On neural networks application in integral sliding mode control

In this paper, the combined use of deep neural networks (DNNs) and integral sliding mode (ISM) control is investigated, giving rise to novel DNN-ISM control strategies for nonlinear systems affine in the control law, characterized by fully unknown dynamics and subject to disturbances. In particular, two feed-forward DNNs are used to approximate the drift term and the control effectiveness matrix of the nonlinear systems model. The DNNs weights are tuned online relying on adaptation laws derived from Lyapunov's stability analysis. The DNNs with their weights tuning mechanism are exploited as building blocks in the design of an ISM control scheme to solve trajectory tracking problems. The proposed framework is then extended to the case in which the system dynamics is subject to time-varying state constraints, producing a second scheme, still of DNN-ISM type. Both control schemes are analyzed, providing interesting theoretical guarantees. Possible solutions to reduce, in practical implementations, the chattering effect, as well as the initial estimation error of the DNNs are also discussed. The proposed DNNs-based control schemes are finally assessed in simulation relying on a realistic model of an anthropomorphic 7-axes robot manipulator.