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Talk Abstract

Controlling Noisy Systems

Controlling Noisy Systems

**Daniel Ocone **

Rutgers University

ocone@math.rutgers.edu

This talk surveys theories
of control in the presence of noise, their
successes and limits. Throughout we pay particular
attention to what types of noise models can be
handled. In optimal stochastic
control, one assumes a full statistical description of
the noise and translates the design objective
into a problem of minimizing an expected cost.
The classical LQG problem so prominent in applications
is an example. In H^{} control, no model on
the noise is assumed; it is considered to be an unknown,
possibly random disturbance. The design objective is
to protect against worst case disturbances by looking for
feedback controls that give dissipative and stable systems.
The important modelling constraint for success in stochastic optimal
control is summarized in the word "Markov."
In practice this means that the noise
is independent increment, white noise, and that state
feedback control leads to Markov processes. In the LQG case
the analysis can be framed in an L^{2} setting in
which only first and second moments of the noise are modelled.
We explain this and relate it to the basis of the optimization
theory, dynamic programming. We shall also summarize
the H^{}
theory. Interestingly, the H^{} theory
also involves. We shall summarize the approach and
describe its relation to risk sensitive stochastic control.

Modeling and Analysis of Noise in Integrated Circuits and Systems