Related papers: Learning Neural Koopman Operators with Dissipativi…
As autonomous systems become more complex and integral in our society, the need to accurately model and safely control these systems has increased significantly. In the past decade, there has been tremendous success in using deep learning…
This paper tackles the data-driven approximation of unknown dynamical systems using Koopman-operator methods. Given a dictionary of functions, these methods approximate the projection of the action of the operator on the finite-dimensional…
We present a data-driven shared control algorithm that can be used to improve a human operator's control of complex dynamic machines and achieve tasks that would otherwise be challenging, or impossible, for the user on their own. Our method…
This paper develops a methodology for adaptive data-driven Model Predictive Control (MPC) using Koopman operators. While MPC is ubiquitous in various fields of engineering, the controller performance can deteriorate if the modeling error…
In this paper, a novel Koopman-type inverse operator for linear time-invariant non-minimum phase systems with stochastic disturbances is proposed. This operator employs functions of the desired output to directly calculate the input.…
This paper investigates the generalisability of Koopman-based representations for chaotic dynamical systems, focusing on their transferability across prediction and control tasks. Using the Lorenz system as a testbed, we propose a…
We propose a scalable reachability-based framework for probabilistic, data-driven safety verification of unknown nonlinear dynamics. We use Koopman theory with a neural network (NN) lifting function to learn an approximate linear…
In this paper, we provide sufficient conditions for dissipativity and local asymptotic stability of discrete-time dynamical systems parametrized by deep neural networks. We leverage the representation of neural networks as pointwise affine…
This paper uses data-driven operator theoretic approaches to explore the global phase space of a dynamical system. We defined conditions for discovering new invariant subspaces in the state space of a dynamical system starting from an…
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…
This work primarily focuses on an operator inference methodology aimed at constructing low-dimensional dynamical models based on a priori hypotheses about their structure, often informed by established physics or expert insights. Stability…
The Koopman operator framework enables global analysis of nonlinear systems through its inherent linearity. This study aims to clarify spectral properties of the Koopman operators for nonlinear systems with control inputs. To this end, we…
The Koopman operator and its data-driven approximations, such as extended dynamic mode decomposition (EDMD), are widely used for analysing, modelling, and controlling nonlinear dynamical systems. However, when the true Koopman…
The modeling of nonlinear dynamics based on Koopman operator theory, which is originally applicable only to autonomous systems with no control, is extended to non-autonomous control system without approximation to input matrix B. Prevailing…
This paper studies the problem of output regulation for a class of nonlinear systems experiencing matched input disturbances. It is assumed that the disturbance signal is generated by an external autonomous dynamical system. First, we show…
Effective and causal observable functions for low-order lifting linearization of nonlinear controlled systems are learned from data by using neural networks. While Koopman operator theory allows us to represent a nonlinear system as a…
The strong performance of simple neural networks is often attributed to their nonlinear activations. However, a linear view of neural networks makes understanding and controlling networks much more approachable. We draw from a dynamical…
The Bellman equation and its continuous form, the Hamilton-Jacobi-Bellman equation, are ubiquitous in reinforcement learning and control theory. However, these equations become intractable for high-dimensional or nonlinear systems. This…
The control of legged robots, particularly humanoid and quadruped robots, presents significant challenges due to their high-dimensional and nonlinear dynamics. While linear systems can be effectively controlled using methods like Model…
We introduce two novel generalizations of the Koopman operator method of nonlinear dynamic modeling. Each of these generalizations leads to greatly improved predictive performance without sacrificing a unique trait of Koopman methods: the…