相关论文: Learning Aligned Stability in Neural ODEs Reconcil…

Training deep neural networks, particularly in computer vision tasks, often suffers from noisy gradients and unstable convergence, which hinder performance and generalization. In this paper, we propose LyAm, a novel optimizer that…

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…

We provide a systematic investigation of using physics-informed neural networks to compute Lyapunov functions. We encode Lyapunov conditions as a partial differential equation (PDE) and use this for training neural network Lyapunov…

We consider the problem of nonlinear system identification when prior knowledge is available on the region of attraction (ROA) of an equilibrium point. We propose an identification method in the form of an optimization problem, minimizing…

This article presents novel methods for synthesizing distributionally robust stabilizing neural controllers and certificates for control systems under model uncertainty. A key challenge in designing controllers with stability guarantees for…

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…

Designing control policies for stabilization tasks with provable guarantees is a long-standing problem in nonlinear control. A crucial performance metric is the size of the resulting region of attraction, which essentially serves as a…

We introduce a method for learning provably stable deep neural network based dynamic models from observed data. Specifically, we consider discrete-time stochastic dynamic models, as they are of particular interest in practical applications…

Estimating the region of attraction (ROA) of general nonlinear autonomous systems remains a challenging problem and requires a case-by-case analysis. Leveraging the universal approximation property of neural networks, in this paper, we…

While training error of most deep neural networks degrades as the depth of the network increases, residual networks appear to be an exception. We show that the main reason for this is the Lyapunov stability of the gradient descent…

Verifying stability and safety guarantees for nonlinear systems has received considerable attention in recent years. This property serves as a fundamental building block for specifying more complex system behaviors and control objectives.…

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…

Analyzing nonlinear systems with attracting robust invariant sets (RISs) requires estimating their domains of attraction (DOAs). Despite extensive research, accurately characterizing DOAs for general nonlinear systems remains challenging…

In this paper, we consider the data-driven discovery of stable dynamical models with a single equilibrium. The proposed approach uses a basis-function parameterization of the differential equations and the associated Lyapunov function. This…

This paper addresses the problem of Neural Network (NN) based adaptive stability certification in a dynamical system. The state-of-the-art methods, such as Neural Lyapunov Functions (NLFs), use NN-based formulations to assess the stability…

Neural-based, data-driven analysis and control of dynamical systems have been recently investigated and have shown great promise, e.g. for safety verification or stability analysis. Indeed, not only do neural networks allow for an entirely…

For any given neural network architecture a permutation of weights and biases results in the same functional network. This implies that optimization algorithms used to `train' or `learn' the network are faced with a very large number (in…

Deep networks are commonly used to model dynamical systems, predicting how the state of a system will evolve over time (either autonomously or in response to control inputs). Despite the predictive power of these systems, it has been…

We develop a unified Lyapunov-integral quadratic constraint (IQC) framework for establishing uniform stability of first-order accelerated optimization algorithms in the $\beta$-smooth and $\gamma$-strongly convex regime. Classical analyses…

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…