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Adaptive tracking control for rigid body dynamics is of critical importance in control and robotics, particularly for addressing uncertainties or variations in system model parameters. However, most existing adaptive control methods are…
The realization of high-fidelity quantum control is crucial for quantum information processing, particularly in noisy environments where control strategies must simultaneously achieve precise manipulation and effective noise suppression.…
We study the exact controllability, by a reduced number of controls, of coupled cascade systems of PDE's and the existence of exact insensitizing controls for the scalar wave equation. We give a necessary and sufficient condition for the…
We discuss the quantum dynamics of an isolated composite system consisting of weakly interacting many-body subsystems. We focus on one of the subsystems, S, and study the dependence of its quantum correlations and decoherence rate on the…
This paper presents graph theoretic conditions for the controllability and accessibility of bilinear systems over the special orthogonal group, the special linear group and the general linear group, respectively, in the presence of drift…
The standard quantum formalism introduced at the undergraduate level treats measurement as an instantaneous collapse. In reality however, no physical process can occur over a truly infinitesimal time interval. A more subtle investigation of…
We investigate the universality of multi-spin systems in architectures of various symmetries of coupling type and topology. Explicit reachability sets under symmetry constraints are provided. Thus for a given (possibly symmetric)…
The optimally designed control of quantum systems is playing an increasingly important role to engineer novel and more efficient quantum technologies. Here, in the scenario represented by controlling an arbitrary quantum system via the…
Feedback control in open quantum dynamics is crucial for the advancement of various coherent platforms. However, currently only a handful of feedback master equations exist in the literature, which are restricted to specific types of…
For periodic linear control systems with bounded control range, an autonomized system is introduced by adding the phase to the state of the system. Here a unique control set (i.e., a maximal set of approximate controllability) with nonvoid…
This dissertation presents and prove the viability of a non-standard method for controlling the state of a quantum system by modifying its boundary conditions instead of relying on the action of external fields. The standard approach to…
This article considers some control problems for closed and open two-level quantum systems. The closed system's dynamics is governed by the Schr\"odinger equation with coherent control. The open system's dynamics is governed by the…
Let $\mathrm{Sl}\left( n,\mathbb{H}\right)$ be the Lie group of $n\times n$ quaternionic matrices $g$ with $\left\vert \det g\right\vert =1$. We prove that a subsemigroup $S \subset \mathrm{Sl}\left( n,\mathbb{H}\right)$ with nonempty…
Symmetry is a fundamentally important concept in many branches of physics. In this work, we discuss two types of symmetries, external symmetry and internal symmetry, which appear frequently in controlled quantum spin chains and apply them…
Coherent control, aka quantum control, is a central concept in quantum computing that is attracting increasing attention from both the quantum foundations and quantum software communities. Defining coherent control in the presence of…
A goal of the emerging field of quantum control is to develop methods for quantum technologies to function robustly in the presence of noise. Central issues are the fundamental limitations on the available information about quantum systems…
This paper addresses the application of quantum entanglement and cryptography for automation and control of dynamic systems. A dynamic system is a system where the rates of changes of its state variables are not negligible. Quantum…
In this paper we establish several results on approximate controllability of a semilinear wave equation by making use of a single multiplicative control. These results are then applied to discuss the exact controllability properties for the…
We present a theoretical study of the optimal control of a qubit interacting with a structured environment. We consider a model system in which the bath is a bosonic reservoir at zero temperature and the qubit frequency is the only control…
This paper deals with controllability properties of a cubic Ginzburg-Landau equation with dynamic boundary conditions. More precisely, we prove a local null controllability result by using a single control supported in a small subset of the…