Please use this identifier to cite or link to this item: http://hdl.handle.net/10397/29959
Title: Solvability of indefinite stochastic Riccati equations and linear quadratic optimal control problems
Authors: Huang, J 
Yu, Z
Keywords: Backward stochastic differential equation (BSDE)
Stochastic linear quadratic optimal control
Stochastic Riccati equation
Issue Date: 2014
Publisher: Elsevier Science Bv
Source: Systems and control letters, 2014, v. 68, no. 1, p. 68-75 How to cite?
Journal: Systems and Control Letters 
Abstract: A new approach to study the indefinite stochastic linear quadratic (LQ) optimal control problems, which we called the "equivalent cost functional method", is introduced by Yu (2013) in the setup of Hamiltonian system. On the other hand, another important issue along this research direction, is the possible state feedback representation of optimal control and the solvability of associated indefinite stochastic Riccati equations. As the response, this paper continues to develop the equivalent cost functional method by extending it to the Riccati equation setup. Our analysis is featured by its introduction of some equivalent cost functionals which enable us to have the bridge between the indefinite and positive-definite stochastic LQ problems. With such bridge, some solvability relation between the indefinite and positive-definite Riccati equations is further characterized. It is remarkable the solvability of the former is rather complicated than the latter, hence our relation provides some alternative but useful viewpoint. Consequently, the corresponding indefinite linear quadratic problem is discussed for which the unique optimal control is derived in terms of state feedback via the solution of the Riccati equation. In addition, some example is studied using our theoretical results.
URI: http://hdl.handle.net/10397/29959
ISSN: 0167-6911
DOI: 10.1016/j.sysconle.2014.03.009
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