Based on a recently developed notion of physical realizability for quantum linear stochastic systems, we formulate a quantum LQG optimal control problem for quantum linear stochastic systems where the controller itself may also be a quantum system and the plant output signal can be fully quantum. Such a control scheme is often referred to in the quantum control literature as “coherent control.”...

In this paper we summarize loop quantum gravity (LQG) and we show how ideas developed in LQG can solve the black hole singularity problem when applied to a minisuperspace model.

The strengthened discrete-time optimal projection equations (SDOPE) are presented in a form based on the delta operator. This form unifies discrete-time and continuous-time results. Based on this unification, recently established results and algorithms for finite and infinite-horizon fixed-order LQG compensation of discrete-time systems are carried over to the continuous-time case. The results ...

One of the well-known deficiencies of most modern control methods [i.e., 2, , and 1 (or 1) design] is that they attempt to represent multiple criteria with scalar cost functions. Hence, in practice the (static or dynamic) weights in the scalar cost function must be determined by an iterative process in order to satisfy the multiple objectives. It is of great time and cost benefit to automate th...

In this paper, we present a new algorithm for solving the LQG control problem with variance constraints which utilizes derivative information about the relevant H2 costs to achieve quasi-Newton convergence. Using a lifting procedure, this algorithm is then generalized to work with linear periodically timevarying systems. This algorithm is then applied to the design of controllers for hard disk ...

In this paper, we study the existence of linear quadratic Gaussian (LQG)–balanced realizations for discrete-time infinite-dimensional systems. LQG-balanced realizations are those for which the smallest nonnegative self-adjoint solutions of the control and filter Riccati equations are equal. We show that the control (filter) Riccati equation has a nonnegative self-adjoint solution if and only if...

This paper presents an overview of some recent results concerning the emerging theory of minimax LQG control for uncertain systems with a relative entropy constraint uncertainty description. This is an important new robust control system design methodology providing minimax optimal performance in terms of a quadratic cost functional. The paper first considers some standard uncertainty descripti...

Using the dual Youla parametrizations of controller based coprime factor plant perturbations and plant based co-prime factor controller perturbations, we provide a computational procedure for computing an optimal innnite horizon Linear Quadratic Gaussian (LQG) controller from any stabilizing controller. The method allows us to calculate a new optimal LQG controller from a previous one when the ...

The strengthened discrete-time optimal projection equations (SDOPE) are presented in a form based on the delta operator. This form unifies discrete-time and continuous-time results. Based on this unification, recently established results and algorithms for finite and infinite-horizon fixed-order LQG compensation of discrete-time systems are carried over to the continuous-time case. The results ...