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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…
The study of the Two-Body and Circular Restricted Three-Body Problems in the field of aerospace engineering and sciences is deeply important because they help describe the motion of both celestial and artificial satellites. With the growing…
The design and analysis of optimal control policies for dynamical systems can be complicated by nonlinear dependence in the state variables. Koopman operators have been used to simplify the analysis of dynamical systems by mapping the flow…
Koopman operator theory has served as the basis to extract dynamics for nonlinear system modeling and control across settings, including non-holonomic mobile robot control. There is a growing interest in research to derive robustness…
Nonlinear optimal control is vital for numerous applications but remains challenging for unknown systems due to the difficulties in accurately modelling dynamics and handling computational demands, particularly in high-dimensional settings.…
We study a problem of simultaneous system identification and model predictive control of nonlinear systems. Particularly, we provide an algorithm for systems with unknown residual dynamics that can be expressed by Koopman operators. Such…
This paper presents a class of linear predictors for nonlinear controlled dynamical systems. The basic idea is to lift the nonlinear dynamics into a higher dimensional space where its evolution is approximately linear. In an uncontrolled…
This paper presents a novel episodic method to learn a robot's nonlinear dynamics model and an increasingly optimal control sequence for a set of tasks. The method is based on the {\em Koopman operator} approach to nonlinear dynamical…
We propose spectral methods for long-term forecasting of temporal signals stemming from linear and nonlinear quasi-periodic dynamical systems. For linear signals, we introduce an algorithm with similarities to the Fourier transform but…
The long-timescale behavior of complex dynamical systems can be described by linear Markov or Koopman models in a suitable latent space. Recent variational approaches allow the latent space representation and the linear dynamical model to…
In model-based reinforcement learning, the agent interleaves between model learning and planning. These two components are inextricably intertwined. If the model is not able to provide sensible long-term prediction, the executed planner…
Inspired by the success of the Transformer architecture in natural language processing and computer vision, we investigate the use of Transformers in Reinforcement Learning (RL), specifically in modeling the environment's dynamics using…
Recent advances in diffusion-based robot policies have demonstrated significant potential in imitating multi-modal behaviors. However, these approaches typically require large quantities of demonstration data paired with corresponding robot…
Model-based Reinforcement Learning (MBRL) holds promise for data-efficiency by planning with model-generated experience in addition to learning with experience from the environment. However, in complex or changing environments, models in…
In many scenarios, it is necessary to monitor a complex system via a time-series of observations and determine when anomalous exogenous events have occurred so that relevant actions can be taken. Determining whether current observations are…
Given the complexity and nonlinearity inherent in traffic dynamics within vehicular platoons, there exists a critical need for a modeling methodology with high accuracy while concurrently achieving physical analyzability. Currently, there…
Koopman operator theory yields powerful tools for modeling, analysis, and control of nonlinear dynamical systems. Prominently, linear time-invariant (LTI) Koopman representations have been proposed to enable the application of linear…
The Koopman operator has recently garnered much attention for its value in dynamical systems analysis and data-driven model discovery. However, its application has been hindered by the computational complexity of extended dynamic mode…
Koopman operator theory has found significant success in learning models of complex, real-world dynamical systems, enabling prediction and control. The greater interpretability and lower computational costs of these models, compared to…
Learning long-term dynamics models is the key to understanding physical common sense. Most existing approaches on learning dynamics from visual input sidestep long-term predictions by resorting to rapid re-planning with short-term models.…