This article provides a detailed investigation into the motion of surrounding particles around polymer black hole in loop quantum gravity (LQG). Using effective potential, critical bound orbits and innermost stable circular (ISCO) are analyzed. The study finds that radii angular momentum decrease with an increase parameter $A_\lambda$ which labels LQG effects, while energy ISCO also decreases $...

A manifestly Lorentz-covariant formulation of Loop Quantum Gravity (LQG) is given in terms finite-dimensional representations the Lorentz group. The accounts for discrete symmetries, such as parity and time-reversal, it establishes a link with Wigner classification particles. resulting quantum model can be seen LQG internal $SU(2)\otimes SU(2)$ group free Immirzi parameter, while scalar constra...

In this paper we survey recent works on rational inattention (RI) in macroeconomics within the dynamic linear-quadratic-Gaussian (LQG) setting. We first discuss how RI affects consumption smoothness and sensitivity, precautionary savings, asset pricing, portfolio choice, and aggregate fluctuations in the univariate case. We then discuss the applications of RI to macroeconomic models of permanen...

The problem of deriving a suboptimal LQG controller which is internally stable is considered. In the case where the controller is internally unstable a procedure is given for modifying the optimization parameters, i.e. the state weighting matrix and/or the process noise intensity. Sufficient conditions for controller stability of appropriately modified optimization problems are given for both t...

A two-wheeled self-balancing robot system bases on the physical problem of an inverted pendulum. Stabilization this type mobile requires applying active control approach. This paper proposes efficient Linear Quadratic Gaussian (LQG) optimal for system. The LQG (a combination a Kalman Filter (KF) and Regulator (LQR)) controller is designed to stabilize while reducing effect process measurement n...

Guaranteed performance control is considered in this paper for discretetime LQG problems by minimizing the probability that the performance index is over a preselected threshold. It is proven that this guaranteed performance control problem can be converted into a mean-variance control problem which can be solved by using an embedding scheme. An optimal open-loop feedback control law is derived...

Linear quadratic gaussian (LQG) optimal control techniques can control linear multivariable systems that are precisely known [1,2]. Within the framework of the design, they achieve a best possible performance. However, if the plant is imprecisely known, actual performance can be intolerably poor. The guaranteed gain and phase margins for the case of the nominal plant may evaporate in the presen...

The discrete logarithm problem in Jacobians of curves of high genus g over finite fields Fq is known to be computable with subexponential complexity Lqg (1/2, O(1)). We present an algorithm for a family of plane curves whose degrees in X and Y are low with respect to the curve genus, and suitably unbalanced. The finite base fields are arbitrary, but their sizes should not grow too fast compared...

1 Grad. stud., Univ. of Michigan (UM) & intern, United Tech. Res. Center (UTRC). 2 Research eng., UTRC. 3 Prof., UM. ABSTRACT This paper studies the combined optimization of an elevator’s design (plant) and LQG controller for ride comfort. Elevator dynamics and primary vibration sources (drive motor torque ripple and guide rail irregularity) are modeled using an object-oriented language. The re...

The Linear-Quadratic Gaussian (LQG) design is the most efficient and widely used design approach in the field of linear stochastic control systems. From theoretical point of view this approach is reduced to the synthesis of a LQ state regulator and of a Kalman filter for the controlled system. From computational point of view the LQG design consists of solving a pair of matrix Riccati equations...