptation laws were determined using Lyapunov analysis.; Two types of controllers, actual compensation adaptive law (ACAL) controllers and desired compensation adaptive law (DCAL) controllers were developed. In DCAL controllers the activation functions of OAFNNs can be computed off-line and stored for later on-line implementation reducing significantly the on-line computational load especially when the network sizes grow large. Multiple OAFNNs were employed in the controller structure so as to keep the number of inputs per network as small as possible which helps in keeping the network size(s) as small as possible. Full state feedback as well as partial state feedback controllers were developed. The overall stability of all the controllers was theoretically proved using Lyapunov analysis.; The developed neuro-controllers were evaluated using simulations as well as experiments. A cast iron disk mounted on a motor drive and subjected to a physical static-dynamic friction load was used as a test bed for the experimental evaluation. The simulation and experimental results demonstrated the trajectory tracking capability of all controllers for an unknown system. The analysis further showed that the OAFNNs in these controllers were able to model the friction characteristic with a remarkably close accuracy including the slip-stick friction characteristic. The effect of the number of neurons on modeling accuracy of the OAFNNs as well as on trajectory tracking error of the controllers was studied and is discussed. The theoretical developments and the experimental results show that the OAFNNs have the appropriate architecture and activation functions for real time adaptive neural control systems.