A recurrent neural-network-based real-time learning control strategy applying to nonlinear systems with unknown dynamics

In this paper, the authors present a real-time learning control scheme for unknown nonlinear dynamical systems using recurrent neural networks (RNNs). Two RNNs, based on the same network architecture, are utilized in the learning control system. One is used to approximate the nonlinear system, and the other is used to mimic the desired system response output. The learning rule is achieved by combining the two RNNs to form the neural network control system. A generalized real-time iterative learning algorithm is developed and used to train the RNNs. The algorithm is derived by means of two-dimensional (2-D) system theory that is different from the conventional algorithms that employ the steepest optimization to minimize a cost function. This paper shows that an RNN using the real-time iterative learning algorithm can approximate any trajectory tracking to a very high degree of accuracy. The proposed learning control scheme is applied to numerical problems, and simulation results are included. The results are very promising, and this paper suggests that the 2-D system theory-based RNN learning algorithm provides a new dimension in real-time neural control systems.