This letter deals with the design of a novel neural network based integral sliding mode (NN-ISM) control for nonlinear systems with uncertain drift term and control effectiveness matrix. Specifically, this letter extends the classical integral sliding mode control law to the case of unknown nominal model. The latter is indeed reconstructed by two deep neural networks capable of approximating the unknown terms, which are instrumental to design the so-called integral sliding manifold. In this letter, the ultimate boundedness of the system state is formally proved by using Lyapunov stability arguments, thus providing the conditions to enforce practical integral sliding modes. The possible generation of ideal integral sliding modes is also discussed. Moreover, the effectiveness of the proposed NN-ISM control law is assessed in simulation relying on the classical Duffing oscillator.
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