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On the optimality of state feedback in linear quadratic control

On the optimality of state feedback in linear quadratic control
On the optimality of state feedback in linear quadratic control
We study the linear quadratic control problem from a representation-free point of view, and we show that this formulation brings forth several results of independent interest. Among these results are two self-contained, new proofs of the optimality of state feedback control laws which do not depend on an a priori state-space representation, and an orthogonality property characterizing the set of optimal trajectory of a LQ-control problem. The relationship of these ideas with the difference Riccati equation is also investigated. We also give recursive formulas for the computation of the optimal trajectories in LQ -optimal control problems for systems described by higher-order difference equations.
Rapisarda, Paolo
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Markovsky, Ivan
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Rapisarda, Paolo
79efc3b0-a7c6-4ca7-a7f8-de5770a4281b
Markovsky, Ivan
7d632d37-2100-41be-a4ff-90b92752212c

Rapisarda, Paolo and Markovsky, Ivan (2007) On the optimality of state feedback in linear quadratic control. Mathematics of Control, Signals, and Systems (MCSS).

Record type: Article

Abstract

We study the linear quadratic control problem from a representation-free point of view, and we show that this formulation brings forth several results of independent interest. Among these results are two self-contained, new proofs of the optimality of state feedback control laws which do not depend on an a priori state-space representation, and an orthogonality property characterizing the set of optimal trajectory of a LQ-control problem. The relationship of these ideas with the difference Riccati equation is also investigated. We also give recursive formulas for the computation of the optimal trajectories in LQ -optimal control problems for systems described by higher-order difference equations.

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Published date: July 2007
Organisations: Southampton Wireless Group

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Local EPrints ID: 264590
URI: http://eprints.soton.ac.uk/id/eprint/264590
PURE UUID: cc47e258-4135-4acf-8df4-adedc868edd5

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Date deposited: 25 Sep 2007
Last modified: 14 Mar 2024 07:52

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Contributors

Author: Paolo Rapisarda
Author: Ivan Markovsky

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