By Topic

Structural Invariant Subspaces of Singular Hamiltonian Systems and Nonrecursive Solutions of Finite-Horizon Optimal Control Problems

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

1 Author(s)
Elena Zattoni ; Dept. of Electron., Comput. Sci., & Syst., Bologna Univ., Bologna

This note introduces an analytic, nonrecursive approach to the solution of finite-horizon optimal control problems formulated for discrete- time stabilizable systems. The procedure, which adapts to handle both the case where the final state is weighted by a generic quadratic function and the case where the final state is an admissible, sharply assigned one, provides the optimal control sequences, as well as the corresponding optimal state trajectories, in closed form, as functions of time, by exploiting an original characterization of a pair of structural invariant subspaces associated to the singular Hamiltonian system. The results hold on the fairly general assumptions which guarantee the existence and uniqueness of the stabilizing solution of the corresponding discrete algebraic Riccati equation and, as a consequence, solvability of an appropriately defined symmetric Stein equation. Some issues to be considered in the numerical implementation of the proposed approach are mentioned. The application of the suggested methodology to H2 optimal rejection with preview is also discussed.

Published in:

IEEE Transactions on Automatic Control  (Volume:53 ,  Issue: 5 )