Related papers: Regional stability conditions for recurrent neural…
The paper considers a stabilizing stochastic control which can be applied to a variety of unstable and even chaotic maps. Compared to previous methods introducing control by noise, we relax assumptions on the class of maps, as well as…
The performance of graph neural networks (GNNs) is susceptible to discrepancies between training and testing sample distributions. Prior studies have attempted to mitigating the impact of distribution shift by reconstructing node features…
The paper investigates sufficient conditions on a differential inclusion which guarantee that the origin is a finite time stable equilibrium, namely a weak local one, a weak global one or a strong local one. The analysis relies on the…
Motivated by biochemical reaction networks, a generalization of the classical secant condition for the stability analysis of cyclic interconnected commensurate fractional-order systems is provided. The main result presents a sufficient…
For a given stable recurrent neural network (RNN) that is trained to perform a classification task using sequential inputs, we quantify explicit robustness bounds as a function of trainable weight matrices. The sequential inputs can be…
We present necessary and sufficient optimality conditions for finite time optimal control problems for a class of hybrid systems described by linear complementarity models. Although these optimal control problems are difficult in general…
It is quite often claimed, and correctly so, that linear methods cannot achieve global stability results for attitude control, and conversely that nonlinear control is essential in order to achieve (almost) globally stable tracking of…
This paper introduces a novel method for the stability analysis of positive feedback systems with a class of fully connected feedforward neural networks (FFNN) controllers. By establishing sector bounds for fully connected FFNNs without…
This study presents a sampling-based method to guarantee robust stability of general control systems with uncertainty. The method allows the system dynamics and controllers to be represented by various data-driven models, such as Gaussian…
This paper proposes a reinforcement learning-based approach for optimal transient frequency control in power systems with stability and safety guarantees. Building on Lyapunov stability theory and safety-critical control, we derive…
We study deterministic, discrete linear time-invariant systems with infinite-horizon discounted quadratic cost. It is well-known that standard stabilizability and detectability properties are not enough in general to conclude stability…
An approach to stabilization of control systems with ultimately wide ranges of uncertainly disturbed parameters is offered. The method relies on using of nonlinear structurally stable functions from catastrophe theory as controllers.…
In this paper we consider the training of single hidden layer neural networks by pseudoinversion, which, in spite of its popularity, is sometimes affected by numerical instability issues. Regularization is known to be effective in such…
A novel representation of reset control systems with a zero-crossing resetting law, in the framework of hybrid inclusions, is postulated. The problems of well-posedness and stability of the resulting hybrid dynamical system are…
The goal of this paper is to analyze Long Short Term Memory (LSTM) neural networks from a dynamical system perspective. The classical recursive equations describing the evolution of LSTM can be recast in state space form, resulting in a…
An input-output approach to stability analysis is explored for networked systems with uncertain link dynamics. The main result consists of a collection of integral quadratic constraints, which together imply robust stability of the…
This paper presents a general framework for the design of linear controllers for linear systems subject to time-domain constraints. The design framework exploits sums-of-squares techniques to incorporate the time-domain constraints on…
Recurrent neural networks are capable of learning the dynamics of an unknown nonlinear system purely from input-output measurements. However, the resulting models do not provide any stability guarantees on the input-output mapping. In this…
We provide a general framework for studying recurrent neural networks (RNNs) trained by injecting noise into hidden states. Specifically, we consider RNNs that can be viewed as discretizations of stochastic differential equations driven by…
We address a class of Markov jump linear systems that are characterized by the underlying Markov process being time-inhomogeneous with a priori unknown transition probabilities. Necessary and sufficient conditions for uniform stochastic…