Research ArticleDiagonal recurrent neural network based adaptive control of nonlinear dynamical systems using lyapunov stability criterion

- DRNN is successfully applied to control non linear dynamical systems (both SISO and MIMO systems).
- Lyapunov stability criterion is used to derive weight update rule.
- Learning ability of DRNN is tested and compared with MLFFNN and FCRNN.
- Robustness of DRNN, FCRNN and MLFFNN is tested and compared. Both parameter variations and disturbance signal impact are considered.
- Structure of DRNN is compared with MLFFNN and FCRNN in terms of dynamical behavior and count of weights.

In this paper adaptive control of nonlinear dynamical systems using diagonal recurrent neural network (DRNN) is proposed. The structure of DRNN is a modification of fully connected recurrent neural network (FCRNN). Presence of self-recurrent neurons in the hidden layer of DRNN gives it an ability to capture the dynamic behaviour of the nonlinear plant under consideration (to be controlled). To ensure stability, update rules are developed using lyapunov stability criterion. These rules are then used for adjusting the various parameters of DRNN. The responses of plants obtained with DRNN are compared with those obtained when multi-layer feed forward neural network (MLFFNN) is used as a controller. Also, in example 4, FCRNN is also investigated and compared with DRNN and MLFFNN. Robustness of the proposed control scheme is also tested against parameter variations and disturbance signals. Four simulation examples including one-link robotic manipulator and inverted pendulum are considered on which the proposed controller is applied. The results so obtained show the superiority of DRNN over MLFFNN as a controller.