Parameter sensitivities of a neuro-based adaptive controller with guaranteed stability
M B Menhaj, Swakshar Ray · 2004
This paper provides a detailed analysis and study on the parameter sensitivities and domain of attraction of the novel neuro-based adaptive controller based on the previously published paper. The special learning algorithm similar to back propagation provides better stability and wide domain of attraction for the controller provided that the neural network parameters are chosen carefully. The controller acts as a direct adaptive controller and the weight and bias matrices are updated online without any prier offline training. It is easy to implement in real time due to less complexity in terms of absence of several neural networks and robustness terms. This paper reveals the domain of attraction based on different parameter values and the sensitivities of the error surface with respect to designed parameters. We have tested the controller on a two link robot arm system and extensive simulation results show the dependence and effectiveness of the controller with respect to parameters of the designed neural network. This gives a better insight of the controller that has been investigated with systems of the form x=f(x)+u+w and x=f(x)+g(x)u(t)+w. The theoretical proof on the stability of the closed loop nonlinear systems with the adaptive controller has been investigated in detail in this paper. The paper also summarizes the potential advantages, disadvantages, prospective developments and real life applicability of the controller scheme at the end.