Related papers: Non-Holonomic Control I
In this paper we use an affine connection formulation to study an optimal control problem for a class of nonholonomic, under-actuated mechanical systems. In particular, we aim at minimizing the norm-squared of the control input to move the…
A novel control design approach for general nonlinear systems is presented in this paper. The approach is based on the identification of a polynomial model of the system to control and on the on-line inversion of this model. An efficient…
We present a control-theoretic analysis of the system consisting of a two-level atom coupled with a quantum harmonic oscillator. We show that by applying external fields with just two resonant frequencies, any desired unitary operator can…
Quantum coherence inherently affects the dynamics and the performances of a quantum machine. Coherent control can, at least in principle, enhance the work extraction and boost the velocity of evolution in an open quantum system. Using…
In this paper a method of controlling nonholonomic systems within the port-Hamiltonian (pH) framework is presented. It is well known that nonholonomic systems can be represented as pH systems without Lagrange multipliers by considering a…
The physical resources available to access and manipulate the degrees of freedom of a quantum system define the set $\cal A$ of operationally relevant observables. The algebraic structure of $\cal A$ selects a preferred tensor product…
Current studies about the continuous-variable systems in non-Hermitian quantum mechanics heavily revolved around the singularities in the eigenspectrum by mimicking their discrete-variable counterparts. Discussions over the nonunitary…
We present a fast scheme for arbitrary unitary control of interacting bosonic atoms in a double-well. Assuming fixed inter-well tunnelling rate and intra-well interaction strength, we control the many-atom state by a discrete sequence of…
We propose a technique to design control algorithms for a class of finite dimensional quantum systems so that the control law does not present discontinuities. The class of models considered admits a group of symmetries which allows us to…
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…
In this Note, we review the main existing results, methods, and some key open problems on the controllability of nonlinear hyperbolic and parabolic equations. Especially, we describe our recent universal approach to solve the local…
Perfect transfer of {\em unknown} states across distinct nodes is a basic function in bosonic quantum networks. Here we develop a general theory to construct an $N$-node bosonic network governed by the time-dependent Hamiltonian, as the…
A stable and fast path linking two arbitrary states of a quantum system is generally required for state-engineering protocols, such as stimulated Raman adiabatic passage, shortcuts to adiabaticity, and holonomic transformation. Such a path…
Any quantum system with a non-trivial Hamiltonian is able to simulate any other Hamiltonian evolution provided that a sufficiently large group of unitary control operations is available. We show that there exist finite groups with this…
Virtual constraints are relations imposed on a control system that become invariant via feedback control, as opposed to physical constraints acting on the system. Nonholonomic systems are mechanical systems with non-integrable constraints…
We present control schemes for open quantum systems that combine decoupling and universal control methods with coding procedures. By exploiting a general algebraic approach, we show how appropriate encodings of quantum states result in…
We present a scheme for controlling the state of a quantum system by modifying the boundary conditions. This constitutes an infinite-dimensional control problem. We provide conditions for the existence of solutions of the dynamics and prove…
Structured decompositions of a desired unitary operator are employed to derive control schemes that achieve certain control objectives for finite-level quantum systems using only sequences of simple control pulses such as square waves with…
One major objective of controlling classical chaotic dynamical systems is exploiting the system's extreme sensitivity to initial conditions in order to arrive at a predetermined target state. In a recent letter [Phys.~Rev.~Lett. 130, 020201…
Sufficient conditions for complete controllability of $N$-level quantum systems subject to a single control pulse that addresses multiple allowed transitions concurrently are established. The results are applied in particular to Morse and…