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A suboptimal active disturbance rejection controller (S-ADRC) is proposed for second-order systems with unknown time-varying nonlinear dynamics. The output-feedback controller guarantees a global convergence to the vicinity of an optimal solution by means of dynamic control gains, based on the estimated main and extended state variables obtained through a high-gain observer. Three numerical examples compare the performance of the proposed control scheme applied to linear and nonlinear systems with that of a fixed-gain conventional ADRC as well as several model-based optimal and suboptimal controllers., Comment: 6 pages, 4 figures, accepted for publication in IEEE Control Systems Letters

Unitary recurrent neural networks (URNNs) have been proposed as a method to overcome the vanishing and exploding gradient problem in modeling data with long-term dependencies. A basic question is how restrictive is the unitary constraint on the possible input-output mappings of such a network? This work shows that for any contractive RNN with ReLU activations, there is a URNN with at most twice the number of hidden states and the identical input-output mapping. Hence, with ReLU activations, URNNs are as expressive as general RNNs. In contrast, for certain smooth activations, it is shown that the input-output mapping of an RNN cannot be matched with a URNN, even with an arbitrary number of states. The theoretical results are supported by experiments on modeling of slowly-varying dynamical systems.