Related papers: Multi-Agent, Multi-Scale Systems with the Koopman …
Reachability analysis of nonlinear dynamical systems is a challenging and computationally expensive task. Computing the reachable states for linear systems, in contrast, can often be done efficiently in high dimensions. In this paper, we…
We consider infinite horizon dynamic programming problems, where the control at each stage consists of several distinct decisions, each one made by one of several agents. In an earlier work we introduced a policy iteration algorithm, where…
This report presents the results of a simulation study of the linear model and bilinear model approximations of the Koopman system model of the nonlinear utility functions in optimal control of a 3-robot system. In such a control problem,…
This paper presents a data-driven method to find a closed-loop optimal controller, which minimizes a specified infinite-horizon cost function for systems with unknown dynamics. Suppose the closed-loop optimal controller can be parameterized…
Multi-agent networked linear dynamic systems have attracted attention of researchers in power systems, intelligent transportation, and industrial automation. The agents might cooperatively optimize a global performance objective, resulting…
Over the last few years, several works have proposed deep learning architectures to learn dynamical systems from observation data with no or little knowledge of the underlying physics. A line of work relies on learning representations where…
The majority of multi-agent system (MAS) implementations aim to optimise agents' policies with respect to a single objective, despite the fact that many real-world problem domains are inherently multi-objective in nature. Multi-objective…
This paper presents a novel Koopman composition operator representation framework for control systems in reproducing kernel Hilbert spaces (RKHSs) that is free of explicit dictionary or input parametrizations. By establishing fundamental…
We review existing approaches to mathematical modeling and analysis of multi-agent systems in which complex collective behavior arises out of local interactions between many simple agents. Though the behavior of an individual agent can be…
We develop a Koopman operator framework for studying the {computational properties} of dynamical systems. Specifically, we show that the resolvent of the Koopman operator provides a natural abstraction of halting, yielding a ``Koopman…
We extend Kirman's model by introducing variable event time scale. The proposed flexible time scale is equivalent to the variable trading activity observed in financial markets. Stochastic version of the extended Kirman's agent based model…
This paper deals with solving distributed optimization problems with equality constraints by a class of uncertain nonlinear heterogeneous dynamic multi-agent systems. It is assumed that each agent with an uncertain dynamic model has limited…
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…
Quantum computation offers potential exponential speedups for simulating certain physical systems, but its application to nonlinear dynamics is inherently constrained by the requirement of unitary evolution. We propose the quantum Koopman…
Motivated by the control theoretic distinction between controllable and uncontrollable events, we distinguish between two types of agents within a multi-agent system: controllable agents, which are directly controlled by the system's…
The control of legged robots, particularly humanoid and quadruped robots, presents significant challenges due to their high-dimensional and nonlinear dynamics. While linear systems can be effectively controlled using methods like Model…
This paper introduces a multi-agent application system designed to enhance office collaboration efficiency and work quality. The system integrates artificial intelligence, machine learning, and natural language processing technologies,…
In this paper, we propose a novel approach to solving optimization problems by reformulating the optimization problem into a dynamical system, followed by the adaptive spectral Koopman (ASK) method. The Koopman operator, employed in our…
We develop algorithms built around properties of the transfer operator and Koopman operator which 1) test for possible multiscale dynamics in a given dynamical system, 2) estimate the magnitude of the time-scale separation, and finally 3)…
Dynamical systems have a wide range of applications in mechanics, electrical engineering, chemistry, and so on. In this work, we propose the adaptive spectral Koopman (ASK) method to solve nonlinear autonomous dynamical systems. This novel…