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A new Bayesian approach to linear system identification
has been proposed in a series of recent papers. The
main idea is to frame linear system identification as predictor
estimation in an infinite dimensional space, with the aid of
regularization/Bayesian techniques. This approach guarantees
the identification of stable predictors based on the prediction
error minimization. Unluckily, the stability of the predictors
does not guarantee the stability of the impulse response of
the system. In this paper we propose and compare various
techniques to guarantee that the final model identified following
this Bayesian approach is stable. First, we consider the socalled
“LMI - constraint” approach and adapt it to constrain
the eigenvalues of the estimated model within the unit circle.
A second possibility which is being considered is to add to the
“classic” Stable-Spline algorithm a penalty term, depending on
the maximum absolute value of the eigenvalue of the system.
This last technique has the advantage of being integrated
directly inside the pre-existing optimization problem and not to
simply post-process the estimated model to guarantee stability.
Finally, we considered a Monte Carlo Markov Chain approach
sampling in both the space of hyper-parameters and of impulse
responses. Simulations results comparing these techniques will
be provided.

We describe tradeoffs between the performance in visual decision problems and the control authority that the agent can exercise on the sensing process. We focus on problems of “coverage” (ensuring that all regions in the scene are seen) and “change estimation” (finding and learning an unknown object in an otherwise known and static scene), propose a measure of control authority and empirically relate it to the expected risk and its proxy (conditional entropy of the posterior density). We then show that a “passive” agent can provide no guarantees on performance beyond what is afforded by the priors, and that an “omnipotent” agent, capable of infinite control authority, can achieve arbitrarily good performance (asymptotically).