Robust Data-Driven Neuro-Adaptive Observers with Lipschitz Activation Functions

While the use of neural networks for learning has gained traction in control and system identification problems, their use in data-driven estimator design is not as prevalent. Prior art on neuro-adaptive observers limit the type of activation functions to radial basis function networks and provide conservative bounds on the resulting observer estimation error because they leverage boundedness of the activation functions rather than exploiting their underlying structure. This paper proposes the use of Lipschitz activation functions in the neuroadaptive observer: utilizing the Lipschitz constants of these activations simplifies the data-driven observer design procedure via recently discovered LMI conditions. Furthermore, in spite of measurement noise and approximation error, pre-computable robust stability guarantees are provided on the resulting state estimation error.