Computationally Efficient Trajectory Optimization for Linear Control Systems with Input and State Constraints

This paper presents a trajectory generation method that optimizes a quadratic cost functional with respect to linear system dynamics and to linear input and state constraints. The method is based on continuous-time flatness-based trajectory generation, and the outputs are parameterized using a polynomial basis. A method to parameterize the constraints is introduced using a result on polynomial nonpositivity. The resulting parameterized problem remains linear-quadratic and can be solved using quadratic programming. The problem can be further simplified to a linear programming problem by linearization around the unconstrained optimum. The method promises to be computationally efficient for constrained systems with a high optimization horizon. As application, a predictive torque controller for a permanent magnet synchronous motor which is based on real-time optimization is presented.Comment: Proceedings of the American Control Conference (ACC), pp. 1904-1909, San Francisco, USA, June 29 - July 1, 201

Influence of nonideal LRL or TRL calibration elements on VNA S-parameter measurements

For the 7-term LRL and TRL calibration of a four-sampler vector network analyser (VNA), expressions for the deviations of the measured S-parameters of two-port test objects from their actual values are presented as functions of the deviations of the S-parameters of the LRL/TRL calibration elements from their ideal values. The obtained sensitivity coefficients are suitable for establishing the Type-B uncertainty budget for S-parameter measurements. They show how the measurements are affected by imperfect calibration elements and nonideal connections

Equilibrium and stability properties of a coupled two-component Bose-Einstein condensate

The equilibrium and stability properties of a coupled two-component BEC is studied using a variational method and the one-dimensional model of Williams and collaborators. The variational parameters are the population fraction, translation and scaling transformation of the condensate densities, assumed to have a Gaussian shape. We study the equilibrium and stability properties as a function of the strength of the laser field and the traps displacement. We find many branches of equilibrium configurations, with a host of critical points. In all cases, the signature of the onset of criticality is the collapse of a normal mode which is a linear combination of the out of phase translation and an in phase breathing oscillation of the condensate densities. Our calculations also indicate that we have symmetry breaking effects when the traps are not displacedComment: 13 pages,3 figure

Macroscopic boundary effects in the one-dimensional extended Bose-Hubbard model

We study the effect of different open boundary conditions on the insulating ground states of the one-dimensional extended Bose-Hubbard model at and near unit filling. To this end, we employ the density matrix renormalization group method with system sizes up to 250 sites. To characterize the system, various order parameters and entanglement entropies are calculated. When opposite edge potentials are added to the two ends of the chain, the inversion symmetry is explicitly broken, and the regular bulk phases appear. On the other hand, simple open boundary conditions often exhibit non-degenerate ground states with a domain wall in the middle of the chain, which induces a sign-flip of an order parameter. Such a domain wall can lead to an algebraic behavior of the off-diagonals of the single particle density matrix. We show that this algebraic behavior adds only a finite contribution to the entanglement entropy, which does not diverge as the system size increases. Therefore, it is not an indication of a superfluid phase. We confirm this picture by analytical calculations based on an effective Hamiltonian for a domain wall.Comment: 17 pages, 12 figure

Localization and spectrum of quasiparticles in a disordered fermionic Dicke model

We study a fermionic two-band model with the interband transition resonantly coupled to a cavity. This model was recently proposed to explain cavity-enhanced charge transport, but a thorough characterization of the closed system, in particular localization of various excitations, is lacking. In this work, using exact diagonalization, we characterize the system by its spectrum under various filling factors and variable disorder. As in the Dicke model, the effective light-matter coupling scales with the square root of the system size. However, there is an additional factor that decreases with increasing doping density. The transition from the weak-coupling regime to the strong-coupling regime occurs when the effective light-matter coupling is larger than the electronic bandwidth. Here, the formation of exciton-polaritons is accompanied by the formation of bound excitons. Photon spectral functions exhibit significant weights on the in-gap states between the polaritons, even without disorder. Finally, while the localization of electron-hole excitations in a disordered system is lifted by strong coupling, the same is not true for free charges, which remain localized at strong and even ultrastrong coupling. Based on this finding, we discuss scenarios for charge transport

Pubertal Stage and Depression: A Test of Within-Person Effects and Psychosocial Mediators

It has been hypothesized that pubertal development may contribute to the gender gap indepression that emerges during adolescence, but past work has been limited by the use of crosssectional analyses. The current study utilized multilevel parallel process growth models to test sex and racial differences in the association between within-person change in pubertal stage and within-person change in depressive symptoms across adolescence, controlling for age. Models were tested in a community sample of 608 youth aged 13 at baseline (Boys: M = 13.03, SD = 0.80; Girls: M = 13.08, SD = 1.00) balanced on sex and race (Caucasian/White and African American/Black). It also tested body esteem, stressful life events, and peer victimization as mediators of this relation. Results suggested that depression increased with adrenal stage among boys, but depression was unrelated to pubertal stage among girls. Further, there was no evidence of racial differences in these associations. We did not find any evidence for body esteem, stressful life events, or peer victimization as mediators of the association between pubertal stage (adrenal or gonadal) and depressive symptoms. Limitations such as the age and advanced development among participants may explain these findings.Psycholog