Related papers: Auxiliary Functions as Koopman Observables: Data-D…
In this paper, a novel adaptive optimal control strategy is proposed to achieve the cooperative optimal output regulation of continuous-time linear multi-agent systems based on adaptive dynamic programming (ADP). The proposed method is…
This paper is devoted to the investigation of inertial dynamical systems with implicit Hessian-driven damping for strongly quasiconvex optimization which is a specific class of nonconvex optimization problems. We first establish exponential…
In stochastic systems, numerically sampling the relevant trajectories for the estimation of the large deviation statistics of time-extensive observables requires overcoming their exponential (in space and time) scarcity. The optimal way to…
This paper considers an optimization problem for a dynamical system whose evolution depends on a collection of binary decision variables. We develop scalable approximation algorithms with provable suboptimality bounds to provide…
Linear dynamical systems are the foundational statistical model upon which control theory is built. Both the celebrated Kalman filter and the linear quadratic regulator require knowledge of the system dynamics to provide analytic…
For continuous-time dynamical systems with reversible trajectories, the nowhere-vanishing eigenfunctions of the Koopman operator of the system form a multiplicative group. Here, we exploit this property to accelerate the systematic…
We study the convergence analysis of continuous-time dynamical systems associated with optimization methods for strongly convex functions. Recent works have proposed systematic constructions of Lyapunov functions for such analysis, while…
We analyze the dynamics of an algorithm for approximate inference with large Gaussian latent variable models in a student-teacher scenario. To model nontrivial dependencies between the latent variables, we assume random covariance matrices…
Conserved quantities, i.e. constants of motion, are critical for characterizing many dynamical systems in science and engineering. These quantities are related to underlying symmetries and they provide fundamental knowledge about physical…
In this paper we present a data driven approach for approximating dynamical systems. A dynamics is approximated using basis functions, which are derived from maximization of the information-theoretic entropy, and can be generated directly…
In this paper, we propose an efficient data-driven predictive control approach for general nonlinear processes based on a reduced-order Koopman operator. A Kalman-based sparse identification of nonlinear dynamics method is employed to…
We propose a data-driven method for controlling the frequency and convergence rate of black-box nonlinear dynamical systems based on the Koopman operator theory. With the proposed method, a policy network is trained such that the…
Data-driven surrogate models of dynamical systems based on the extended dynamic mode decomposition are nowadays well-established and widespread in applications. Further, for non-holonomic systems exhibiting a multiplicative coupling between…
We present a theory of causality in dynamical systems using Koopman operators. Our theory is grounded on a rigorous definition of causal mechanism in dynamical systems given in terms of flow maps. In the Koopman framework, we prove that…
Isostable reduction is a powerful technique that can be used to characterize behaviors of nonlinear dynamical systems in a basis of slowly decaying eigenfunctions of the Koopman operator. When the underlying dynamical equations are known,…
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…
Soft robots are challenging to model due in large part to the nonlinear properties of soft materials. Fortunately, this softness makes it possible to safely observe their behavior under random control inputs, making them amenable to…
The Distributional Koopman Operator (DKO) is introduced as a way to perform Koopman analysis on random dynamical systems where only aggregate distribution data is available, thereby eliminating the need for particle tracking or detailed…
Externally driven dense packings of particles can exhibit nonlinear wave phenomena that are not described by effective medium theory or linearized approximate models. Such nontrivial wave responses can be exploited to design…
The paper presents a framework for online learning of the Koopman operator using streaming data. Many complex systems for which data-driven modeling and control are sought provide streaming sensor data, the abundance of which can present…