Matching Equation Research Articles

Robust dynamic state feedback for underactuated systems with linearly parameterized disturbances

SummaryThis article investigates the control problem for underactuated port‐controlled Hamiltonian systems with multiple linearly parameterized additive disturbances including matched, unmatched, constant, and state‐dependent components. The notion of algebraic solution of the matching equations is employed to design an extension of the interconnection and damping assignment passivity‐based control methodology that does not rely on the solution of partial differential equations. The result is a dynamic state‐feedback that includes a disturbance compensation term, where the unknown parameters are estimated adaptively. A simplified implementation of the proposed approach for underactuated mechanical systems is detailed. The effectiveness of the controller is demonstrated with numerical simulations for the magnetic‐levitated‐ball system and for the ball‐on‐beam system.

Climate-smart agriculture, household income and asset accumulation among smallholder farmers in the Nyando basin of Kenya

Climate change, characterized by rising average temperatures and changes in rainfall amounts and patterns, remains a major threat to rural livelihoods. For smallholder households that heavily depend on agriculture, adaptation and mitigation measures, including coping strategies are therefore needed to secure household livelihoods and incomes. In this article, we assess the impacts on livelihood outcomes, of climate smart agricultural (CSA) practices that are promoted as adaptative strategies against effects of climate change. Using data from a survey of households in Nyando basin in Kenya, we combine statistical matching and simultaneous equation econometric modelling, to evaluate pathways through which CSA practices impact on household asset accumulation and income. We find that uptake of multiple stress-tolerant crops improves household income by 83%, which in turn improves household asset accumulation. Impact pathway modelling also show that adoption of improved livestock breeds significantly reduces household income by 76%. For improved livestock, however, household income does not impact on asset accumulation, possibly because income is invested in form of livestock rather than household assets. These findings show that adoption of multiple stress-tolerant crops improves household assets accumulation via the income pathway. However, given an option, households would invest increased incomes in livestock assets, confirming that livestock are a form of savings, which can be liquidated to bridge household income gaps. This is a better resilience measure as compared to investment in domestic household assets.

Automatic Method for Extraction of Complex Road Intersection Points From High-Resolution Remote Sensing Images Based on Fuzzy Inference

Automatic extracting road intersection points is essential for applications such as data registration between vector data and remote sensing images, aircraft-assisted navigation. However, at a large scale, it is difficult to quickly and accurately extract road intersection points due to the problems caused by complex structures, geometric texture noise interference. In this context, taking OpenStreetMap (OSM) data as priori knowledge, we propose a method for automatic extraction of complex road intersection points based on fuzzy inference. First, OSM data are analyzed to obtain structural information of intersection points. Local search areas are built around the intersection points. Second, within the local search area, the candidate intersection point set are generated. Meanwhile the input image is segmented using multiresolution segmentation; then we establish a fuzzy rule to infer the road area from the segmentation result. The fuzzy indexes and rules are established for the candidate intersection point set to deduce the road intersection area. Finally, based on the results of the previous step, the road intersection points are extracted based on the line segment constraint, structure matching, and linkage equation. Three sets of high-resolution remote sensing images were used to verify the feasibility of the method. We demonstrate that the correctness and positioning accuracy of this method are superior to those of other methods through contrastive analysis.

Near Crack Line Elastic‐Plastic Field for Mode I Cracks under Plane Stress Condition in Rectangular Coordinates

By using the crack line analysis method, this paper carries out an elastic‐plastic analysis for mode I cracks under plane stress condition in an elastic perfectly plastic solid and obtains the general form of matching equations of the elastic stress field and the plastic stress field near the crack line in rectangular coordinate form. The analysis in rectangular coordinates in this paper avoids the conversion from rectangular coordinates into polar coordinates in the existing analysis and greatly simplifies the power series forms of the elastic stress field and plastic stress field near the crack line during the solving process. Furthermore, by focusing on a new problem, i.e., the center‐cracked plate with finite width under unidirectional uniform tension, this paper obtains the elastic stress field, plastic stress field, and the length of the elastic‐plastic boundary near the crack line by using the general form of the solution. When the dimensions of the plate tend to be infinite, the results of this paper are consistent with those obtained for an infinite plate with a mode I crack. Furthermore, the variation curves of the length of the elastic‐plastic boundary are also delineated in different sized center‐cracked plates, and the results are compared with those obtained under the small‐scale yielding conditions. The solving process and the results in this paper abandon the small‐scale yielding conditions completely. The method used in this paper not only makes the solving process simpler during the elastic‐plastic analysis near the crack line but also enriches the crack line analysis method.

A novel finite element method for predicting the tensile properties of 3D braided composites

A novel unit-cell model which considers the structure interference of braiding yarns in the external region is proposed to describe the geometric structure of 3D braided composites. Based on the multi-scale homogenization theory, mesoscopic structure finite element analysis model is established to predict the stiffness matrix of unit-cells. Periodic boundary conditions are applied on the periodic surfaces of unit-cells to reflect the repeating feature. And the node deformation matching equations are applied on the internal connected faces of the surface unit-cell and the corner-cell, so that the displacement continuity conditions and traction continuity conditions are satisfied. In allusion to 3D braided composites with small braiding angle, principal tensile strength forecasting model is developed.

Low-energy effective field theory below the electroweak scale: matching at one loop

We compute the one-loop matching between the Standard Model Effective Field Theory and the low-energy effective field theory below the electroweak scale, where the heavy gauge bosons, the Higgs particle, and the top quark are integrated out. The complete set of matching equations is derived including effects up to dimension six in the power counting of both theories. We present the results for general flavor structures and include both the C P -even and C P -odd sectors. The matching equations express the masses, gauge couplings, as well as the coefficients of dipole, three-gluon, and four-fermion operators in the low-energy theory in terms of the parameters of the Standard Model Effective Field Theory. Using momentum insertion, we also obtain the matching for the C P -violating theta angles. Our results provide an ingredient for a model-independent analysis of constraints on physics beyond the Standard Model. They can be used for fixed- order calculations at one-loop accuracy and represent a first step towards a systematic next-to-leading-log analysis.

Application of the matching law to Mixed Martial Arts

In the contemporary behavior-analytic literature, athletic performance (e.g.,choice of shot or movement) across multiple team sports has been found to correspond with predictions of the generalized matching equation. However, the research in this area has focused primarily on team sports. In the current study the Generalized Matching Equation (GME) was applied to Mixed Martial Arts (MMA) performance by examining strike selection as a function of landing significant strikes among fighters from various weight classes in the Ultimate Fighting Championship. The results suggest that the GME is a good descriptor of strike selection in MMA, an individual sport that is dynamic and fast paced where responding results in immediate feedback from an opponent.

A Low-Complexity Massive MIMO Detection Based on Approximate Expectation Propagation

Among various massive multiple-input multiple-output (MIMO) signal detection schemes, expectation propagation (EP) achieves superior performance in high-dimensional systems with high-order modulations and flexible antenna configurations. However, the inevitable matrix inversion in each iteration of EP brings unbearable computational burden, which hinders the efficient implementation. Several reduced-complexity variants of EP are proposed recently, which effectively alleviate the computational cost but at the expense of unacceptable performance loss. In this paper, a low-complexity massive MIMO detection is first proposed based on approximate EP, which relieves the computational complexity of the exact EP while maintaining the good performance. Particularly, the EP moment matching equations are reformulated to simplify the sequential updating procedure. In addition, an approximation based on the channel-hardening phenomenon is proposed to eliminate the matrix inversion at each iteration. Numerical results show that, for high-dimensional MIMO the proposed detector approaches the exact EP in term of bit-error-rate (BER) by a small number of iterations. No matter with symmetric or asymmetric antenna configuration, it outperforms other EP variants, Gaussian tree approximation, and channel-hardening exploiting message passing. An analysis of computational complexity reveals the high efficiency of the proposed detection compared to the state-of-the-art with flexible antenna configurations.

Determining the complex refractive index of cellulose nanocrystals by combination of Beer-Lambert and immersion matching methods

Nanocelluloses have received significant interest due to their unique structural, mechanical, and optical properties. Nanocellulose refractive indices can be used to indicate many crucial characteristics, such as crystallinity, transparency, and purity. Thus, accurate measurement is important. This study describes a new method to determine the wavelength dependent complex refractive index of cellulose nanocrystals (CNCs) by the measurement of light transmittance with a spectrophotometer. The data analysis is based on a combination of the Beer-Lambert and immersion liquid matching equations. The immersion liquid method's main advantage is that it is independent of particle shape and size. Moreover, the measurement is easy and relatively quick to perform. The present procedure is not restricted to the nanocellulose and could potentially be applied to other nanomaterials, such as hyphenate nanoparticle-based, lignin nanoparticles, nanopigments, biological entities, structural elements of dielectric metamaterials, and nanoparticle-based composites.

Control of Nonprehensile Planar Rolling Manipulation: A Passivity-Based Approach

This paper presents a new procedure to design a control law using the classical interconnection and damping assignment technique within the passivity-based port-Hamiltonian framework. The sought goal is to reduce the complexity of solving the so-called matching equations. The proposed approach is applied to two case studies of planar rolling nonprehensile manipulation, namely, the ball-and-beam and the eccentric disk-on-disk. The performance of the resulting controllers is illustrated through both simulations and experimental results, showing the applicability of the design in a real setup.

Experimental evaluation of matching via a commercially available basketball video game.

Many recent nonlaboratory-based quantitative analyses of behavior have relied on archival competitive sporting data. However, the ratio-based reinforcement schedules in most athletic competitions and the correlational nature of archival data analyses raise concern over the contributions of such findings to the behavior analytic literature. The current experiment evaluated whether matching in a human operant paradigm would approximate matching observed in nonlaboratory-based sports data. To this end, we used in-game attributes to parametrically manipulate 2- and 3-point shooting in a commercially available basketball video game. The behavior of 6 of 9 participants conformed to the generalized matching equation. These results suggest matching in sporting contexts may be a product of restricted nonindependent concurrent random-ratio schedules. Implications of this experiment, including those in applied behavior analysis and potential influence on gamification, are discussed.

Structure Preserving Observer Design for Port-Hamiltonian Systems

In this paper, a full-order observer design method is proposed for port-Hamiltonian systems. The proposed method is based on the notion of contractive port-Hamiltonian systems. It is the first structure preserving observer design for a broad class of input-state-output port-Hamiltonian systems. The design procedure consists of solving a matching equation, similar to the Interconnection and Damping Assignment Passivity-Based Control (IDA-PBC) for controller design. The matching equation, as shown in the paper, has some closed-form solutions for general class of mechanical and electromechanical systems. As another feature of the proposed method, it is shown that the existence of solution of the corresponding matching equation for a linear port-Hamiltonian system is equivalent to the detectability property of that system. Upon these facts, the proposed method can be considered as a counterpart of IDA-PBC for observer design. Simulations for some benchmark examples, including ball and beam, magnetic levitation, and permanent magnetic synchronous motor, show the potency and applicability of the method.

A robust unscented transformation for uncertain moments

This paper proposes a robust version of the unscented transform (UT) for one-dimensional random variables. It is assumed that the moments are not exactly known, but are known to lie in intervals. In this scenario, the moment matching equations are reformulated as a system of polynomial equations and inequalities, and it is proposed to use the Chebychev center of the solution set as a robust UT. This method yields a parametrized polynomial optimization problem, which in spite of being NP-Hard, can be relaxed by some algorithms that are proposed in this paper.

Rapid and accurate method for resizing CMOS operational amplifiers

A new method for resizing CMOS operational amplifiers is presented in this paper. The basic idea is to match the operating currents and some small signal conductances of transistors in a circuit by solving the matching equations based on the accurate MOSFET model. The resizing experiments of a two-stage OpAmp for the process migration from a 0.35 µm CMOS technology to a 0.18 µm one have been performed to validate the proposed method. The simulation results show that the method generates the resized circuits with smaller area and almost the same performance at a lower computational cost compared with the existing approaches.

Thermodynamic simulation of two-shaft gas turbine to study invasive weeds optimization and Min-Max controller strategies considering air-cooled blades

Proper estimation of dynamic behavior of gas turbines is essential to control of these systems. This paper investigates a thermodynamic model of two-shaft gas turbines based on thermodynamic principles, component maps and matching equations considering the blade air cooling effects. An iterative method is applied to analyze design point condition and also to evaluate steady states and transient modes. An open loop control procedure is applied to regulate inlet guide vane position. An industrial min-max control strategy is also adopted to adjust proper fuel flow rate value considering physical limits. Moreover, an invasive weed optimization (IWO) algorithm as a proper optimization method is used to find out the optimal gain values of control structure. Finally, the results are analyzed and performance of control structure has been studied in part load conditions.

Structure preserving feedback of port-thermodynamic systems

Recently a class of Hamiltonian control systems was defined for open irreversible thermodynamic systems. These systems are Hamiltonian control systems defined on a symplectic manifold, however departing from standard Hamiltonian control systems, due to the property that the Hamiltonian function is homogeneous in the generalized momentum variables. In this paper we study the class of state feedbacks preserving the geometric structure of such Homogeneous Hamiltonian control systems and rendering the closed-loop system again a Homogeneous Hamiltonian control system. It is shown that only a constant control preserves the canonical Liouville form. Hence a non-trivial state feedback necessarily changes the geometric structure in closed-loop defined by a modified Pfaffian form. Finally we derive a matching equation on the nonlinear feedback and the closed-loop Pfaffian form.

Three-dimensional Dynamic Tracking Learning Algorithm for Pedestrians on Indefinite Shape Base Based on Deep Learning

In order to improve the three-dimensional dynamic tracking and recognition ability to pedestrians, a three-dimensional dynamic tracking learning algorithm for pedestrians on indefinite shape base based on deep learning is proposed in this paper. First, the indefinite shape base mesh of body imaging is segmented to extract three-dimensional dynamic similarity features of pedestrians, and the three-dimensional feature points are marked; the deep learning method is adopted for fusion of gray pixel value and extraction of difference feature to images during three-dimensional dynamic tracking. Then a motion vector library is constructed based on the extraction results, and the template matching equation of three-dimensional dynamic feature points of pedestrians is obtained. The simulation results show that this method can accurately track moving bodies in three-dimensional dynamic tracking and recognition and can provide good robustness in moving body target extraction with accuracy up to 100% at maximum and detection time of 48.83ms at maximum.

Control of a self-balancing robot with two degrees of freedom via IDA-PBC

This paper presents an interconnection and damping assignment passivity-based control (IDA-PBC) to drive a self-balancing robot restricted to two degrees of freedom including the dynamics of the actuators. The design of the control law, stability analysis and estimation of the domain of attraction are shown in detail. A convenient change of variables and an appropriate handling of the matching equations have been key to design the control law and to get the asymptotic stability analysis, respectively. Two scalar functions have been used in the design of the controller to underscore how different proposals for the desired potential energy can shape the behavior of the self-balancing robot in closed loop. Experimental results are presented in order to confirm the theoretical proposal and to illustrate the performance of the proposed control law in the regulation task and the practical robustness against external disturbances.

High-Temperature Ultrasonic Sensor for Fission Gas Characterization in MTR Harsh Environment

In this paper, we present the first steps in the development of a new generation of ultrasonic sensors devoted to fission gas characterization in a material testing reactor harsh environment. The piezoelectric active material is a sodium bismuth titanate thick film fabricated using a screen-printing method. Characterization of piezoelectric and dielectric properties and material parameter studies based on temperature were carried out. The key results of this paper are demonstrated and discussed in terms of feasibility for application to a new sensor device operating at high temperature (350 °C). An acoustic test in a cylindrical cavity shows high sensitivity to measurements of liquid substances at room temperature. To verify its applicability to gas detection, a theoretical model based on electromechanical properties and impedance matching equations was introduced. This model was used in the studies on gas measurement under room temperature and at 350 °C. It was theoretically shown that the sensor was able to operate for gas in situ under harsh temperature conditions.

Light-cone distribution amplitudes of vector meson in a large momentum effective theory

We investigate the leading twist light-cone distribution amplitudes (LCDAs) of vector meson in the framework of large momentum effective theory. We derive the matching equation for the LCDAs and quasi distribution amplitudes. The matching coefficients are determined to one loop accuracy, both in the ultraviolet cut-off and dimensional regularization schemes. This calculation provides the possibility of studying the full $x$ behavior of LCDAs and extracting LCDAs of vector mesons from lattice simulations.