7,862 research outputs found
Lower Bounds on Exponential Moments of the Quadratic Error in Parameter Estimation
Considering the problem of risk-sensitive parameter estimation, we propose a
fairly wide family of lower bounds on the exponential moments of the quadratic
error, both in the Bayesian and the non--Bayesian regime. This family of
bounds, which is based on a change of measures, offers considerable freedom in
the choice of the reference measure, and our efforts are devoted to explore
this freedom to a certain extent. Our focus is mostly on signal models that are
relevant to communication problems, namely, models of a parameter-dependent
signal (modulated signal) corrupted by additive white Gaussian noise, but the
methodology proposed is also applicable to other types of parametric families,
such as models of linear systems driven by random input signals (white noise,
in most cases), and others. In addition to the well known motivations of the
risk-sensitive cost function (i.e., the exponential quadratic cost function),
which is most notably, the robustness to model uncertainty, we also view this
cost function as a tool for studying fundamental limits concerning the tail
behavior of the estimation error. Another interesting aspect, that we
demonstrate in a certain parametric model, is that the risk-sensitive cost
function may be subjected to phase transitions, owing to some analogies with
statistical mechanics.Comment: 28 pages; 4 figures; submitted for publicatio
Linear estimation in Krein spaces. Part II. Applications
We have shown that several interesting problems in H∞-filtering, quadratic game theory, and risk sensitive control and estimation follow as special cases of the Krein-space linear estimation theory developed in Part I. We show that all these problems can be cast into the problem of calculating the stationary point of certain second-order forms, and that by considering the appropriate state space models and error Gramians, we can use the Krein-space estimation theory to calculate the stationary points and study their properties. The approach discussed here allows for interesting generalizations, such as finite memory adaptive filtering with varying sliding patterns
A Quantum Langevin Formulation of Risk-Sensitive Optimal Control
In this paper we formulate a risk-sensitive optimal control problem for
continuously monitored open quantum systems modelled by quantum Langevin
equations. The optimal controller is expressed in terms of a modified
conditional state, which we call a risk-sensitive state, that represents
measurement knowledge tempered by the control purpose. One of the two
components of the optimal controller is dynamic, a filter that computes the
risk-sensitive state.
The second component is an optimal control feedback function that is found by
solving the dynamic programming equation. The optimal controller can be
implemented using classical electronics.
The ideas are illustrated using an example of feedback control of a two-level
atom
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