Quadratic Theory Research Articles

A fully-coupled quadratic strip theory/finite element method for predicting global ship structure response in head seas

This paper outlines the theoretical development and some validation of a quadratic strip theory method coupled to a global finite element model to predict the global structural response of the Korea Research Institute of Ships and Ocean Engineering (KRISO) hull geometry due to regular, head seas waves in the time-domain. The method attempts to capture some body-nonlinear effects of the dynamic problem due to time-varying underwater hull geometry by drawing a relationship between the coefficients, A 33 , B 33 , and C 33 and the local draft, T s . In addition, the hull girder is considered flexible and structural damping may be included. A segmented model test in head seas was also performed, and the linear and nonlinear numerical results are compared to the experimental data. It is found that the theory shows reasonably good agreement with the model test data, and that nonlinear effects account for a significant increase in predicted bending moment.

Stability of Algorithms for Electro-Magnetic-Transient Simulation of Networks With Switches and Non-Linear Inductors

This paper extends the analysis of the stability of electromagnetic transient simulation algorithms to non-linear systems with switching elements and non-linear inductor branches. A theoretical analysis based on common quadratic Lyapunov function theory is used to investigate the stability of numerical algorithms for the simulation of lumped strictly passive switched circuits (LSPSC). It is proved that only when certain fundamental physical properties, i.e., passivity and invariance of Lyapunov energy function, are satisfied, the widely used trapezoidal method results in stable simulations of such networks for any time-step size. This is different from the simulation of linear time invariant systems where any real-world stable system has a stable simulation if an A-stable integration method (e.g., trapezoidal rule) is used. Subsequently, it is shown that the problem of simulating a piecewise linear inductor can be equivalent to simulating a LSPSC; and ergo its simulation with the trapezoidal rule is also stable.

Mode control of electro-mechanical suspension systems for vehicle height, levelling and ride comfort

This paper proposes a mode control algorithm of electro-mechanical suspension for vehicle height, attitude control and improvement of ride quality. The proposed control algorithm consists of mode selector, upper-level and lower-level controllers, and suspension state estimator. The mode selector determines the present driving mode using vehicle signals, such as longitudinal speed, steering wheel angle, accelerator pedal position, brake pedal position and vertical acceleration of wheels. The upper-level controller determines the desired suspension state using the present driving mode. The lower-level controller derives the desired stroke speed of the actuator in each suspension by linear quadratic control theory. The suspension state estimator has been designed using accessible sensor measurement by discrete-time Kalman filter theory. The control and estimation algorithms have been developed based on a novel reduced-order vehicle model that includes only the vehicle body dynamics. The model enables the observer to completely remove the effect of unknown road disturbance on the estimation error. The performance of the proposed control algorithm has been evaluated via computer simulation study. The simulation results show that the proposed control algorithm is effective at controlling the electro-mechanical suspension systems. The paper also shows that the considered actuator is suited for vehicle height and levelling control, but not for improvement of ride comfort, due to voltage input constraints.

LQ Secure Control for Cyber-Physical Systems Against Sparse Sensor and Actuator Attacks

This paper investigates the problem of secure control for cyber-physical systems (CPSs) under sensor and actuator attacks. The attacks are assumed to be sparse but arbitrary. The strong detectability under the sparse attacks is characterized by computing the rank of the so-called structural matrix pencil. An adaptive hybrid control strategy is proposed by automatically excluding the tampered measurement and input data. First, a hybrid system consisting of all possible combinations of models is implemented. Then, combining classical linear quadratic control theory, an adaptive switching logic is designed to online locate the proper system mode by observing the optimal performance index. As a result, the closed-loop system is ensured to be asymptotically stable in the presence of the attacks, while the performance loss can be mitigated. Also, the performance degradation under attacks is also analyzed quantificationally based on the quadratic cost function. Simulation results on an aircraft system are given to substantiate the proposed method.

Feedback Stackelberg strategies for the discrete-time mean-field stochastic systems in infinite horizon

This paper deals with the feedback Stackelberg strategies for the discrete-time mean-field stochastic systems in infinite horizon. The optimal control problem of the follower is first studied. Employing the discrete-time linear quadratic (LQ) mean-field stochastic optimal control theory, the sufficient conditions for the solvability of the optimization of the follower are presented and the optimal control is obtained based on the stabilizing solutions of two coupled generalized algebraic Riccati equations (GAREs). Then, the optimization of the leader is transformed into a constrained optimal control problem. Applying the Karush-Kuhn-Tucker (KKT) conditions, the necessary conditions for the existence and uniqueness of the Stackelberg strategies are derived and the Stackelberg strategies are expressed as linear feedback forms involving the state and its mean based on the solutions (Ki,K^i),i=1,2 of a set of cross-coupled stochastic algebraic equations (CSAEs). An iterative algorithm is put forward to calculate efficiently the solutions of the CSAEs. Finally, an example is solved to show the effectiveness of the proposed algorithm.

Simulation and Experimental Study on the Active Stability of High-Speed Trains

An active hunting stability scheme is proposed for the high-speed trains based on frame lateral vibration control. The stability of the vehicle is improved by exerting active control force on the front and rear frames of the bogie. First, a simplified lateral vibration model of a single bogie is established to the control system design. The feedback gain matrix is obtained according to the linear quadratic optimal control theory. Then, the multibody dynamics model of the vehicle is built using SIMPACK, and the linear stability and straight running performance are analyzed under different working configurations. Finally, the active control effects are verified by a scaled roller rig. The results show that this active control scheme to improve the stability performances of vehicles through the feedback of frame vibration state is feasible.

Kalman 1960: The birth of modern system theory

ABSTRACTRudolph E. Kalman is mainly known for the Kalman filter, first published in 1960. In this year, he published two equally important contributions, one about linear state space system theory and the other about linear quadratic optimal control theory. These three domains are intertwined in the later theory of linear quadratic Gaussian control. An extended version of linear quadratic optimal control is put into practice in an example of cooperation in population ecology.

Cooperative Guidance and Collision Avoidance for Multiple Pursuers

This paper presents a cooperative guidance law for an -on- engagement scenario that ensures target interception and collision avoidance between the pursuers along with minimizing their team effort. The guidance law is derived using linear quadratic optimal control theory for a linearized engagement model. The pursuers cooperate with each other to accommodate differences in maneuver capabilities of different team members. A special case of 2-on-2 engagement is also analyzed, for which analytical closed-form formulas for the pursuer’s guidance law are obtained. Various simulation results and experimental validation results, exemplifying the cooperation in different engagements, are also presented.

Witt groups of smooth projective quadrics

Let k be a commutative ring containing 12. In this paper, we construct exact sequences connecting Witt groups of smooth projective quadrics over k and Clifford algebras. The exact sequences have an application to a classical problem in quadratic form theory: the Witt kernel of function fields of quadrics. We also apply the exact sequences to compute Witt groups of certain kinds of smooth projective quadrics.

Interaction of intermediates with transition metal surfaces in the dehydrogenation of ethanol to ethyl acetate: A theoretical investigation

By employing a combined approach of the unity bond index–quadratic exponential potential method and density functional theory within the generalized gradient approximation, we have studied the interaction of intermediates in the ethanol dehydrogenation process to ethyl acetate on Cu, Ag, Ni, Pd, Pt, Co, Au and Ir(111) transition metal surfaces. Binding energies and geometries were optimized for the main intermediates of this process. Electronic structures were computed for some intermediates/transition metal systems. We also calculated the activation energies for the elementary steps of the reactions. The results show that amid the studied surfaces, Cu(111) stabilizes ethoxy and acetyl species, preventing their dissociation. Inducing the η2 binding mode of acetaldehyde by alloying Cu with Ni, Co, Pd, Pt or Ir can enhance the catalytic proprieties of the Cu(111) clean surface.

Nonlinear anisotropy growth in Bianchi-I spacetime in metric f(R) cosmology

The present work is related to anisotropic cosmological evolution in metric $f(R)$ theory of gravity. The initial part of the paper develops the general cosmological dynamics of homogeneous anisotropic Bianchi-I spacetime in $f(R)$ cosmology. The anisotropic spacetime is pervaded by a barotropic fluid which has isotropic pressure. The paper predicts nonlinear growth of anisotropy in such spacetimes. In the later part of the paper we display the predictive power of the nonlinear differential equation responsible for the cosmological anisotropy growth in various relevant cases. We present the exact solutions of anisotropy growth in Starobinsky inflation driven by quadratic gravity and exponential gravity theory. Semi-analytical results are presented for the contraction phase in quadratic gravity bounce. The various examples of anisotropy growth in Bianchi-I model universe shows the complex nature of the problem at hand.

Design of Quadratic D-Stable Fuzzy Controller for DC Microgrids With Multiple CPLs

The dc microgrid (MG) system has several advantages over the ac one. Therefore, it recently became a preferred architecture in numerous industrial applications. Many loads in dc MGs are electronically regulated and they challenge the stability of the system due to their constant power load (CPL) behavior. This letter proposes a systematic and simple approach to design an improved state feedback controller for the power buffer that can stabilize the dc MGs with multiple CPLs. Based on the so-called sector nonlinearity approach, the nonlinear dc MG with several CPLs is exactly represented in a Takagi–Sugeno fuzzy model. Then, by employing the quadratic D-stability theory, the sufficient conditions to guarantee the stability and transient performance of the closed-loop system are obtained in terms of linear matrix inequalities (LMIs), such that the decay rate and oscillatory behavior of the closed-loop dc MG system are guaranteed to lie inside a predefined region. The LMI conditions can be numerically solved by utilizing the YALMIP toolbox in the MATLAB. Finally, to illustrate the merits and implementation validity of the proposed approach, some hardware-in-the-loop real-time simulation (RTS) results on a dc MG, which feeds two CPLs, are presented. In comparison with the state-of-the-art techniques, the RTS results indicate the simplicity, validity, and better performance of the proposed approach. According to the results, one can conclude that the proposed approach not only theoretically assures the stability but also guarantees the fast convergence and less oscillatory response of the dc MGs with multiple CPLs.

Contrasting bending energies from bulk elastic theories.

The choice of elastic energies for thin plates and shells is an unsettled issue with consequences for much recent modeling of soft matter. Through consideration of simple deformations of a thin body in the plane, we demonstrate that four bulk isotropic quadratic elastic theories have fundamentally different predictions with regard to bending behavior. At finite thickness, these qualitative effects persist near the limit of mid-surface isometry, and not all theories predict an isometric ground state. We discuss how certain kinematic measures that arose in early studies of rod mechanics lead to coherent definitions of stretching and bending, and promote the adoption of these quantities in the development of a covariant theory based on stretches rather than metrics.

Time-Coordinated Control for Unmanned Aerial Vehicle Swarm Cooperative Attack on Ground-Moving Target

In this paper, cooperative attack control law analysis and design problems for unmanned aerial vehicle (UAV) swarm attack on ground-moving target with time-coordinated strategies are investigated. First, the time-coordinated control problem for a single UAV is formulated, which is the foundation of solving the problem of a single UAV arriving at the desired attack position relative to ground-moving target at a specific terminal time. Then, relative motion between each UAV and ground-moving target is considered as a finite-time time-varying tracking system problem, and the difference between expected output and system output is defined as tracking error vector. The control law is obtained by linear quadratic optimal control theory to minimize the energy cost in the whole process and the tracking error at the terminal time. Besides, time-coordinated function, which is critical to coordinate terminal time among all UAVs in the UAV swarm, is proposed to model time-coordinated strategies. Finally, numerical simulations show that the proposed control law can steer UAV swarm to arrive at the desired attack positions and achieve the time-coordinated strategies effectively.

Adaptive Optimal Control With Guaranteed Convergence Rate for Continuous-Time Linear Systems With Completely Unknown Dynamics

The traditional linear quadratic optimal control can be summarized as finding the state feedback controller so that the closed-loop system is stable and the performance index is minimum. And, it is well-known that the solution of the linear quadratic optimal control problem can be solved by algebraic Riccati equation. However, the feature of the traditional linear quadratic optimal control theory is that the convergence rate is not specified. This may result in the phenomena of slow convergence. In this paper, we mainly consider the linear quadratic optimal control with guaranteed convergence rate (LQOCGCR) and propose a policy iteration-based adaptive dynamic programming algorithm that includes offline and online versions for finding the solution of the LQOCGCR. Finally, a numerical example is worked out to show the effectiveness of the proposed approach.

Networked Delay Control for 5G Wireless Machine-Type Communications Using Multiconnectivity

Automatic control using ultrareliable and low latency communication is one of the potential applications of the new fifth-generation wireless systems. A remaining challenge is then to guarantee a low end-to-end delay with low jitter over combined internet and wireless interfaces that are packet switched and capacity optimized. The main novelty of this paper is to introduce stringent delay control to meet this challenge, over simultaneous multiple data paths. The proposed multiple-input-multiple-output (MIMO) cascade control system is nonlinear since the dwell times of the transmission node queues used as actuators cannot be negative. Stability analysis based on integral quadratic constraint theory is, therefore, applied to characterize the global stability of the controller. The practical performance is evaluated with experiments using product like test bed C++ code. It is stressed that the proposed controller does not require internode time synchronization.

Casimir effect in quadratic theories of gravity

In this paper, we study the Casimir effect in a curved spacetime described by gravitational actions quadratic in the curvature. In particular, we consider the dynamics of a massless scalar field confined between two nearby plates and compute the corresponding mean vacuum energy density and pressure in the framework of quadratic theories of gravity. Since we are interested in the weak-field limit, as far as the gravitational sector is concerned we work in the linear regime. Remarkably, corrections to the flat spacetime result due to extended models of gravity (although very small) may appear at the first-order of our perturbative analysis, whereas general relativity contributions start appearing at the second order. Future experiments on the Casimir effect might represent a useful tool to test and constrain extended theories of gravity.

First-order nonadiabatic couplings in extended systems by time-dependent density functional theory.

We propose an ab initio formulation that enables a rigorous calculation of the first-order nonadiabatic couplings (NAC) between electronic states based on time-dependent density functional theory in conjunction with planewave bases, projector augmented-wave pseudopotentials, and hybrid exchange-correlation functionals. The linear and quadratic time-dependent response theory is used to derive analytic expressions for the NAC matrix elements. In contrast to the previous formulation in atomic basis sets, the present formulation eliminates explicit references to Kohn-Sham virtual orbitals. With the introduction of Lagrangian functionals, the present formulation circumvents expensive derivative calculations of Kohn-Sham orbitals with respect to ionic coordinates. As a validation of the formulation, the NAC matrix elements of small molecules LiH and HeH+ are calculated and compared to previous results with the atomic orbital basis. This development paves the way for accurate ab initio nonadiabatic molecular dynamics in extended systems.

A finite strain incremental-secant homogenization model for elasto-plastic composites

This paper presents a finite strain extension of the incremental-secant mean-field homogenization (MFH) formulation for two-phase elasto-plastic composites. The formulation of the local finite strain elasto-plastic constitutive equations of each phase is based on a multiplicative decomposition of the deformation gradient as suggested by Simo in (Computer Methods in Applied Mechanics and Engineering, 99(1):61–112, 1992.). The latter has proposed algorithms which preserve the classical return mapping schemes of the infinitesimal theory by using principal Kirchhoff stresses and logarithmic eigenvalues of the left elastic Cauchy–Green strain. Relying on this property, we show that, by considering a quadratic logarithmic free energy and J2-flow theory at the local level, infinitesimal strain incremental-secant MFH is readily extended to finite strains. The proposed formulation and corresponding numerical algorithms are then presented. Finally, the predictions are illustrated with several numerical simulations which are verified against full-field finite element simulations of composite cells, demonstrating that the micro-mechanically based approach is able to predict the influence of the micro-structure and of its evolution on the macroscopic properties in a very cost-effective manner.

Anharmonic Stretching Frequencies of Local OH Bonds in Water Dimer: Ab Initio Potential Energy and Discrete Variable Representation

The fundamental and first overtone transition frequencies of local OH bonds of the hydrogen bond donor molecule in a water dimer were calculated by numerically solving one‐dimensional Schrödinger equation with anharmonic potential energies obtained by ab initio quantum chemical methods at the near basis set limit. Among the various ab initio theories considered, the coupled cluster theory is found to give the most accurate frequencies in comparison with experiments, and the quadratic configuration interaction theory exhibits a similar accuracy. The calculated frequencies of the free and hydrogen‐bonded OH bonds excellently agree with experimental frequencies of a gaseous dimer. It was found that the anharmonicity of the fundamental transition frequency is influenced by hydrogen bonding to a larger extent than the anharmonicity of the 1–2 transition frequency.