Related papers: Learning Certified Neural Network Controllers Usin…
In the previous article, we introduced a neural network framework based on symmetric differential equations. This novel framework exhibits complete symmetry, endowing it with perfect mathematical properties. While we have examined some of…
Inverter-based distributed energy resources provide the possibility for fast time-scale voltage control by quickly adjusting their reactive power. The power-electronic interfaces allow these resources to realize almost arbitrary control…
Model-based controllers can offer strong guarantees on stability and convergence by relying on physically accurate dynamic models. However, these are rarely available for high-dimensional mechanical systems such as deformable objects or…
Training a neural network using backpropagation algorithm requires passing error gradients sequentially through the network. The backward locking prevents us from updating network layers in parallel and fully leveraging the computing…
Owing to their superior modeling capabilities, gated Recurrent Neural Networks, such as Gated Recurrent Units (GRUs) and Long Short-Term Memory networks (LSTMs), have become popular tools for learning dynamical systems. This paper aims to…
This paper is concerned with the training of neural networks (NNs) under semidefinite constraints, which allows for NN training with robustness and stability guarantees. In particular, we focus on Lipschitz bounds for NNs. Exploiting the…
Neural Networks (NNs) can provide major empirical performance improvements for robotic systems, but they also introduce challenges in formally analyzing those systems' safety properties. In particular, this work focuses on estimating the…
This paper investigates the use of extended Kalman filtering to train recurrent neural networks with rather general convex loss functions and regularization terms on the network parameters, including $\ell_1$-regularization. We show that…
In this paper, we focus on the problem about direct way to design a stable controller for nonlinear system. A framework of learning controller with Lyapunov-based constraint is proposed, which is intended to transform designing and analyis…
This paper proposes a computationally efficient framework, based on interval analysis, for rigorous verification of nonlinear continuous-time dynamical systems with neural network controllers. Given a neural network, we use an existing…
A Learning Model Predictive Controller (LMPC) for linear system in presented. The proposed controller is an extension of the LMPC [1] and it aims to decrease the computational burden. The control scheme is reference-free and is able to…
This paper proposes a theoretical and computational framework for training and robustness verification of implicit neural networks based upon non-Euclidean contraction theory. The basic idea is to cast the robustness analysis of a neural…
In this work, we consider the problem of learning a feed-forward neural network controller to safely steer an arbitrarily shaped planar robot in a compact and obstacle-occluded workspace. Unlike existing methods that depend strongly on the…
In this paper, we present a method to analyze local and global stability in offset-free setpoint tracking using neural network controllers and we provide ellipsoidal inner approximations of the corresponding region of attraction. We…
Neural networks offer a computationally efficient approximation of model predictive control, but they lack guarantees on the resulting controlled system's properties. Formal certification of neural networks is crucial for ensuring safety,…
The Jacobian matrix (or the gradient for single-output networks) is directly related to many important properties of neural networks, such as the function landscape, stationary points, (local) Lipschitz constants and robustness to…
This paper proposes a Recurrent Neural Network (RNN) controller for lane-keeping systems, effectively handling model uncertainties and disturbances. First, quadratic constraints cover the nonlinearities brought by the RNN controller, and…
This work presents several improvements to the closed-loop stability verification framework using semialgebraic sets and convex semidefinite programming to examine neural-network-based control systems regulating nonlinear dynamical systems.…
Neural networks have become increasingly popular in controller design due to their versatility and efficiency. However, their integration into feedback systems can pose stability challenges, particularly in the presence of uncertainties.…
This paper presents a neural network filter method based on contraction operators to address model collapse in recursive training of generative models. Unlike \cite{xu2024probabilistic}, which requires superlinear sample growth…