A mean-reverting stochastic model for the political business cycle

In this article, we look at the political business cycle problem through the lens of uncertainty. The feedback control used by us is the famous NKPC with stochasticity and wage rigidities. We extend the New Keynesian Phillips Curve model to the continuous time stochastic set up with an Ornstein-Uhlenbeck process. We minimize relevant expected quadratic cost by solving the corresponding Hamilton-Jacobi-Bellman equation. The basic intuition of the classical model is qualitatively carried forward in our set up but uncertainty also plays an important role in determining the optimal trajectory of the voter support function. The internal variability of the system acts as a base shifter for the support function in the risk neutral case. The role of uncertainty is even more prominent in the risk averse case where all the shape parameters are directly dependent on variability. Thus, in this case variability controls both the rates of change as well as the base shift parameters. To gain more insight we have also studied the model when the coefficients are time invariant and studied numerical solutions. The close relationship between the unemployment rate and the support function for the incumbent party is highlighted. The role of uncertainty in creating sampling fluctuation in this set up, possibly towards apparently anomalous results, is also explored.

First-passage failure of quasi-integrable Hamiltonian systems

The first-passage failure of quasi-integrable Hamiltonian si-stems (multidegree-of-freedom integrable Hamiltonian systems subject to light dampings and weakly random excitations) is investigated. The motion equations of such a system are first reduced to a set of averaged Ito stochastic differential equations by using the stochastic averaging method for quasi-integrable Hamiltonian systems. Then, a backward Kolmogorov equation governing the conditional reliability function and a set of generalized Pontryagin equations governing the conditional moments of first-passage time are established. Finally, the conditional reliability function, and the conditional probability density and moments of first-passage time are obtained by solving these equations with suitable initial and boundary conditions. Two examples are given to illustrate the proposed procedure and the results from digital simulation are obtained to verify the effectiveness of the procedure.

一种基于比例反馈控制原理的动载荷时域反演方法

通过借鉴系统控制论中的比例反馈控制原理，提出了一种新的结构动载荷时域反演方法。该方法在原开环系统的输出与结构模型之间连接一个虚拟的比例反馈增益，使得原来的开环系统成为一个虚拟的闭环反馈控制系统，系统控制信号为实测的结构加速度响应。反馈控制器将系统输出与控制信号之间的差值进行放大后作为反馈不断输入到结构模型中，直到差值趋于稳定，此时该差值与反馈增益的乘积经过高通滤波后即得到所反演的动态载荷。该方法将载荷反演问题的求解转化为正问题中的结构瞬态响应求解，采用一般的数值解法如New-mark法即可实现，因此计算比较简便迅速。该方法仅需要测量结构的加速度响应即可进行反演，便于实际应用，而且并不十分依赖于真实的初始条件，由于不存在误差累积的现象，反演结果具有较好的稳定性。最后，通过海洋平台结构冰载荷反演的模型实验和数值仿真证明了该方法的有效性。

切削加工中刀具颤振的迟滞反馈控制

从金属切削加工的实际情况出发,分析了刀具在切削加工中产生颤振的原因.从力学的角度解释了刀具径向非线性颤振的机理,说明这是一种自激振荡,可以通过施加线性迟滞反馈力加以控制.这种反馈力是位移信号的迟滞函数,可以用于抑制振幅,增加刀具的平稳性.数值仿真验证了理论结果.

Coherent enhancement of broadband frequency up-conversion in BBO crystal by shaping femtosecond laser pulses

An optimal feedback control of broadband frequency up-conversion in BBO crystal is experimentally demonstrated by shaping femto-second laser pulses based on genetic algorithm, and the frequency up-conversion efficiency can be enhanced by similar to 16%. SPIDER results show that the optimal laser pulses have shorter pulse-width with the little negative chirp than the original pulse with the little positive chirp. By modulating the fundamental spectral phase with periodic square distribution on SLM-256, the frequency up-conversion can be effectively controlled by the factor of about 17%. The experimental results indicate that the broadband frequency up-conversion efficiency is related to both of second harmonic generation (SHG) and sum frequency generation (SFG), where the former depends on the fundamental pulse intensity, and the latter depends on not only the fundamental pulse intensity but also the fundamental pulse spectral phase. (c) 2006 Elsevier B.V. All rights reserved.

Lock Acquisition and Sensitivity Analysis of Advanced LIGO Interferometers

Laser interferometer gravitational wave observatory (LIGO) consists of two complex large-scale laser interferometers designed for direct detection of gravitational waves from distant astrophysical sources in the frequency range 10Hz - 5kHz. Direct detection of space-time ripples will support Einstein's general theory of relativity and provide invaluable information and new insight into physics of the Universe.

Initial phase of LIGO started in 2002, and since then data was collected during six science runs. Instrument sensitivity was improving from run to run due to the effort of commissioning team. Initial LIGO has reached designed sensitivity during the last science run, which ended in October 2010.

In parallel with commissioning and data analysis with the initial detector, LIGO group worked on research and development of the next generation detectors. Major instrument upgrade from initial to advanced LIGO started in 2010 and lasted till 2014.

This thesis describes results of commissioning work done at LIGO Livingston site from 2013 until 2015 in parallel with and after the installation of the instrument. This thesis also discusses new techniques and tools developed at the 40m prototype including adaptive filtering, estimation of quantization noise in digital filters and design of isolation kits for ground seismometers.

The first part of this thesis is devoted to the description of methods for bringing interferometer to the linear regime when collection of data becomes possible. States of longitudinal and angular controls of interferometer degrees of freedom during lock acquisition process and in low noise configuration are discussed in details.

Once interferometer is locked and transitioned to low noise regime, instrument produces astrophysics data that should be calibrated to units of meters or strain. The second part of this thesis describes online calibration technique set up in both observatories to monitor the quality of the collected data in real time. Sensitivity analysis was done to understand and eliminate noise sources of the instrument.

Coupling of noise sources to gravitational wave channel can be reduced if robust feedforward and optimal feedback control loops are implemented. The last part of this thesis describes static and adaptive feedforward noise cancellation techniques applied to Advanced LIGO interferometers and tested at the 40m prototype. Applications of optimal time domain feedback control techniques and estimators to aLIGO control loops are also discussed.

Commissioning work is still ongoing at the sites. First science run of advanced LIGO is planned for September 2015 and will last for 3-4 months. This run will be followed by a set of small instrument upgrades that will be installed on a time scale of few months. Second science run will start in spring 2016 and last for about 6 months. Since current sensitivity of advanced LIGO is already more than factor of 3 higher compared to initial detectors and keeps improving on a monthly basis, upcoming science runs have a good chance for the first direct detection of gravitational waves.

Controle a estrutura variável para atenuar modos ressonantes em servomecanismos.

Nesta dissertação é mostrada experimentalmente a existência de modos ressonantes em servomotores de corrente contínua sem núcleo de ferro. Até onde se sabe, não já publicações ou documentos técnicos de fabricantes que relatam esse efeito neste tipo de motor. Foi observado também que a frequência da ressonância é variável e que possivelmente depende da temperatura interna do motor. Conforme e mostrado em simulações técnicas tradicionais para o controle de motores podem não ser eficazes para lidar com esses modos ressonantes. Com o objetivo de amortecer a ressonância e obter o controle de velocidade e posição desses motores, são desenvolvidos controladores por modo deslizante baseados em funções de chaveamento obtidas por observadores de alto ganho. Esse controle e robusto a incertezas paramétricas e perturbações. Com o auxílio de simulações são mostrados os pontos fortes e limitações de cada um dos controladores.

Internal models in the cerebellum.

This review will focus on the possibility that the cerebellum contains an internal model or models of the motor apparatus. Inverse internal models can provide the neural command necessary to achieve some desired trajectory. First, we review the necessity of such a model and the evidence, based on the ocular following response, that inverse models are found within the cerebellar circuitry. Forward internal models predict the consequences of actions and can be used to overcome time delays associated with feedback control. Secondly, we review the evidence that the cerebellum generates predictions using such a forward model. Finally, we review a computational model that includes multiple paired forward and inverse models and show how such an arrangement can be advantageous for motor learning and control.

Human muscle spindles act as forward sensory models.

Modern theories of motor control incorporate forward models that combine sensory information and motor commands to predict future sensory states. Such models circumvent unavoidable neural delays associated with on-line feedback control. Here we show that signals in human muscle spindle afferents during unconstrained wrist and finger movements predict future kinematic states of their parent muscle. Specifically, we show that the discharges of type Ia afferents are best correlated with the velocity of length changes in their parent muscles approximately 100-160 ms in the future and that their discharges vary depending on motor sequences in a way that cannot be explained by the state of their parent muscle alone. We therefore conclude that muscle spindles can act as "forward sensory models": they are affected both by the current state of their parent muscle and by efferent (fusimotor) control, and their discharges represent future kinematic states. If this conjecture is correct, then sensorimotor learning implies learning how to control not only the skeletal muscles but also the fusimotor system.

CLADP - THE CAMBRIDGE LINEAR ANALYSIS AND DESIGN PROGRAMS USER REFERENCE MANUAL (4TH ISSUE: APRIL 1983).

CLADP is an engineering software program developed at Cambridge University for the interactive computer aided design of feedback control systems. CLADP contains a wide range of tools for the analysis of complex systems, and the assessment of their performance when feedback control is applied, thus enabling control systems to be designed to meet difficult performance objectives. The range of tools within CLADP include the latest techniques in the field whose central theme is the extension of classical frequency domain concepts (well known and well proven for single loop systems) to multivariable or multiloop systems, and by making extensive use of graphical presentation information is provided in a readily understood form.

Task-dependent coordination of rapid bimanual motor responses.

Optimal feedback control postulates that feedback responses depend on the task relevance of any perturbations. We test this prediction in a bimanual task, conceptually similar to balancing a laden tray, in which each hand could be perturbed up or down. Single-limb mechanical perturbations produced long-latency reflex responses ("rapid motor responses") in the contralateral limb of appropriate direction and magnitude to maintain the tray horizontal. During bimanual perturbations, rapid motor responses modulated appropriately depending on the extent to which perturbations affected tray orientation. Specifically, despite receiving the same mechanical perturbation causing muscle stretch, the strongest responses were produced when the contralateral arm was perturbed in the opposite direction (large tray tilt) rather than in the same direction or not perturbed at all. Rapid responses from shortening extensors depended on a nonlinear summation of the sensory information from the arms, with the response to a bimanual same-direction perturbation (orientation maintained) being less than the sum of the component unimanual perturbations (task relevant). We conclude that task-dependent tuning of reflexes can be modulated online within a single trial based on a complex interaction across the arms.

Implementation of a PI phase angle controller for finite element analysis of the BDFM

Time-stepping finite element analysis of the BDFM for a specific load condition is shown to be a challenging problem because the excitation required cannot be predetermined and the BDFM is not open loops stable for all operating conditions. A simulation approach using feedback control to set the torque and stabilise the BDFM is presented together with implementation details. The performance of the simulation approach is demonstrated with an example and computed results are compared with measurements.

Collective motion, sensor networks, and ocean sampling

This paper addresses the design of mobile sensor networks for optimal data collection. The development is strongly motivated by the application to adaptive ocean sampling for an autonomous ocean observing and prediction system. A performance metric, used to derive optimal paths for the network of mobile sensors, defines the optimal data set as one which minimizes error in a model estimate of the sampled field. Feedback control laws are presented that stably coordinate sensors on structured tracks that have been optimized over a minimal set of parameters. Optimal, closed-loop solutions are computed in a number of low-dimensional cases to illustrate the methodology. Robustness of the performance to the influence of a steady flow field on relatively slow-moving mobile sensors is also explored © 2006 IEEE.

Collective motion of self-propelled particles: Stabilizing symmetric formations on closed curves

We provide feedback control laws to stabilize formations of multiple, unit speed particles on smooth, convex, and closed curves with definite curvature. As in previous work we exploit an analogy with coupled phase oscillators to provide controls which isolate symmetric particle formations that are invariant to rigid translation of all the particles. In this work, we do not require all particles to be able to communicate; rather we assume that inter-particle communication is limited and can be modeled by a fixed, connected, and undirected graph. Because of their unique spectral properties, the Laplacian matrices of circulant graphs play a key role. The methodology is demonstrated using a superellipse, which is a type of curve that includes circles, ellipses, and rounded rectangles. These results can be used in applications involving multiple autonomous vehicles that travel at constant speed around fixed beacons. ©2006 IEEE.

Rhythmic stabilization of periodic orbits in a wedge

The paper addresses the rhythmic stabilization of periodic orbits in a wedge billiard with actuated edges. The output feedback strategy, based on the sole measurement of impact times, results from the combination of a stabilizing state feedback control law and a nonlinear deadbeat state estimator. It is shown that the robustness of both the control law and the observer leads to a simple rhythmic controller achieving a large basin of attraction. Copyright © 2005 IFAC.