Related papers: A Simulation Preorder for Koopman-like Lifted Cont…
In this work we approach the dual optimal reach-safe control problem using sparse approximations of Koopman operator. Matrix approximation of Koopman operator needs to solve a least-squares (LS) problem in the lifted function space, which…
In this paper, we consider the problem of verifying pre-opacity for discrete-time control systems. Pre-opacity is an important information-flow security property that secures the intention of a system to execute some secret behaviors in the…
A system is Koopman super-linearizable if it admits a finite-dimensional embedding as a linear system. Super-linearization is used to leverage methods from linear systems theory to design controllers or observers for nonlinear systems. We…
Koopman operator theory and Willems' fundamental lemma both can provide (approximated) data-driven linear representation for nonlinear systems. However, choosing lifting functions for the Koopman operator is challenging, and the quality of…
We present a new framework for optimal and feedback control of PDEs using Koopman operator-based reduced order models (K-ROMs). The Koopman operator is a linear but infinite-dimensional operator which describes the dynamics of observables.…
This article presents an identification methodology to capture general relationships, with application to piecewise nonlinear approximations of model predictive control for constrained (non)linear systems. The mathematical formulation…
To precondition a large and sparse linear system, two direct methods for approximate factoring of the inverse are devised. The algorithms are fully parallelizable and appear to be more robust than the iterative methods suggested for the…
Enumerating the result set of a first-order query over a relational structure of bounded degree can be done with linear preprocessing and constant delay. In this work, we extend this result towards the compressed perspective where the…
First-order probabilistic models combine representational power of first-order logic with graphical models. There is an ongoing effort to design lifted inference algorithms for first-order probabilistic models. We analyze lifted inference…
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…
The Koopman operator is an useful analytical tool for studying dynamical systems -- both controlled and uncontrolled. For example, Koopman eigenfunctions can provide non-local stability information about the underlying dynamical system.…
We present a framework for designing cheap control architectures for embodied agents. Our derivation is guided by the classical problem of universal approximation, whereby we explore the possibility of exploiting the agent's embodiment for…
The purpose of this tutorial is to give a brief introduction to linear quantum control systems. The mathematical model of linear quantum control systems is presented first, then some fundamental control-theoretic notions such as stability,…
Koopman operator theory has emerged as a powerful tool for system identification, particularly for approximating nonlinear time-invariant systems (NTIS). This paper considers a network of agents with limited observation capabilities that…
Koopman operator theory has found significant success in learning models of complex, real-world dynamical systems, enabling prediction and control. The greater interpretability and lower computational costs of these models, compared to…
In this paper, we explore the embedding of nonlinear dynamical systems into linear ordinary differential equations (ODEs) via the Carleman linearization method. Under dissipative conditions, numerous previous works have established rigorous…
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…
We present an efficient algorithm for computing the partial bisimulation preorder and equivalence for labeled transitions systems. The partial bisimulation preorder lies between simulation and bisimulation, as only a part of the set of…
This paper integrates prior knowledge into direct learning of safe controllers for linear uncertain systems under disturbances. To this end, we characterize the set of all closed-loop systems that can be explained by available prior…
Nonlinearity in dynamics has long been a major challenge in robotics, often causing significant performance degradation in existing control algorithms. For example, the navigation of bipedal robots can exhibit nonlinear behaviors even under…