Stability of Model Predictive Control with Soft Constraints

We derive stability conditions for Model Predictive Control (MPC) with hard constraints on the inputs and "soft" constraints on the outputs for an infinitely long output horizon. We show that with state feedback MPC is globally asymptotically stabilizing if and only if all the eigenvalues of the open loop system are in the closed unit disk. With output feedback the eigenvalues must be strictly inside the unit circle. The on-line optimization problem defining MPC can be posed as a finite dimensional quadratic program even though the output constraints are specified over an infinite horizon

Высшее образование в Китае

Данная статья посвящена особенностям высшего образования в Китае. Автор делает акцент на отличительных чертах обучения в университетах Китая и студенческой жизни.The article is devoted to the features of higher education in China. The author focuses on the distinctive features of studying at Chinese universities and student life

Phase diagram of two-species Bose-Einstein condensates in an optical lattice

The exact macroscopic wave functions of two-species Bose-Einstein condensates in an optical lattice beyond the tight-binding approximation are studied by solving the coupled nonlinear Schrodinger equations. The phase diagram for superfluid and insulator phases of the condensates is determined analytically according to the macroscopic wave functions of the condensates, which are seen to be traveling matter waves.Comment: 13 pages, 2 figure

First-principles materials design of high-performing bulk photovoltaics with the LiNbO3_3 structure

The bulk photovoltaic effect is a long-known but poorly understood phenomenon. Recently, however, the multiferroic bismuth ferrite has been observed to produce strong photovoltaic response to visible light, suggesting that the effect has been underexploited as well. Here we present three polar oxides in the LiNbO$_3$ structure that we predict to have band gaps in the 1-2 eV range and very high bulk photovoltaic response: PbNiO$_3$, Mg$_{1/2}$Zn$_{1/2}$PbO$_3$, and LiBiO$_3$. All three have band gaps determined by cations with $d^{10}s^0$ electronic configurations, leading to conduction bands composed of cation $s$-orbitals and O $p$-orbitals. This both dramatically lowers the band gap and increases the bulk photovoltaic response by as much as an order of magnitude over previous materials, demonstrating the potential for high-performing bulk photovoltaics

Constrained Stabilization of Discrete-Time Systems

Based on the growth rate of the set of states reachable with unit-energy inputs, we show that a discrete-time controllable linear system is globally controllable to the origin with constrained inputs if and only if all its eigenvalues lie in the closed unit disk. These results imply that the constrained Infinite-Horizon Model Predictive Control algorithm is globally stabilizing for a sufficiently large number of control moves if and only if the controlled system is controllable and all its eigenvalues lie in the closed unit disk. In the second part of the paper, we propose an implementable Model Predictive Control algorithm and show that with this scheme a discrete-time linear system with n poles on the unit disk (with any multiplicity) can be globally stabilized if the number of control moves is larger than n. For pure integrator systems, this condition is also necessary. Moreover, we show that global asymptotic stability is preserved for any asymptotically constant disturbance entering at the plant input

Projector operators for the no-core shell model

Projection operators for the use within ab initio no-core shell model, are suggested.Comment: 3 page

Non-markovian dynamics of double quantum dot charge qubit with static bias

The dynamics of charge qubit in double quantum dot coupled to phonons is investigated theoretically. The static bias is considered. By means of the perturbation approach based on unitary transformations, the dynamical tunneling current is obtained explicitly. The biased system displays broken symmetry and a significantly larger coherence-incoherence transition critical point $\alpha _{c}$. We also analyzed the decoherence induced by piezoelectric coupling phonons in detail. The results show that reducing the coupling between system and bath make coherence frequency increase and coherence time prolong. To maintain quantum coherence, applying static bias also is a good means.Comment: 13 pages, 5 figure