Adaptive control of limit cycle for unknown nonlinear hysteretic system using dynamic recurrent RBF networks

This paper reports the design of an online, dynamic, self-adjusting, neural network control methodology that will allow the neuron to add/drop to an optimum size during the identification of an unknown nonlinear hysteretic system responsible for the generation of limit cycle. Simultaneously, the identified model is used in the design of an adaptive control to suppress the limit cycle oscillation. Hysteresis is difficult to model or identify. The ensemble average concept based on the properties of the Preisach hysteresis model is used in the design of the neural networks during the network training phase. The radial basis function (RBF) networks employ two separate adaptation schemes where RBF´s centers and width are adjusted by an extended Kalman filter, while the outer layer weights are updated using Lyapunov stability analysis to ensure the stable closed loop control. The effectiveness of the proposed dynamic neural control methodology is demonstrated through simulations to suppress the wing rock in the AFTI/F-16 test-bed aircraft having delta wing configuration.