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This thesis addresses the problem of developing a quantum counter-part of the well established classical theory of control. We dwell on the fundamental fact that quantum states are generally not perfectly distinguishable, and quantum…
Two observables are called complementary if preparing a physical object in an eigenstate of one of them yields a completely random result in a measurement of the other. We investigate small sets of complementary observables that cannot be…
This paper is devoted to the study of controllability of linear systems on generalized Heisenberg groups. Some general necessary controllability conditions and some sufficient ones are provided. We introduce the notion of decoupled systems,…
Infinite-dimensional control systems with outputs are considered in the Hamiltonian formulation with generalized coordinates. An explicit scheme for constructing a dynamic observer for this class of systems is proposed with arbitrary gain…
A general scheme to seek for the relations between entanglement and bservables is proposed in principle. In two-qubit systems with enough general Hamiltonian, we find the entanglement to be the functions of observables for six kinds of…
A mapping is obtained relating analytical radial Coulomb systems in any dimension greater than one to analytical radial oscillators in any dimension. This mapping, involving supersymmetry-based quantum-defect theory, is possible for…
We consider a terminal control problem for processes governed by a nonlinear system of fractional ODEs. In order to show existence of the control, we first consider the linear counterpart of the system and reprove a number of classical…
Relative observability has been introduced and studied in the framework of partially observed discrete-event systems as a condition stronger than observability, but weaker than normality. However, unlike observability, relative…
We give a constructive proof of a global controllability result for an autonomous system of ODEs guided by bounded locally Lipschitz and divergence free (i.e.\ incompressible) vector field, when the phase space is the whole Euclidean space…
An input-output model of a two-level quantum system in the Heisenberg picture is of bilinear form with constant system matrices, which allows the introduction of the concepts of controllability and observability in analogy with those of…
Various notions from geometric control theory are used to characterize the behavior of the Markovian master equation for N-level quantum mechanical systems driven by unitary control and to describe the structure of the sets of reachable…
For systems that are not observable at the very equilibrium of interest to be stabilized, output-feedback stabilization is considerably challenging. In this paper we solve this control problem for the case-study of a second-order system…
Designing Luenberger observers for nonlinear systems involves the challenging task of transforming the state to an alternate coordinate system, possibly of higher dimensions, where the system is asymptotically stable and linear up to output…
The paper studies a class of quadratic optimal control problems for partially observable linear dynamical systems. In contrast to the full information case, the control is required to be adapted to the filtration generated by the…
Building on the recent notion of non-uniform complete observability, and on the fact that this property ensures non-uniform exponential detectability, this paper establishes the converse implication under suitable additional assumptions.…
We propose a correlation of local observables on many sites in macroscopic quantum systems. By measuring the correlation one can detect, if any, superposition of macroscopically distinct states, which we call macroscopic entanglement, in…
We consider the problem of adaptive observer design in the settings when the system is allowed to be nonlinear in the parameters, and furthermore they are to satisfy additional feasibility constraints. A solution to the problem is proposed…
We study state estimation for nonlinear differential-algebraic systems, where the nonlinearity satisfies a Lipschitz condition or a generalized monotonicity condition or a combination of these. The presented observer design unifies earlier…
This paper studies the problem of steering a linear time-invariant system subject to state and input constraints towards a goal location that may be inferred only through partial observations. We assume mixed-observable settings, where the…
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…