Paper Info
Title
Solvability of indefinite stochastic Riccati equations and linear quadratic optimal control problems.
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.
Year
DOI
Venue
2014
10.1016/j.sysconle.2014.03.009
Systems & Control Letters
Keywords
Field
DocType
Stochastic Riccati equation,Stochastic linear quadratic optimal control,Backward stochastic differential equation (BSDE)
Mathematical optimization,Optimal control,Linear-quadratic-Gaussian control,Control theory,Hamiltonian system,Algebraic Riccati equation,Riccati equation,Linear-quadratic regulator,Linear quadratic optimal control,Mathematics,Stochastic control
Journal
Volume
ISSN
Citations 
68
0167-6911
6
PageRank 
References 
Authors
0.49
7
2
Name
Order
Citations
PageRank
Jianhui Huang18114.20
Zhiyong Yu243640.86