Related papers: Finite-data error bounds for Koopman-based predict…
We provide a data-driven framework for optimal control of a continuous-time stochastic dynamical system. The proposed framework relies on the linear operator theory involving linear Perron-Frobenius (P-F) and Koopman operators. Our first…
Recently, deep Convolutional Neural Networks (CNNs) have proven to be successful when employed in areas such as reduced order modeling of parametrized PDEs. Despite their accuracy and efficiency, the approaches available in the literature…
Providing efficient and accurate parametrizations for model reduction is a key goal in many areas of science and technology. Here we present a strong link between data-driven and theoretical approaches to achieving this goal. Formal…
Koopman operator is a composition operator defined for a dynamical system described by nonlinear differential or difference equation. Although the original system is nonlinear and evolves on a finite-dimensional state space, the Koopman…
In many applications, and in systems/synthetic biology, in particular, it is desirable to compute control policies that force the trajectory of a bistable system from one equilibrium (the initial point) to another equilibrium (the target…
In this paper, we analyze stability of nonlinear model predictive control (MPC) using data-driven surrogate models in the optimization step. First, we establish asymptotic stability of the origin, a controlled steady state, w.r.t. the MPC…
This work presents a novel data-driven framework for constructing eigenfunctions of the Koopman operator geared toward prediction and control. The method leverages the richness of the spectrum of the Koopman operator away from attractors to…
This paper presents preliminary work on computing upper bounds on the estimation error covariance in the framework of the extended Kalman filter. The approach taken is using quadratic constraints to bound the dynamic nonlinearities and use…
This paper proposes Koopman operator-based Stochastic Model Predictive Control (K-SMPC) for enhanced lateral control of autonomous vehicles. The Koopman operator is a linear map representing the nonlinear dynamics in an infinite-dimensional…
Constraint handling during tracking operations is at the core of many real-world control implementations and is well understood when dynamic models of the underlying system exist, yet becomes more challenging when data-driven models are…
Neural networks hold great potential to act as approximate models of nonlinear dynamical systems, with the resulting neural approximations enabling verification and control of such systems. However, in safety-critical contexts, the use of…
In this article a special class of nonlinear optimal control problems involving a bilinear term in the boundary condition is studied. These kind of problems arise for instance in the identification of an unknown space-dependent Robin…
This research presents a novel, analytical, Koopman Operator based formulation for position and attitude dynamics which can be used to derive control strategies for underactuated systems. Compared to data driven Koopman based techniques,…
We consider the problem of synthesis of safe controllers for nonlinear systems with unknown dynamics using Control Barrier Functions (CBF). We utilize Koopman operator theory (KOT) to associate the (unknown) nonlinear system with a higher…
We study the evolution of distributions under the action of an ergodic dynamical system, which may be stochastic in nature. By employing tools from Koopman and transfer operator theory one can evolve any initial distribution of the state…
Koopman operator theory has proven to be a promising approach to nonlinear system identification and global linearization. For nearly a century, there had been no efficient means of calculating the Koopman operator for applied engineering…
Data-driven approximations of the Koopman operator are promising for predicting the time evolution of systems characterized by complex dynamics. Among these methods, the approach known as extended dynamic mode decomposition with dictionary…
Recurrent neural networks are widely used on time series data, yet such models often ignore the underlying physical structures in such sequences. A new class of physics-based methods related to Koopman theory has been introduced, offering…
This paper derives conditions under which Model Predictive Control (MPC) with terminal conditions, using a data-driven surrogate model as a prediction model, asymptotically stabilizes the plant despite approximation errors. In particular,…
An important class of physical systems that are of interest in practice are input-output open quantum systems that can be described by quantum stochastic differential equations and defined on an infinite-dimensional underlying Hilbert…