By Topic

Optimization of stochastic linear systems with additive measurement and process noise using exponential performance criteria

Sign In

Cookies must be enabled to login.After enabling cookies , please use refresh or reload or ctrl+f5 on the browser for the login options.

Formats Non-Member Member
$33 $13
Learn how you can qualify for the best price for this item!
Become an IEEE Member or Subscribe to
IEEE Xplore for exclusive pricing!
close button

puzzle piece

IEEE membership options for an individual and IEEE Xplore subscriptions for an organization offer the most affordable access to essential journal articles, conference papers, standards, eBooks, and eLearning courses.

Learn more about:

IEEE membership

IEEE Xplore subscriptions

3 Author(s)
J. Speyer ; C.S. Draper Laboratory, Cambridge, MA, USA ; J. Deyst ; D. Jacobson

The expected value of a multiplicative performance criterion, represented by the exponential of a quadratic function of the state and control variables, is minimized subject to a discrete stochastic linear system with additive Gaussian measurement and process noise. This cost function, which is a generalization of the mean quadratic cost criterion, allows a degree of shaping of the probability density function of the quadratic cost criterion. In general, the control law depends upon a gain matrix which operates linearly on the smoothed history of the state vector from the initial to the current time. This gain matrix explicitly includes the covariance of the estimation errors of the entire state history. The separation theorem holds although the certainty equivalence principle does not. Two special cases are of importance. The first occurs when only the terminal state is costed. A feedback control law, linear in the current estimate of the state, results where the feedback gains are functionally dependent upon the error covariance of the current state estimate. The second occurs if all the intermediate states are costed but there is no process noise except for an initial condition uncertainty. A feedback law results which depends not only upon the current dynamical state estimate but also on an additional vector which is path dependent.

Published in:

IEEE Transactions on Automatic Control  (Volume:19 ,  Issue: 4 )