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The control of ensembles of dynamical systems is an intriguing and challenging problem, arising for example in quantum control. We initiate the investigation of optimal control of ensembles of discrete-time systems, focusing on minimising…
Inhomogeneity, in its many forms, appears frequently in practical physical systems. Readily apparent in quantum systems, inhomogeneity is caused by hardware imperfections, measurement inaccuracies, and environmental variations, and…
Controlling a large population, in the limit, a continuum, of structurally identical dynamical systems with parametric variations is a pervasive task in diverse applications in science and engineering. However, the severely underactuated…
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…
In this paper, we propose a novel probabilistic control framework for efficiently controlling an ensemble of quantum systems that can also compensate for the interaction of the systems with the external environment. The main challenge in…
We study the controlled dynamics of the {\it ensembles of points} of a Riemannian manifold $M$. Parameterized ensemble of points of $M$ is the image of a continuous map $\gamma:\Theta \to M$, where $\Theta$ is a compact set of parameters.…
In formation control, an ensemble of autonomous agents is required to stabilize at a given configuration in the plane, doing so while agents are allowed to observe only a subset of the ensemble. As such, formation control provides a rich…
Ensemble control aims to steer a population of dynamical systems using a shared control input. This paper introduces a constrained ensemble control framework for parameterized, heterogeneous robotic systems operating under state and…
Optimal control of bilinear systems has been a well-studied subject in the areas of mathematical and computational optimal control. However, effective methods for solving emerging optimal control problems involving an ensemble of…
Coherent optical control schemes exploit the coherence of laser pulses to change the phases of interfering dynamical pathways in order to manipulate dynamical processes. These active control methods are closely related to dynamical…
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…
It has recently been shown, by application of statistical mechanical methods to determine the canonical ensemble governing the equilibrium distribution of operator initial values, that complex quantum field theory can emerge as a…
Scientists, engineers, biologists, and technology specialists universally leverage image segmentation to extract shape ensembles containing many thousands of curves representing patterns in observations and measurements. These large curve…
Control theory of dynamical systems offers a powerful framework for tackling challenges in deep neural networks and other machine learning architectures. We show that concepts such as simultaneous and ensemble controllability offer new…
Research on control using models based on machine-learning methods has now shifted to the practical engineering stage. Achieving high performance and theoretically guaranteeing the safety of the system is critical for such applications. In…
Ensemble systems appear frequently in many engineering applications and, as a result, they have become an important research topic in control theory. These systems are best characterized by the evolution of their underlying state…
Calculating thermodynamic potentials and observables efficiently and accurately is key for the application of statistical mechanics simulations to materials science. However, naive Monte Carlo approaches, on which such calculations are…
Several theorems on the volume computing of the polyhedron spanned by a n-dimensional vector set with the finite-interval parameters are presented and proved firstly, and then are used in the analysis of the controllable regions of the…
Controlled Lagrangian and matching techniques are developed for the stabilization of relative equilibria and equilibria of discrete mechanical systems with symmetry as well as broken symmetry. Interesting new phenomena arise in the…
Quantum machine learning witnesses an increasing amount of quantum algorithms for data-driven decision making, a problem with potential applications ranging from automated image recognition to medical diagnosis. Many of those algorithms are…