Constant Constraint Research Articles

A Constant Rank Constraint Qualification in Continuous-Time Nonlinear Programming

The paper addresses continuous-time nonlinear programming problems with equality and inequality constraints. First and second order necessary optimality conditions are obtained under a constant rank type constraint qualification. The first order necessary conditions are of Karush-Kuhn-Tucker type.

High-Resolution Radar Waveform Design Based on Target Information Maximization

Although the transmit radar waveform design problem for maximizing target information has been studied widely in the past, the resolution requirement is normally ignored in such designs. Using maximizing target information as a criterion, a new radar waveform design method meeting the high-resolution requirement is proposed in this article, which makes no assumptions on the statistical distribution of target scattering. The objective function is proposed by maximizing the Pearson correlation coefficient and the design is then transformed into an optimization problem, which is solved in two steps. First, a closed-form expression for the discretized waveform with constant power constraint is derived in the time domain. Second, based on the bandwidth analysis of the optimal solution, a resolution improvement method considering information distortion is introduced and a suboptimal waveform is proposed while satisfying the constant power and resolution requirements. Finally, performance of the proposed radar waveform in terms of information acquisition, classification, and resolution is analyzed and compared with the classic high-resolution linear frequency modulated waveform (LFMW). Simulation results show that the resolution of the suboptimal waveform is slightly lower than the LFMW, but more desirable in terms of peak sidelobe ratio, information acquisition, and classification.

The Megamaser Cosmology Project. XIII. Combined Hubble Constant Constraints

Abstract We present a measurement of the Hubble constant made using geometric distance measurements to megamaser-hosting galaxies. We have applied an improved approach for fitting maser data and obtained better distance estimates for four galaxies previously published by the Megamaser Cosmology Project: UGC 3789, NGC 6264, NGC 6323, and NGC 5765b. Combining these updated distance measurements with those for the maser galaxies CGCG 074-064 and NGC 4258, and assuming a fixed velocity uncertainty of 250 km s−1 associated with peculiar motions, we constrain the Hubble constant to be H 0 = 73.9 ± 3.0 km s−1 Mpc−1 independent of distance ladders and the cosmic microwave background. This best value relies solely on maser-based distance and velocity measurements, and it does not use any peculiar velocity corrections. Different approaches for correcting peculiar velocities do not modify H 0 by more than ±1σ, with the full range of best-fit Hubble constant values spanning 71.8–76.9 km s−1 Mpc−1. We corroborate prior indications that the local value of H 0 exceeds the early-universe value, with a confidence level varying from 95% to 99% for different treatments of the peculiar velocities.

Symbol-independent weight magnitude design for antenna array based directional modulation

Directional modulation (DM) as a physical layer security technique has been studied from many different aspects. Recently, a constant magnitude constraint for all antennas of an array for a given modulation symbol was proposed. However, the proposed design does not work for multiple beams. In practice, multi-beam DM may often be required. As a compromise, instead of setting the same magnitude for all antennas for a given symbol, in this paper, a symbol independent magnitude constraint for each antenna is proposed for the first time. With the same magnitude for different symbols for each antenna, only phase changes between different symbols are needed, which can form multiple DM beams simultaneously, while still reducing the implementation complexity of the whole system. Design examples are provided to show the effectiveness of the proposed design.

Obtaining a scalar fifth force via a symmetry-breaking coupling between the scalar field and matter

A matter-coupled scalar field model is presented in obtaining a scalar fifth force when the constraint of the current cosmological constant is satisfied. The interaction potential energy density between the scalar field and matter has a symmetry-breaking form with two potential wells. The cosmological constant is proven to be a value of the scalar-field's self-interaction potential energy density at the minimum of an effective matter-density-dependent potential energy density. The effective potential is a sum of the interaction potential and the self-interaction potential of the scalar field. The scalar field can stably sit at the minimum and then the time-dependent cosmological `constant' behaves like a constant. The observed cosmic acceleration can be accounted for the scalar field. The scalar field is also extrapolated to account for inflation at the inflationary era of the Universe. In this era matter fluid is relativistic and then the interaction potential wells vanish. The unconfined quintessence therefore dominates the evolution of the Universe. It is concluded that `Planck 2018 results' favour the closed space of the Universe. The reasons are not only the measured value of the current Hubble constant, but also the observed feature of a concave potential in the framework of single-field inflationary models. By invoking a pseudo-potential in the inflationary era, the concave feature can be attributed to the pseudo-potential although the self-interaction potential is a convex function. The pseudo-potential is defined by a sum of the self-interaction potential and the energy density scale of the curvature of the Universe. It is that the positive curvature leads to the concave feature of the pseudo-potential.

Stabilization for continuous-time switched linear systems: A mixed switching scheme

For a practical system with switching actions, it is necessary to restrict the switching frequency under the limit of its physical constraints, avoiding potential damage to the equipment. In this paper, a mixed switching scheme with both state-dependent and time-dependent functions is designed to reduce the switching frequency. First, a constant dwell-time constraint is considered and a switching logic called dwell-time min-switching rule is designed to ensure the asymptotic stability of switched system. Particularly, our result is found to be able to cover some previous results for min-switching strategy. Subsequently, a switching function with ranged dwell time scheme which means the dwell time belongs to a range other than a fixed value is taken into account. Furthermore, L2 stabilization is studied, and the feedback controller design is incorporated into the framework of dwell-time min-switching logic. Finally, several numerical examples are presented to illustrate our results.

Updated fundamental constant constraints from Planck 2018 data and possible relations to the Hubble tension

ABSTRACT We present updated constraints on the variation of the fine structure constant, αEM, and effective electron rest mass, me, during the cosmological recombination era. These two fundamental constants directly affect the ionization history at redshift z ≃ 1100 and, thus, modify the temperature and polarization anisotropies of the cosmic microwave background (CMB) measured precisely with Planck . The constraints on αEM tighten slightly due to improved Planck 2018 polarization data but otherwise remain similar to previous CMB analysis. However, a comparison with the 2015 constraints reveals a mildly discordant behaviour for me, which from CMB data alone is found below its local value. Adding baryon acoustic oscillation data brings me back to the fiducial value, $m_{\rm e}=(1.0078\pm 0.0067)\, m_{\rm e,0}$, and also drives the Hubble parameter to H0 = 69.1 ± 1.2(in units of ${\rm km \, s^{-1} \, Mpc^{-1} }$). Further adding supernova data yields $m_{\rm e}=(1.0190\pm 0.0055)\, m_{\rm e,0}$ with H0 = 71.24 ± 0.96. We perform several comparative analyses using the latest cosmological recombination calculations to further understand the various effects. Our results indicate that a single-parameter extension allowing a slightly increased value of me (≃3.5σ above me, 0) could play a role in the Hubble tension.

A new design of double-layered microchannel heat sinks with wavy microchannels and porous-ribs

A new design of double-layered microchannel heat sinks, which combines wavy microchannels with porous vertical ribs, is proposed in this work. The flow and heat transfer behaviors of the new design are investigated via a three-dimensional solid–fluid conjugate heat sink model. The superiority of the new design is highlighted by comparing the new design with three existing double-layered designs under constant pumping power constraints. The three existing designs include a design with straight microchannels and solid-ribs, a design with straight microchannels and porous-ribs, and a design with wavy microchannels and solid-ribs. The results show that porous-ribs reduce the pressure drop across heat sinks, whereas wavy microchannels induce Dean vortices and enhance coolant mixing. In a low pumping power region of 0.005 to 0.01 W, the coolant inlet velocity is found to be the most dominant factor to determine the cooling capacity of heat sinks, whereas in a high pumping power region of 0.1 to 0.2 W, the coolant mixing becomes the dominant one. The new design has both wavy microchannels and porous-ribs, thus providing the best cooling capacity among the four double-layered heat sinks in the whole pumping power range of 0.005 to 0.2 W. The new design is further optimized by single-parameter analyses. It is found that with a fixed pumping power of 0.05 W as constraint, there is an optimal wavelength or an optimal amplitude of wavy units to achieve the lowest thermal resistance; however, the thermal resistance monotonously reduces with the increase in porous permeability or the decrease in quadratic drag factor.

Physics-Based Simulation of Ocean Scenes in Marine Simulator Visual System

The realistic simulation of ocean scenes is of great significance in many scientific fields. We propose an improved Smoothed Particle Hydrodynamics (SPH) framework to simulate the ocean scenes. The improved SPH combines nonlinear constant density constraints and divergence-free velocity field constraint. Density constraints adjust the particle distribution on position layer, so that the density is constrained to a constant state. The addition of the divergence-free velocity field constraint significantly accelerates the convergence of constant density constraint and further reduces the density change. The simulation results show that the improved SPH has high solution efficiency, large time steps, and strong stability. Then, we introduce a unified boundary handling model to simulate coupling scenes. The model samples the boundary geometry as particles by means of single layer nonuniform sampling. The contribution of the boundary particles is taken into account when the physical quantities of fluid particles are computed. The unified model can handle various types of complex geometry adaptively. When rendering the ocean, we propose an improved anisotropic screen space fluid method, which alleviates the discontinuity problem near the boundary and maintains the anisotropy of particles. The research provides a theoretical reference for the highly believable maritime scene simulation in marine simulators.

Hybrid combiner design for downlink massive MIMO systems

We consider a hybrid combiner design for downlink massive multiple-input multiple-output systems when there is residual inter-user interference and each user is equipped with a limited number of radio frequency (RF) chains (less than the number of receive antennas). We propose a hybrid combiner that minimizes the mean-squared error (MSE) between the information symbols and the ones estimated with a constant amplitude constraint on the RF combiner. In the proposed scheme, an iterative alternating optimization method is utilized. At each iteration, one of the analog RF and digital baseband combining matrices is updated to minimize the MSE by fixing the other matrix without considering the constant amplitude constraint. Then, the other matrix is updated by changing the roles of the two matrices. Each element in the RF combining matrix is obtained from the phase component of the solution matrix of the optimization problem for the RF combining matrix. Simulation results show that the proposed scheme performs better than conventional matrix-decomposition schemes.

Energy-Efficient Transceiver Design for Cache-Enabled Millimeter-Wave Systems

In recent years, network densification and edge caching become effective approaches to reduce the burden on the fronthaul links and the content delivery latency for wireless communication systems. However, maximizing system spectral efficiency cannot directly provide any insight on their energy requirements/efficiency for cache-enabled millimeter-wave (mmWave) radio access networks (RANs). In this paper, we study the design of energy-efficient transceiver, consisting of analog and digital precoder/combiner, for the delivery phase of the downlink of cache-enabled mmWave RANs. Due to the non-convexity of the delivery rate and objective, the coupling between the digital and analog precoders/combiners, and the constant module constraint on the elements of analog precoders/combiners, the problem of interest is non-convex and hard to obtain the global optimal solution, even the local optimal solution. To this end, we first overcome these challenges one-by-one and then transform the original problem into tractable one. Finally, an algorithmic framework that converges to the Karush-Kuhn-Tucker solution with provable is developed to achieve the design of energy-efficient transceiver. Numerical results are provided to evaluate the performance of the proposed algorithm, where fully digital precoding is used as benchmark.

Constant Reflection Attenuation Constraint for Incoming Signals on Metasurface in Positional Modulation Design

Metasurface based positional modulation design has been introduced recently, where a given modulation pattern can only be received at certain desired positions by the proposed method. However, the magnitude of weight coefficient of each element on metasurface varies from one other, representing an attenuation of the amplitude of incoming signal in different degrees. In this paper, a constant reflection attenuation constraint for incoming signals is proposed for the first time, and the proposed method can be extended with a post-processing process to the ideal case where there is no reflection attenuation.

On the integrability of the SIRD epidemic model

In this paper, Lie symmetry and Painleve Techniques are applied to the SIRD (Susceptible, Infected, Recovered and Dead) model. A demonstration of the integrability of the model is provided to present an explicit solution. The study revealed a complex chaotic behaviour at a specific value of constant constraints. However, the system fails to pass the Painleve test while constraints reach values equivalent to the corresponding complex chaotic behaviour. The two-dimensional Lie symmetry algebra and the commutator table of the infinitesimal generators are obtained. Lie symmetry analysis serves to linearize the nonlinear system and find the corresponding exact solution.

MPC-based frequency control strategy with a dynamic energy interaction scheme for the grid-connected microgrid system

In a microgrid system (MGS), effective frequency control strategies are extremely significant for maintaining the system frequency stabilization. Therefore, a model predicted control (MPC) method is presented to regulate the frequency fluctuation of the grid-connected microgrid system (GCMGS). The primary frequency control for the diesel generator (DG) and the secondary frequency control with the (MPC) for the energy storage (ES) are proposed in this paper. Simultaneously, in order to mitigate the power fluctuation caused by the load demand side and the renewable energy sources, a dynamic energy interaction scheme (DEIS) is designed. The power exchange between the MGS and utility grid can be achieved. Due to the randomness of the renewable energy sources, the system frequency is hard to remain stable. Thus, a constant constraint renewable energy sources power output is utilized to reduce the uncertainty of the renewable energy sources. Finally, several comparison experiments have been executed to illustrate the availability of the proposed control strategy.

Low-Complexity Analog Beamforming for mmWave Large-Scale MISOME Wiretap Channel

With the popularization of large-scale antenna arrays in wireless communication, the conventional fully digital beamforming, which requires dedicated radio frequency (RF) chain per antenna element, is not viable for large-scale antenna systems due to its prohibitively high hardware cost. On the contrary, the analog beamforming design only requires one RF chain for all antenna elements, and has been widely investigated in recent years. In this letter, we consider the secure analog beamforming design that maximizes the secrecy rate in the large-scale multi-input single-output multi-eavesdropper (MISOME) wiretap channel. However, the associated secrecy rate maximization (SRM) problem is naturally non-convex due to the constant envelope constraint induced by the analog beamformer. To handle the problem, a low-complexity algorithm that combines the Dinkelbach approach and iterative coordinate ascent (ICA) algorithm is proposed to obtain a high-quality suboptimal solution. Numerical results illustrate that the proposed algorithm achieves both higher secrecy rate performance and lower complexity as compared to the existing schemes.

On Lipschitz-like continuity of a class of set-valued mappings

ABSTRACT We study set-valued mappings defined by solution sets of parametric systems of equalities and inequalities. We prove Lipschitz-like continuity of these mappings under relaxed constant rank constraint qualification.

Adaptive Neural Network Control for Uncertain Time-Varying State Constrained Robotics Systems

In this paper, we design an adaptive neural network (NN) controller of uncertain ${n}$ -joint robotic systems with time-varying state constraints. By proposing a nonlinear mapping, the robotic systems are transformed into the multiple-input, multiple-output systems. Compared with constant constraints, the time-varying state constraints are more general in the real systems. To overcome the design challenge, the time-varying barrier Lyapunov function is introduced to ensure that the states of the robotic systems are bounded within the predetermined time-varying range. The NN approximations are employed to approximate the uncertain parametric and unknown functions in the robotic systems. Based on the Lyapunov analysis, it can be proved that all signals of robotic systems are bounded; the tracking errors of system output converge on a small neighborhood of zero and the time-varying state constraints are never violated. Finally, a simulation example is performed to demonstrate the feasibility of the proposed approach.

Fluid-structure coupling topology optimization based on added mass method

A wet model topology optimization method based on added mass method and bidirectional evolutionary structure optimization algorithm is proposed to maximize the natural frequency of fluid-structure coupling system. The fluid-structure coupling equation of the finite element method and the sensitivity formula of the element are analyzed simultaneously, and then the coupling optimization model is established. Under the constraints of structure volume, the weighted natural frequencies of single-objective and multi-objective of the coupled system are maximized to optimize the underwater coupled structure. The numerical results show that the evolutionary methods can be applied to this kind of problem effectively and efficiently. Besides, the optimization results of cases have smooth boundaries and the numerical stability of the optimization algorithm is good. Under constant volume constraints, the single-order natural frequency is increased by more than 380%. The results of multi-objective weighted optimization show that the weighted coefficients are final. The larger the weighting coefficient is, the closer the topological form is to the optimal result of the model.

An Active Boost Power Converter for Improving the Performance of Switched Reluctance Generators in DC Generating Systems

In this article, an active boost power converter is proposed for switched reluctance generators (SRGs) that support low-voltage dc loads or dc microgrids. In the proposed converter, a front-end circuit is added to a conventional asymmetric half bridge power converter. With the front-end circuit, excitation voltage and demagnetization voltage can be regulated flexibly to improve the system efficiency and increase the maximum output power under constant phase current constraints. Then a multiloop control strategy is developed to control the power converter. The multiloop controller contains a power controller and a boost voltage controller. The power controller is designed to control SRG over the entire operating range. The boost voltage controller is designed to control the front-end circuit. Two strategies are compared for the boost voltage control: voltage hysteresis control strategy and power flow control strategy. Comparing with voltage hysteresis control, proposed power flow control shows improvements in minimizing output voltage ripple and is suggested for the proposed converter. In the end, simulation and experimental results are given to verify the feasibility of the proposed power converter and control strategy. Comparisons between the proposed converter and the conventional converter are also given for evaluation.

Inflationary models that generalize the constant roll constraint

Recently a class of inflationary models satisfying the constant rate of roll constraint, ̈ϕ+(3+α)Hϕ̇=0, has been studied and compared with the latest cosmological observational data. We consider the broader class of constraints ̈ϕ+α1/2ϕ̇+α2 Hϕ̇=0 and find an exact particular solution, without initial singularity, which is an attractor of the dynamics governed by a positive periodic potential V(ϕ)=E+ F cos (Ω ϕ )+G cos (2 Ω ϕ ). The spectral index ns and the tensor to scalar ratio r are consistent with the recent observational data.