Related papers: An incremental input-to-state stability condition …
While massive efforts have been investigated in adversarial testing of convolutional neural networks (CNN), testing for recurrent neural networks (RNN) is still limited and leaves threats for vast sequential application domains. In this…
This paper presents a computationally efficient robust model predictive control law for discrete linear time invariant systems subject to additive disturbances that may depend on the state and/or input norms. Despite the dependency being…
Generative models are a promising technology for the enhancement of quantum simulators. These machine learning methods are capable of reconstructing a quantum state from experimental measurements, and can aid in the calculation of physical…
Deep learning research over the past years has shown that by increasing the scope or difficulty of the learning problem over time, increasingly complex learning problems can be addressed. We study incremental learning in the context of…
Recurrent neural networks with a gating mechanism such as an LSTM or GRU are powerful tools to model sequential data. In the mechanism, a forget gate, which was introduced to control information flow in a hidden state in the RNN, has…
In many machine learning problems the output should not depend on the order of the input. Such "permutation invariant" functions have been studied extensively recently. Here we argue that temporal architectures such as RNNs are highly…
Recurrent neural networks are convenient and efficient models for language modeling. However, when applied on the level of characters instead of words, they suffer from several problems. In order to successfully model long-term…
Gated Recurrent Neural Networks (RNNs) are widely used for nonlinear system identification due to their high accuracy, although they often exhibit complex, chaotic dynamics that are difficult to analyze. This paper investigates the…
Input-to-state stability (ISS) unifies global asymptotic stability with respect to variations of initial conditions with robustness with respect to external disturbances. First, we present Lyapunov characterizations for input-to-state…
This paper continues the study of the integral input-to-state stability (IISS) property. It is shown that the IISS property is equivalent to one which arises from the consideration of mixed norms on states and inputs, as well as to the…
Incremental input-to-state stability (delta-ISS) offers a robust framework to ensure that small input variations result in proportionally minor deviations in the state of a nonlinear system. This property is essential in practical…
A recurrent neural network (RNN) is a universal approximator of dynamical systems, whose performance often depends on sensitive hyperparameters. Tuning of such hyperparameters may be difficult and, typically, based on a trial-and-error…
This paper presents a novel framework for analyzing Incremental-Input-to-State Stability ($\delta$ISS) based on the idea of using rewards as "test functions." Whereas control theory traditionally deals with Lyapunov functions that satisfy a…
This paper presents sufficient conditions for the stability and $\ell_2$-gain performance of recurrent neural networks (RNNs) with ReLU activation functions. These conditions are derived by combining Lyapunov/dissipativity theory with…
Input-to-state stability (ISS) unifies the stability and robustness in one notion, and serves as a basis for broad areas of nonlinear control theory. In this contribution, we covered the most fundamental facts in the infinite-dimensional…
We consider the problem of designing learning-based reactive power controllers that perform voltage regulation in distribution grids while ensuring closed-loop system stability. In contrast to existing methods, where the provably stable…
This paper studies a class of random nonlinear systems with time-varying delay, in which the $r$-order moment ($r\geq1$) of the random disturbance is finite. Firstly, some general conditions are proposed to guarantee the existence and…
Recurrent neural networks have gained widespread use in modeling sequential data. Learning long-term dependencies using these models remains difficult though, due to exploding or vanishing gradients. In this paper, we draw connections…
We consider the problem of stabilization of a linear system, under state and control constraints, and subject to bounded disturbances and unknown parameters in the state matrix. First, using a simple least square solution and available…
Recurrent neural networks (RNNs) can be interpreted as discrete-time state-space models, where the state evolution corresponds to an infinite-impulse-response (IIR) filtering operation governed by both feedforward weights and recurrent…