Recent work has shown that for $\gamma \in (0,2)$, a Liouville quantum gravity (LQG) surface can be endowed with canonical metric. We prove several results concerning geodesics this In particular, we completely classify the possible networks of from typical point on to an arbitrary surface, as well types joining two points which occur dense set pairs surface. This latter result is $\gamma$-LQG ...

The present work deals with the problem of frequency weighted controller reduction using balanced singular perturbation approximation. The advanced controller design methods like LQG/LTR or based synthesis methods sometimes leads to an controller of order comparable to plant and sometimes unstable controller whereas lower order controller should be sought out to keep the closed-loop stability a...

The feed-forward and linear quadratic Gaussian (LQG) controllers significantly reduced the servo error at higher rate tracking. However, the servo error due to wind disturbances acting on the antenna structure is still significant. This error cannot be reduced by the feed-forward controller and is only moderately reduced by the LQG controller. The H∞ controller design approach gives the possibi...

The capabilities of a tri-tethered aerostat positioning system are investigated using simulations of a comprehensively validated dynamics model. The physical system studied consists of a payload supported by a helium filled aerostat and attached to three anchored ground tethers actuated using winches. Closed-loop control is achieved by feeding back the position of a payload located at the confl...

In this article, we revisit the sequential source-coding framework to analyze fundamental performance limitations of discrete-time stochastic control systems subject feedback data-rate constraints in finite-time horizon. The basis our results is a new characterization lower bound on minimum total-rate achieved by codes total (across time) distortion constraint and computational algorithm that a...

We consider within the framework of the Mean Field Games theory a dynamic discrete choice model with social interactions, where a large number of agents/players are choosing between two alternatives while influenced by the group’s behavior. We introduce the “Min-LQG” optimal control problem, a modified Linear Quadratic Gaussian (LQG) optimal control problem that includes a minimum term in its f...

This paper presents some studies on partially observed linear quadratic Gaussian (LQG) models where the stochastic disturbances depend on both the states and the controls, and the measurements are bilinear in the noise and the states=controls. While the Separation Theorem of standard LQG design does not apply, suboptimal linear state estimate feedback controllers are derived based on certain li...

An adaptive discrete-time LQG control with loop transfer recovery (LTR) is considered. The control problem is analyzed using state-space model and the parameter estimation problem is implemented for corresponding discrete-time model in transfer function form obtained via ZOH. Thus the direct estimation of model parameters is possible by means of standard RLS or ERLS procedure and the adaptive c...

A large quasar group (LQG) of particularly large size and high membership has been identified in the DR7QSO catalogue of the Sloan Digital Sky Survey. It has characteristic size (volume1/3) ∼500 Mpc (proper size, present epoch), longest dimension ∼1240 Mpc, membership of 73 quasars and mean redshift z̄ = 1.27. In terms of both size and membership, it is the most extreme LQG found in the DR7QSO c...

In this study, mass, stiffness and damping matrices of the Nosrat jacket; located in Persian Gulf; equipped with Semi Active Tuned Mass Damper (SATMD) system have been derived after modeling the structure in SACS software. Owing to huge number of the degrees of freedom in the model, computation of on-line control of SATMD was time consuming. For this purpose, the size of the model was reduced i...