Stabilization of adaptive neural network controllers for nonlinear structural systems using a singular perturbation approach

Generally, the biggest difficulty when designing a neural network controller that will be capable of rapidly and efficiently controlling complex and nonlinear systems is selection of the most appropriate initial values for the parameter vector. Overcoming the coupling effects of each degree-of-freedom is also difficult in multi-variable system control. In this study, an intelligent adaptive controller is proposed to handle these behaviors. First of all, an uncertain and nonlinear plant, for the tracking of a reference trajectory, is well approximated via radial basis function networks. Next, the adjustable parameters of the intelligent system are initialized using a genetic algorithm. Then, novel online parameter tuning algorithms are developed, based on the Lyapunov stability theory. A boundary-layer function is introduced into these updating laws to cover parameter and modeling errors, and to guarantee that the state errors converge to within a specified error bound. The non-square multi-variable system can be decoupled into several reduced-order isolated square multi-variable subsystems using a singular perturbation scheme for different types of time-scale stability analysis. Following this, a decoupled adaptive neural network controller is derived simultaneously to stabilize and control the system. Finally, an example, in the form of a numerical simulation, is provided to demonstrate the effectiveness of the control methodology, which is shown to rapidly and efficiently control nonlinear multi-variable systems.