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Contraction metrics are crucial in control theory because they provide a powerful framework for analyzing stability, robustness, and convergence of various dynamical systems. However, identifying these metrics for complex nonlinear systems…
In this paper, we solve the problem of finding a certified control policy that drives a robot from any given initial state and under any bounded disturbance to the desired reference trajectory, with guarantees on the convergence or bounds…
We present a novel framework that jointly trains a neural network controller and a neural Riemannian metric with rigorous closed-loop contraction guarantees using formal bound propagation. Directly bounding the symmetric Riemannian…
Control design for general nonlinear robotic systems with guaranteed stability and/or safety in the presence of model uncertainties is a challenging problem. Recent efforts attempt to learn a controller and a certificate (e.g., a Lyapunov…
We propose a novel framework for learning stabilizable nonlinear dynamical systems for continuous control tasks in robotics. The key idea is to develop a new control-theoretic regularizer for dynamics fitting rooted in the notion of…
Real-time adaptation is imperative to the control of robots operating in complex, dynamic environments. Adaptive control laws can endow even nonlinear systems with good trajectory tracking performance, provided that any uncertain dynamics…
Real-time adaptation is imperative to the control of robots operating in complex, dynamic environments. Adaptive control laws can endow even nonlinear systems with good trajectory tracking performance, provided that any uncertain dynamics…
This paper studies the design of neural network (NN)-based controllers for unknown nonlinear systems, using contraction analysis. A Neural Ordinary Differential Equation (NODE) system is constructed by approximating the unknown draft…
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…
Composite adaptive control (CAC) that integrates direct and indirect adaptive control techniques can achieve smaller tracking errors and faster parameter convergence compared with direct and indirect adaptive control techniques. However,…
Reinforcement learning is commonly associated with training of reward-maximizing (or cost-minimizing) agents, in other words, controllers. It can be applied in model-free or model-based fashion, using a priori or online collected system…
In this paper, we present a contraction-guided adaptive partitioning algorithm for improving interval-valued robust reachable set estimates in a nonlinear feedback loop with a neural network controller and disturbances. Based on an estimate…
This work proposes a two-layered control scheme for constrained nonlinear systems represented by a class of recurrent neural networks and affected by additive disturbances. In particular, a base controller ensures global or regional…
Neural network (NN) controllers achieve strong empirical performance on nonlinear dynamical systems, yet deploying them in safety-critical settings requires robustness to disturbances and uncertainty. We present a method for jointly…
In this paper, we synthesize two aperiodic-sampled deep neural network (DNN) control schemes, based on the closed-loop tracking stability guarantees. By means of the integral quadratic constraint coping with the input-output behaviour of…
This paper presents a theoretical overview of a Neural Contraction Metric (NCM): a neural network model of an optimal contraction metric and corresponding differential Lyapunov function, the existence of which is a necessary and sufficient…
We propose a novel framework for learning stabilizable nonlinear dynamical systems for continuous control tasks in robotics. The key contribution is a control-theoretic regularizer for dynamics fitting rooted in the notion of…
We present data-based conditions for enforcing contractivity via feedback control and obtain desired asymptotic properties of the closed-loop system. We focus on unknown nonlinear control systems whose vector fields are expressible via a…
This paper presents a constraint-enforcing control framework for a class of discrete-time strict-feedback nonlinear systems. The objective is to guarantee closed-loop stability while ensuring forward invariance of a prescribed safe set…
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…