Generalized Yang-Mills actions from Dirac operator determinants

We consider the quantum effective action of Dirac fermions on four dimensional flat Euclidean space coupled to external vector- and axial Yang-Mills fields, i.e., the logarithm of the (regularized) determinant of a Dirac operator on flat R^4 twisted by generalized Yang-Mills fields. According to physics folklore, the logarithmic divergent part of this effective action in the pure vector case is proportional to the Yang-Mills action. We present an explicit computation proving this fact, generalized to the chiral case. We use an efficient computation method for quantum effective actions which is based on calculation rules for pseudo-differential operators and which yields an expansion of the logarithm of Dirac operators in local and quasi-gauge invariant polynomials of decreasing scaling dimension.Comment: LaTex, 26 page

Robust Multi-Criteria Optimal Fuzzy Control of Discrete-Time Nonlinear Systems

This paper presents a novel fuzzy control design of discrete-time nonlinear systems with multiple performance criteria. The purpose behind this work is to improve the traditional fuzzy controller performance to satisfy several performance criteria simultaneously to secure quadratic optimality with an inherent stability property together with a dissipativity type of disturbance reduction. The Takagi–Sugeno-type fuzzy model is used in our control system design. By solving a linear matrix inequality at each time step, the optimal control solution can be found to satisfy mixed performance criteria. The effectiveness of the proposed technique is demonstrated by simulation of the control of the inverted pendulum system on a cart

The Onset of the Cold HI Phase in Disks of Protogalaxies

We discuss a possible delay experienced by protogalaxies with low column density of gas in forming stars over large scales. After the hydrogen has recombined, as the external ionizing UV flux decreases and the metal abundance $Z$ increases, the HI, initially in the warm phase (T\simgt 5000 K), makes a transition to the cool phase (T\simlt 100 K). The minimum abundance $Z_{min}$ for which this phase transition takes place in a small fraction of the Hubble time decreases rapidly with increasing gas column density. Therefore in the ``anemic'' disk galaxies, where $N_{HI}$ is up to ten times smaller than for normal large spirals, the onset of the cool HI phase is delayed. The onset of gravitational instability is also delayed, since these objects are more likely to be gravitationally stable in the warm phase than progenitors of today's large spiral galaxies. The first substantial burst of star formation may occur only as late as at redshifts $z \sim 0.5$ and give a temporary high peak luminosity, which may be related to the ``faint blue objects". Galaxy disks of lower column density tend to have lower escape velocities and a starburst/galactic fountain instability which decreases the gas content of the inner disk drastically.Comment: TeX file, 24 pages, 4 figures available upon request from [email protected], to appear in The Astrophysical J. (Sept. 1

Robust Multi-Criteria Optimal Fuzzy Control of Continuous-Time Nonlinear Systems

This paper presents a novel fuzzy control design of continuous-time nonlinear systems with multiple performance criteria. The purpose behind this work is to improve the traditional fuzzy controller performance to satisfy several performance criteria simultaneously to secure quadratic optimality with inherent stability property together with dissipativity type of disturbance reduction. The Takagi– Sugeno fuzzy model is used in our control system design. By solving the linear matrix inequality at each time step, the control solution can be found to satisfy the mixed performance criteria. The effectiveness of the proposed technique is demonstrated by simulation of the control of the inverted pendulum system

Second-Order Fault Tolerant Extended Kalman Filter for Discrete Time Nonlinear Systems

As missing sensor data may severely degrade the overall system performance and stability, reliable state estimation is of great importance in modern data-intensive control, computing, and power systems applications. Aiming at providing a more robust and resilient state estimation technique, this paper presents a novel second-order fault-tolerant extended Kalman filter estimation framework for discrete-time stochastic nonlinear systems under sensor failures, bounded observer-gain perturbation, extraneous noise, and external disturbances condition. The failure mechanism of multiple sensors is assumed to be independent of each other with various malfunction rates. The proposed approach is a locally unbiased, minimum estimation error covariance based nonlinear observer designed for dynamic state estimation under these conditions. It has been successfully applied to a benchmark target-trajectory tracking application. Computer simulation studies have demonstrated that the proposed second-order fault-tolerant extended Kalman filter provides more accurate estimation results, in comparison with traditional first- and second-order extended Kalman filter. Experimental results have demonstrated that the proposed second-order fault-tolerant extended Kalman filter can serve as a powerful alternative to the existing nonlinear estimation approaches

Smart Power Grid Synchronization With Fault Tolerant Nonlinear Estimation

Effective real-time state estimation is essential for smart grid synchronization, as electricity demand continues to grow, and renewable energy resources increase their penetration into the grid. In order to provide a more reliable state estimation technique to address the problem of bad data in the PMU-based power synchronization, this paper presents a novel nonlinear estimation framework to dynamically track frequency, voltage magnitudes and phase angles. Instead of directly analyzing in abc coordinate frame, symmetrical component transformation is employed to separate the positive, negative, and zero sequence networks. Then, Clarke\u27s transformation is used to transform the sequence networks into the αβ stationary coordinate frame, which leads to system model formulation. A novel fault tolerant extended Kalman filter based real-time estimation framework is proposed for smart grid synchronization with noisy bad data measurements. Computer simulation studies have demonstrated that the proposed fault tolerant extended Kalman filter (FTEKF) provides more accurate voltage synchronization results than the extended Kalman filter (EKF). The proposed approach has been implemented with dSPACE DS1103 and National Instruments CompactRIO hardware platforms. Computer simulation and hardware instrumentation results have shown the potential applications of FTEKF in smart grid synchronization

Robust and Resilient Finite-Time Control of a Class of Discrete-Time Nonlinear Systems

In this paper, we address the finite-time state-feedback stabilization of a class of discrete-time nonlinear systems with conic type nonlinearities, bounded feedback control gain perturbations, and additive disturbances. Sufficient conditions for the existence of a robust and resilient linear statefeedback controller for this class of systems are derived. Then, using linear matrix inequality techniques, a solution for the controller gain is obtained. The developed controller is robust for all unknown nonlinearities lying in a hyper-sphere and all admissible disturbances. Moreover, it is resilient against any bounded perturbations that may alter the controller’s gain by at most a prescribed amount. We conclude the paper with a numerical example showcasing the applicability of the main result

Selection effects and binary galaxy velocity differences

Measurements of the velocity differences (delta v's) in pairs of galaxies from large statistical samples have often been used to estimate the average masses of binary galaxies. A basic prediction of these models is that the delta v distribution ought to decline monotonically. However, some peculiar aspects of the kinematics have been uncovered, with an anomalous preference for delta v approx. equal to 72 km s(sup-1) appearing to be present in the data. The authors examine a large sample of binary galaxies with accurate redshift measurements and confirm that the distribution of delta v's appears to be non-monotonic with peaks at 0 and approx. 72 km s (exp -1). The authors suggest that the non-zero peak results from the isolation criteria employed in defining samples of binaries and that it indicates there are two populations of binary orbits contributing to the observed delta v distribution