Deterministic learning-based neural network control with adaptive phase compensation

Under the persistent excitation (PE) condition, the real dynamics of the nonlinear system can be obtained through the deterministic learning-based radial basis function neural network (RBFNN) control. However, in this scheme, the learning speed and accuracy are limited by the tradeoff between the PE levels and the approximation capabilities of the neural network (NN). Inspired by the frequency domain phase compensation of linear time-invariant (LTI) systems, this paper presents an adaptive phase compensator employing the pure time delay to improve the performance of the deterministic learningbased adaptive feedforward control with the reference input known a priori. When the adaptive phase compensation is applied to the hidden layer of the RBFNN, the nonlinear approximation capability of the RBFNN is effectively improved such that both the learning performance (learning speed and accuracy) and the control performance of the deterministic learning-based control scheme are improved. Theoretical analysis is conducted to prove the stability of the proposed learning control scheme for a class of systems which are affine in the control. Simulation studies demonstrate the effectiveness of the proposed phase compensation method.