Related papers: Data-driven optimal control under safety constrain…
In the Sparse Linear Regression (SLR) problem, given a $d \times n$ matrix $M$ and a $d$-dimensional query $q$, the goal is to compute a $k$-sparse $n$-dimensional vector $\tau$ such that the error $||M \tau-q||$ is minimized. This problem…
The most frequently used condition for sampling matrices employed in compressive sampling is the restricted isometry (RIP) property of the matrix when restricted to sparse signals. At the same time, imposing this condition makes it…
The Koopman operator approach provides a powerful linear description of nonlinear dynamical systems in terms of the evolution of observables. While the operator is typically infinite-dimensional, it is crucial to develop finite-dimensional…
Koopman decomposition is a non-linear generalization of eigen-decomposition, and is being increasingly utilized in the analysis of spatio-temporal dynamics. Well-known techniques such as the dynamic mode decomposition (DMD) and its linear…
Koopman analysis of a general dynamics system provides a linear Koopman operator and an embedded eigenfunction space, enabling the application of standard techniques from linear analysis. However, in practice, deriving exact operators and…
Sparsity-constrained optimization underlies many problems in signal processing, statistics, and machine learning. State-of-the-art hard-thresholding (HT) algorithms rely on an appropriately selected continuous step-size parameter to ensure…
Low-rank matrix approximation (LRMA) is a powerful technique for signal processing and pattern analysis. However, its potential for data compression has not yet been fully investigated in the literature. In this paper, we propose sparse…
Providing rigorous reachability guarantees for unknown complex systems is a crucial and challenging task. In this paper, we present a novel data-driven framework that addresses this challenge by leveraging Koopman operator theory. Instead…
Classically, the optimal control problem in the presence of an adversary is formulated as a two-player zero-sum differential game or an $H_\infty$ control problem. The solution to these problems can be obtained by solving the…
The accurate modeling and control of nonlinear dynamical effects are crucial for numerous robotic systems. The Koopman formalism emerges as a valuable tool for linear control design in nonlinear systems within unknown environments. However,…
The path-integral control, which stems from the stochastic Hamilton-Jacobi-Bellman equation, is one of the methods to control stochastic nonlinear systems. This paper gives a new insight into nonlinear stochastic optimal control problems…
We consider the sparse optimization problem with nonlinear constraints and an objective function, which is given by the sum of a general smooth mapping and an additional term defined by the $ \ell_0 $-quasi-norm. This term is used to obtain…
In recent years, the success of the Koopman operator in dynamical systems analysis has also fueled the development of Koopman operator-based control frameworks. In order to preserve the relatively low data requirements for an approximation…
The present work deals with quantitative two-phase reach-avoid problems on nonlinear control systems. This class of optimal control problem requires the plant's state to visit two (rather than one) target sets in succession while minimizing…
The modeling of nonlinear dynamics based on Koopman operator theory, which is originally applicable only to autonomous systems with no control, is extended to non-autonomous control system without approximation to input matrix B. Prevailing…
The study of the Two-Body and Circular Restricted Three-Body Problems in the field of aerospace engineering and sciences is deeply important because they help describe the motion of both celestial and artificial satellites. With the growing…
Koopman liftings have been successfully used to learn high dimensional linear approximations for autonomous systems for prediction purposes, or for control systems for leveraging linear control techniques to control nonlinear dynamics. In…
In many human-in-the-loop robotic applications such as robot-assisted surgery and remote teleoperation, predicting the intended motion of the human operator may be useful for successful implementation of shared control, guidance virtual…
We present a systematic approach to the optimal placement of finitely many sensors in order to infer a finite-dimensional parameter from point evaluations of the solution of an associated parameter-dependent elliptic PDE. The quality of the…
The Koopman operator enables simplified representations for nonlinear systems in data-driven optimal control, but the accompanying uncertainties inevitably induce deviations in the optimal controller and associated value function. This…