Related papers: Koopman-based control using sum-of-squares optimiz…

A promising direction towards improving the performance of wave energy converter (WEC) farms is to leverage a system-level integrated approach known as control co-design (CCD). A WEC farm CCD problem may entail decision variables associated…

Nonlinearity in dynamics has long been a major challenge in robotics, often causing significant performance degradation in existing control algorithms. For example, the navigation of bipedal robots can exhibit nonlinear behaviors even under…

This paper addresses the problem of optimally controlling nonlinear systems with norm-bounded disturbances and parametric uncertainties while robustly satisfying constraints. The proposed approach jointly optimizes a nominal nonlinear…

Data-driven transformations that reformulate nonlinear systems in a linear framework have the potential to enable the prediction, estimation, and control of strongly nonlinear dynamics using linear systems theory. The Koopman operator has…

This paper introduces new model parameterizations for learning discrete-time dynamical systems from data via the Koopman operator and studies their properties. Whereas most existing works on Koopman learning do not take into account the…

Advances in machine learning and the growing trend towards effortless data generation in real-world systems has led to an increasing interest for data-inferred models and data-based control in robotics. It seems appealing to govern robots…

We propose a noise-robust learning framework for the Koopman operator of nonlinear dynamical systems, with guaranteed long-term stability and improved model performance for better model-based predictive control tasks. Unlike some existing…

Accurate modeling and control of autonomous vehicles remain a fundamental challenge due to the nonlinear and coupled nature of vehicle dynamics. While Koopman operator theory offers a framework for deploying powerful linear control…

Nonlinear coupled systems are ubiquitous in science and engineering. The analysis and modeling of such systems is challenging due to their high dimensionality and complex interactions among subsystems. In recent years, operator-theoretic…

We investigate nonlinear model predictive control (MPC) with terminal conditions in the Koopman framework using extended dynamic mode decomposition (EDMD) to generate a data-based surrogate model for prediction and optimization. We…

The Koopman operator framework provides a perspective that non-linear dynamics can be described through the lens of linear operators acting on function spaces. As the framework naturally yields linear embedding models, there have been…

Safety is closely related to set invariance for dynamical systems. However, synthesizing a safe invariant set and at the same time synthesizing the associated safe controller still remains challenging. In this note we introduce a simple…

In this paper, an extension to rules-based fault detection is demonstrated utilizing properties of the Koopman operator. The Koopman operator is an infinite-dimensional, linear operator that captures nonlinear, finite dimensional dynamics.…

We develop a new generalization of Koopman operator theory that incorporates the effects of inputs and control. Koopman spectral analysis is a theoretical tool for the analysis of nonlinear dynamical systems. Moreover, Koopman is intimately…

This paper develops a parametric Koopman operator framework for Stochastic Model Predictive Control (SMPC), where the Koopman operator is parametrized by Polynomial Chaos Expansions (PCEs). The model is learned from data using the Extended…

This paper develops a data-driven safe control framework for nonlinear discrete-time systems with parametric uncertainty and additive disturbances. The proposed approach constructs a data-consistent closed-loop representation that enables…

Within this work, we investigate how data-driven numerical approximation methods of the Koopman operator can be used in practical control engineering applications. We refer to the method Extended Dynamic Mode Decomposition (EDMD), which…

In this paper, we present a novel sufficient condition for the stability of discrete-time linear systems that can be represented as a set of piecewise linear constraints, which make them suitable for quadratic programming optimization…

Koopman-based learning methods can potentially be practical and powerful tools for dynamical robotic systems. However, common methods to construct Koopman representations seek to learn lifted linear models that cannot capture nonlinear…

Recently, subsynchronous oscillations (SSOs) have emerged frequently worldwide, with the high penetration of renewable power generation in modern power systems. The SSO introduced by renewables has become a prominent new stability problem,…