Related papers: Limits of Learning Dynamical Systems
Determining the reachable set for a given nonlinear control system is crucial for system control and planning. However, computing such a set is impossible if the system's dynamics are not fully known. This paper is motivated by a scenario…
In this paper, we view a policy or plan as a transition system over a space of information states that reflect a robot's or other observer's perspective based on limited sensing, memory, computation, and actuation. Regardless of whether…
The Koopman operator provides a linear perspective on non-linear dynamics by focusing on the evolution of observables in an invariant subspace. Observables of interest are typically linearly reconstructed from the Koopman eigenfunctions.…
In many applications, one needs to learn a dynamical system from its solutions sampled at a finite number of time points. The learning problem is often formulated as an optimization problem over a chosen function class. However, in the…
Slow-fast dynamical systems, i.e., singularly or non-singularly perturbed dynamical systems possess slow invariant manifolds on which trajectories evolve slowly. Since the last century various methods have been developed for approximating…
Bounded agents are limited by intrinsic constraints on their ability to process information that is available in their sensors and memory and choose actions and memory updates. In this dissertation, we model these constraints as…
Learning by interaction is the key to skill acquisition for most living organisms, which is formally called Reinforcement Learning (RL). RL is efficient in finding optimal policies for endowing complex systems with sophisticated behavior.…
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…
Modern robotics is gravitating toward increasingly collaborative human robot interaction. Tools such as acceleration policies can naturally support the realization of reactive, adaptive, and compliant robots. These tools require us to model…
Reinforcement learning usually assumes a given or sometimes even fixed environment in which an agent seeks an optimal policy to maximize its long-term discounted reward. In contrast, we consider agents that are not limited to passive…
Continuous state spaces and stochastic, switching dynamics characterize a number of rich, realworld domains, such as robot navigation across varying terrain. We describe a reinforcementlearning algorithm for learning in these domains and…
We extend the methodology in [Yang et al., 2023] to learn autonomous continuous-time dynamical systems from invariant measures. The highlight of our approach is to reformulate the inverse problem of learning ODEs or SDEs from data as a…
Data-driven neural Koopman operator theory has emerged as a powerful tool for linearizing and controlling nonlinear robotic systems. However, the performance of these data-driven models fundamentally depends on the trade-off between sample…
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…
Stable concurrent learning and control of dynamical systems is the subject of adaptive control. Despite being an established field with many practical applications and a rich theory, much of the development in adaptive control for nonlinear…
The Koopman operator lifts nonlinear dynamical systems into a functional space of observables, where the dynamics are linear. In this paper, we provide three different Koopman representations for hybrid systems. The first is specific to…
Machine learning techniques applied to the problem of financial market forecasting struggle with dynamic regime switching, or underlying correlation and covariance shifts in true (hidden) market variables. Drawing inspiration from the…
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…
Invariant foliations are geometric structures for describing and understanding the qualitative behaviors of nonlinear dynamical systems. For stochastic dynamical systems, however, these geometric structures themselves are complicated random…
Dynamic programming is a class of algorithms used to compute optimal control policies for Markov decision processes. Dynamic programming is ubiquitous in control theory, and is also the foundation of reinforcement learning. In this paper,…