63,378 research outputs found
Optimal controller/observer gains of discounted-cost LQG systems
The linear-quadratic-Gaussian (LQG) control paradigm is well-known in
literature. The strategy of minimizing the cost function is available, both for
the case where the state is known and where it is estimated through an
observer. The situation is different when the cost function has an exponential
discount factor, also known as a prescribed degree of stability. In this case,
the optimal control strategy is only available when the state is known. This
paper builds on from that result, deriving an optimal control strategy when
working with an estimated state. Expressions for the resulting optimal expected
cost are also given
Control-theoretic Approach to Communication with Feedback: Fundamental Limits and Code Design
Feedback communication is studied from a control-theoretic perspective,
mapping the communication problem to a control problem in which the control
signal is received through the same noisy channel as in the communication
problem, and the (nonlinear and time-varying) dynamics of the system determine
a subclass of encoders available at the transmitter. The MMSE capacity is
defined to be the supremum exponential decay rate of the mean square decoding
error. This is upper bounded by the information-theoretic feedback capacity,
which is the supremum of the achievable rates. A sufficient condition is
provided under which the upper bound holds with equality. For the special class
of stationary Gaussian channels, a simple application of Bode's integral
formula shows that the feedback capacity, recently characterized by Kim, is
equal to the maximum instability that can be tolerated by the controller under
a given power constraint. Finally, the control mapping is generalized to the
N-sender AWGN multiple access channel. It is shown that Kramer's code for this
channel, which is known to be sum rate optimal in the class of generalized
linear feedback codes, can be obtained by solving a linear quadratic Gaussian
control problem.Comment: Submitted to IEEE Transactions on Automatic Contro
A quantum mechanical version of Price's theorem for Gaussian states
This paper is concerned with integro-differential identities which are known
in statistical signal processing as Price's theorem for expectations of
nonlinear functions of jointly Gaussian random variables. We revisit these
relations for classical variables by using the Frechet differentiation with
respect to covariance matrices, and then show that Price's theorem carries over
to a quantum mechanical setting. The quantum counterpart of the theorem is
established for Gaussian quantum states in the framework of the Weyl functional
calculus for quantum variables satisfying the Heisenberg canonical commutation
relations. The quantum mechanical version of Price's theorem relates the
Frechet derivative of the generalized moment of such variables with respect to
the real part of their quantum covariance matrix with other moments. As an
illustrative example, we consider these relations for quadratic-exponential
moments which are relevant to risk-sensitive quantum control.Comment: 11 pages, to appear in the Proceedings of the Australian Control
Conference, 17-18 November 2014, Canberra, Australi
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