Stochastic Linear Quadratic Optimal Control Problems In Infinite Horizon

Keywords

49N10; 49N35; 93D15; 93E20; Algebraic Riccati equation; Closed-loop representation; Closed-loop solvability; Open-loop solvability; Stabilizability; Static stabilizing solution; Stochastic linear quadratic optimal control

Abstract

This paper is concerned with stochastic linear quadratic (LQ, for short) optimal control problems in an infinite horizon with constant coefficients. It is proved that the non-emptiness of the admissible control set for all initial state is equivaleznt to the L2-stabilizability of the control system, which in turn is equivalent to the existence of a positive solution to an algebraic Riccati equation (ARE, for short). Different from the finite horizon case, it is shown that both the open-loop and closed-loop solvabilities of the LQ problem are equivalent to the existence of a static stabilizing solution to the associated generalized ARE. Moreover, any open-loop optimal control admits a closed-loop representation. Finally, the one-dimensional case is worked out completely to illustrate the developed theory.

Publication Date

8-1-2018

Publication Title

Applied Mathematics and Optimization

Volume

78

Issue

1

Number of Pages

145-183

Document Type

Article

Personal Identifier

scopus

DOI Link

https://doi.org/10.1007/s00245-017-9402-8

Socpus ID

85013668928 (Scopus)

Source API URL

https://api.elsevier.com/content/abstract/scopus_id/85013668928

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