Tailconstraining stochastic linearquadratic control: a large deviation and statistical physics approach
Abstract
The standard definition of the stochastic risksensitive linearquadratic (RSLQ) control depends on the risk parameter, which is normally left to be set exogenously. We reconsider the classical approach and suggest two alternatives, resolving the spurious freedom naturally. One approach consists in seeking for the minimum of the tail of the probability distribution function (PDF) of the cost functional at some large fixed value. Another option suggests minimizing the expectation value of the cost functional under a constraint on the value of the PDF tail. Under the assumption of resulting control stability, both problems are reduced to static optimizations over a stationary control matrix. The solutions are illustrated using the examples of scalar and 1D chain (string) systems. The large deviation selfsimilar asymptotic of the cost functional PDF is analyzed.
 Publication:

Journal of Statistical Mechanics: Theory and Experiment
 Pub Date:
 August 2012
 DOI:
 10.1088/17425468/2012/08/P08007
 arXiv:
 arXiv:1204.0820
 Bibcode:
 2012JSMTE..08..007C
 Keywords:

 Condensed Matter  Statistical Mechanics;
 Mathematics  Optimization and Control
 EPrint:
 11 pages