Solvability Conditions for Indefinite Linear Quadratic Optimal Stochastic Control Problems and Associated Stochastic Riccati Equations
نویسندگان
چکیده
منابع مشابه
Solvability Conditions for Indefinite Linear Quadratic Optimal Stochastic Control Problems and Associated Stochastic Riccati Equations
A linear quadratic optimal stochastic control problem with random coefficients and indefinite state/control weight costs is usually linked to an indefinite stochastic Riccati equation (SRE), which is a matrix-valued quadratic backward stochastic differential equation along with an algebraic constraint involving the unknown. Either the optimal control problem or the SRE is solvable only if the g...
متن کاملSolvability of indefinite stochastic Riccati equations and linear quadratic optimal control problems
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 [15] 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 indefini...
متن کاملIndefinite Stochastic Linear Quadratic Control and Generalized Differential Riccati
A stochastic linear quadratic (LQ) control problem is indefinite when the cost weighting matrices for the state and the control are allowed to be indefinite. Indefinite stochastic LQ theory has been extensively developed and has found interesting applications in finance. However, there remains an outstanding open problem, which is to identify an appropriate Riccati-type equation whose solvabili...
متن کاملIndefinite Stochastic Linear Quadratic Control and Generalized Differential Riccati Equation
We consider a stochastic linear–quadratic (LQ) problem with possible indefinite cost weighting matrices for the state and the control. An outstanding open problem is to identify an appropriate Riccati-type equation whose solvability is equivalent to the solvability of this possibly indefinite LQ problem. In this paper we introduce a new type of differential Riccati equation, called the generali...
متن کاملCharacterization of optimal feedback for stochastic linear quadratic control problems
One of the fundamental issues in Control Theory is to design feedback controls. It is well-known that, the purpose of introducing Riccati equations in the study of deterministic linear quadratic control problems is exactly to construct the desired feedbacks. To date, the same problem in the stochastic setting is only partially well-understood. In this paper, we establish the equivalence between...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: SIAM Journal on Control and Optimization
سال: 2015
ISSN: 0363-0129,1095-7138
DOI: 10.1137/140956051