相关论文: Deep Koopman Operator-based degradation modelling
The Koopman operator has gained significant attention in recent years for its ability to verify evolutionary properties of continuous-time nonlinear systems by lifting state variables into an infinite-dimensional linear vector space. The…
Dynamic mode decomposition (DMD) is a data-driven technique used for capturing the dynamics of complex systems. DMD has been connected to spectral analysis of the Koopman operator, and essentially extracts spatial-temporal modes of the…
Long-horizon dynamical prediction is fundamental in robotics and control, underpinning canonical methods like model predictive control. Yet, many systems and disturbance phenomena are difficult to model due to effects like nonlinearity,…
Dynamic mode decomposition (DMD) gives a practical means of extracting dynamic information from data, in the form of spatial modes and their associated frequencies and growth/decay rates. DMD can be considered as a numerical approximation…
Accurately finding and predicting dynamics based on the observational data with noise perturbations is of paramount significance but still a major challenge presently. Here, for the Hamiltonian mechanics, we propose the Hamiltonian Neural…
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…
This paper investigates the impact of approximation error in data-driven optimal control problem of nonlinear systems while using the Koopman operator. While the Koopman operator enables a simplified representation of nonlinear dynamics…
The discovery of linear embedding is the key to the synthesis of linear control techniques for nonlinear systems. In recent years, while Koopman operator theory has become a prominent approach for learning these linear embeddings through…
System representations inspired by the infinite-dimensional Koopman operator (generator) are increasingly considered for predictive modeling. Due to the operator's linearity, a range of nonlinear systems admit linear predictor…
In this paper, we provide an algorithm for online computation of Koopman operator in real-time using streaming data. In recent years, there has been an increased interest in data-driven analysis of dynamical systems, with operator theoretic…
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…
Autonomous driving has attracted lots of attention in recent years. An accurate vehicle dynamics is important for autonomous driving techniques, e.g. trajectory prediction, motion planning, and control of trajectory tracking. Although…
Koopman operator theory is a key tool in data assimilation of complex dynamical systems, with the potential to be applied to multimodal data. We formulate the problem of learning Koopman eigenfunctions from observations at arbitrary,…
Recent years have seen rapid advances in the data-driven analysis of dynamical systems based on Koopman operator theory and related approaches. On the other hand, low-rank tensor product approximations -- in particular the tensor train (TT)…
It has become common to perform kinetic analysis using approximate Koopman operators that transforms high-dimensional time series of observables into ranked dynamical modes. Key to a practical success of the approach is the identification…
Koopman operator theory is a kind of data-driven modelling approach that accurately captures the nonlinearities of mechatronic systems such as vehicles against physics-based methods. However, the infinite-dimensional Koopman operator is…
We present a data-driven optimization approach for robotic controlled deposition with a degradable tool. Existing methods make the assumption that the tool tip is not changing or is replaced frequently. Errors can accumulate over time as…
Koopman operators provide tractable means of learning linear approximations of non-linear dynamics. Many approaches have been proposed to find these operators, typically based upon approximations using an a-priori fixed class of models.…
Reinforcement Learning (RL) has made significant strides in various domains, and policy gradient methods like Proximal Policy Optimization (PPO) have gained popularity due to their balance in performance, training stability, and…
Advanced autonomous driving systems require accurate vehicle dynamics modeling. However, identifying a precise dynamics model remains challenging due to strong nonlinearities and the coupled longitudinal and lateral dynamic characteristics.…