Related papers: On Separating Points for Ensemble Controllability
In this paper, we consider the problem of quantifying controllability and observability of a nonlinear discrete time dynamical system. We introduce the Koopman operator as a canonical representation of the system and apply a lifting…
Effective control requires knowledge of the process dynamics to guide the system toward desired states. In many control applications this knowledge is expressed mathematically or through data-driven models, however, as complexity grows…
A number of important modern applications in optimal control can be formulated as open loop control problems in which the underlying dynamical systems are subject to random inputs. These so-called ensemble control problems require the…
Ensemble control deals with the problem of using a finite number of control inputs to simultaneously steer a large population (in the limit, a continuum) of control systems. Dual to the ensemble control problem, ensemble estimation deals…
To achieve control objectives for extremely large-scale complex networks using standard methods is essentially intractable. In this work a theory of the approximate control of complex network systems is proposed and developed by the use of…
In this paper, we study uniform ensemble controllability (UEC) of linear ensemble systems defined in an infinite-dimensional space through finite-dimensional settings. Specifically, with the help of the Stone-Weierstrass theorem for…
Given a finite-dimensional time continuous control system and $\varepsilon>0$, we address the question of the existence of controls that maintain the corresponding state trajectories in the $\varepsilon$-neighborhood of any prescribed path…
For linear infinite systems the approximate controllability problem by control constraints is considered. Controllability conditions represented via system parameters are obtained. Partial differential control systems and control systems…
The control of dynamical, networked systems continues to receive much attention across the engineering and scientific research fields. Of particular interest is the proper way to determine which nodes of the network should receive external…
Scaling ideas and renormalization group approaches proved crucial for a deep understanding and classification of critical phenomena in thermal equilibrium. Over the past decades, these powerful conceptual and mathematical tools were…
We introduce a numerically stable reformulation of controllability scoring based on a scaled controllability Gramian, which remains reliably computable even for unstable systems. The resulting optimization problems define dynamics-aware…
This paper is concerned with linear parameter-dependent systems and considers the notion uniform ensemble reachability. The focus of this work is on constructive methods to compute suitable parameter-independent open-loop inputs for such…
This paper develops a closed-form spectral decomposition framework for the Gramian matrices of discrete-time linear dynamical systems. The main results provide explicit decompositions of the discrete-time controllability Gramian and its…
This work proposes a decision-making framework for partially observable systems in continuous time with discrete state and action spaces. As optimal decision-making becomes intractable for large state spaces we employ approximation methods…
Ensemble systems, pervasive in diverse scientific and engineering domains, pose challenges to existing control methods due to their massive scale and underactuated nature. This paper presents a dynamic moment approach to addressing…
State-space models (SSMs) are effective architectures for sequential modeling, but a rigorous theoretical understanding of their training dynamics is still lacking. In this work, we formulate the training of SSMs as an ensemble optimal…
Symmetric spaces arise in wide variety of problems in Mathematics and Physics. They are mostly studied in Representation theory, Harmonic analysis and Differential geometry. As many physical systems have symmetric spaces as their…
Controllability -- the possibility of performing any target dynamics by applying a set of available operations -- is a fundamental requirement for the practical use of any physical system. For finite-dimensional systems, as for instance…
We introduce a novel algorithm for the task of coherently controlling a quantum mechanical system to implement any chosen unitary dynamics. It performs faster than existing state of the art methods by one to three orders of magnitude…
A fundamental concept in control theory is that of controllability, where any system state can be reached through an appropriate choice of control inputs. Indeed, a large body of classical and modern approaches are designed for controllable…