Related papers: Lyapunov-Net: A Deep Neural Network Architecture f…
We propose an automatic and formally sound method for synthesising Lyapunov functions for the asymptotic stability of autonomous non-linear systems. Traditional methods are either analytical and require manual effort or are numerical but…
Deep learning has had a far reaching impact in robotics. Specifically, deep reinforcement learning algorithms have been highly effective in synthesizing neural-network controllers for a wide range of tasks. However, despite this empirical…
We propose new methods for learning control policies and neural network Lyapunov functions for nonlinear control problems, with provable guarantee of stability. The framework consists of a learner that attempts to find the control and…
This paper considers the problem of characterizing the stability region of a large-scale networked system comprised of dissipative nonlinear subsystems, in a distributed and computationally tractable way. One standard approach to estimate…
Deep learning methods have been widely used in robotic applications, making learning-enabled control design for complex nonlinear systems a promising direction. Although deep reinforcement learning methods have demonstrated impressive…
Deep neural networks (DNNs) have emerged as a powerful tool with a growing body of literature exploring Lyapunov-based approaches for real-time system identification and control. These methods depend on establishing bounds for the second…
This paper deals with a special type of Lyapunov functions, namely the solution of Zubov's equation. Such a function can be used to characterize the domain of attraction for systems of ordinary differential equations. We derive and prove an…
Learning algorithms have shown considerable prowess in simulation by allowing robots to adapt to uncertain environments and improve their performance. However, such algorithms are rarely used in practice on safety-critical systems, since…
When neural networks are used to model dynamics, properties such as stability of the dynamics are generally not guaranteed. In contrast, there is a recent method for learning the dynamics of autonomous systems that guarantees global…
Graph Neural Networks (GNNs) are highly vulnerable to adversarial perturbations in both topology and features, making the learning of robust representations a critical challenge. In this work, we bridge GNNs with control theory to introduce…
Learning control strategies with provable stability guarantees continues to be a challenging problem. In this work, we examine a family of training-time behaviors exhibited by existing neural Lyapunov control methods under specific…
We explicitly construct global strict Lyapunov functions for rapidly time-varying nonlinear control systems. The Lyapunov functions we construct are expressed in terms of oftentimes more readily available Lyapunov functions for the limiting…
The inherent approximation ability of neural networks plays an essential role in adaptive neural control, where the prerequisite for existence of the compact set is crucial in the control designs. Instead of using practical system state, in…
We study the expressive power of deep ReLU neural networks for approximating functions in dilated shift-invariant spaces, which are widely used in signal processing, image processing, communications and so on. Approximation error bounds are…
Autonomous Dynamic System (DS)-based algorithms hold a pivotal and foundational role in the field of Learning from Demonstration (LfD). Nevertheless, they confront the formidable challenge of striking a delicate balance between achieving…
Deep neural network (DNN)-based adaptive controllers can be used to compensate for unstructured uncertainties in nonlinear dynamic systems. However, DNNs are also very susceptible to overfitting and co-adaptation. Dropout regularization is…
We train an artificial neural network which distinguishes chaotic and regular dynamics of the two-dimensional Chirikov standard map. We use finite length trajectories and compare the performance with traditional numerical methods which need…
The network structure (or topology) of a dynamical network is often unavailable or uncertain. Hence, we consider the problem of network reconstruction. Network reconstruction aims at inferring the topology of a dynamical network using…
We build on the dynamical systems approach to deep learning, where deep residual networks are idealized as continuous-time dynamical systems, from the approximation perspective. In particular, we establish general sufficient conditions for…
This paper establishes the nearly optimal rate of approximation for deep neural networks (DNNs) when applied to Korobov functions, effectively overcoming the curse of dimensionality. The approximation results presented in this paper are…