Related papers: Koopman System Approximation Based Optimal Control…
While Koopman operator lifts a nonlinear system into an infinite-dimensional function space and represents it as a linear dynamics, its definition is restricted to autonomous systems, i.e., does not incorporate inputs or disturbances. To…
We consider the application of Koopman theory to nonlinear partial differential equations. We demonstrate that the observables chosen for constructing the Koopman operator are critical for enabling an accurate approximation to the nonlinear…
The Koopman operator approach to the state estimation problem for nonlinear systems is a promising research area. The main goal of this paper is an attempt to provide a rigorous theoretical framework for this approach. In particular, the…
Online optimal control of quadrupedal robots would enable them to plan their movement in novel scenarios. Linear Model Predictive Control (LMPC) has emerged as a practical approach for real-time control. In LMPC, an optimization problem…
We propose an alternating optimization algorithm to the nonconvex Koopman operator learning problem for nonlinear dynamic systems. We show that the proposed algorithm will converge to a critical point with rate $O(1/T)$ and $O(\frac{1}{\log…
Nonlinear dynamical effects are crucial to the operation of many agile robotic systems. Koopman-based model learning methods can capture these nonlinear dynamical system effects in higher dimensional lifted bilinear models that are amenable…
Autonomous Underwater Vehicles (AUVs) play an essential role in modern ocean exploration, and their speed control systems are fundamental to their efficient operation. Like many other robotic systems, AUVs exhibit multivariable nonlinear…
This paper presents a model-based reinforcement learning (RL) framework for optimal closed-loop control of nonlinear robotic systems. The proposed approach learns linear lifted dynamics through Koopman operator theory and integrates the…
Koopman liftings have been successfully used to learn high dimensional linear approximations for autonomous systems for prediction purposes, or for control systems for leveraging linear control techniques to control nonlinear dynamics. In…
Developing agents that can perform complex control tasks from high-dimensional observations is a core ability of autonomous agents that requires underlying robust task control policies and adapting the underlying visual representations to…
Analyzing synchronized nonlinear oscillators is one of the most important and attractive topics in nonlinear science. By understanding the interactions between the oscillators, we can figure out the synchronization process. A promising…
We present a flexible data-driven method for dynamical system analysis that does not require explicit model discovery. The method is rooted in well-established techniques for approximating the Koopman operator from data and is implemented…
Optimal sensor placement is an important yet unsolved problem in control theory. In biological organisms, genetic activity is often highly nonlinear, making it difficult to design libraries of promoters to act as reporters of the cell…
Koopman analysis of a general dynamics system provides a linear Koopman operator and an embedded eigenfunction space, enabling the application of standard techniques from linear analysis. However, in practice, deriving exact operators and…
Dynamical systems are ubiquitous and are often modeled using a non-linear system of governing equations. Numerical solution procedures for many dynamical systems have existed for several decades, but can be slow due to high-dimensional…
The highly nonlinear dynamics of vehicles present a major challenge for the practical implementation of optimal and Model Predictive Control (MPC) approaches in path planning and following. Koopman operator theory offers a global linear…
We propose a fully data-driven, Koopman-based framework for statistically robust control of discrete-time nonlinear systems with linear embeddings. Establishing a connection between the Koopman operator and contraction theory, it offers…
This paper proposes Koopman operator-based Stochastic Model Predictive Control (K-SMPC) for enhanced lateral control of autonomous vehicles. The Koopman operator is a linear map representing the nonlinear dynamics in an infinite-dimensional…
Learning dexterous manipulation skills presents significant challenges due to complex nonlinear dynamics that underlie the interactions between objects and multi-fingered hands. Koopman operators have emerged as a robust method for modeling…
Controlling soft continuum manipulator arms is difficult due to their infinite degrees of freedom, nonlinear material properties, and large deflections under loading. This paper presents a data-driven approach to identifying soft…