Delayed Stochastic Linear-Quadratic Control Problem and Related Applications

Delayed Stochastic Linear-Quadratic Control Problem and Related Applications

We discuss a quadratic criterion optimal control problem for stochastic linear system with delay in both state and control variables. This problem will lead to a kind of generalized forward-backward stochastic differential equations FBSDEs with Itô’s stochastic delay equations as forward equations and anticipated backward stochastic differential equations as backward equations. Especially, we p...

Linear Quadratic Optimal Control Problem of Stochastic Switching Systems

Switched systems have numerous applications in control of real systems as mechanical systems, automotive industry, aircraft and air traffic control, switching power converters, and many other fields. Optimal control problems of switching systems require the decision of both the optimal solutions and switching sequences. The stochastic optimal control problem of linear switching systems with qua...

Stochastic linear quadratic control problem of switching systems with constraints

Time-Inconsistent Stochastic Linear-Quadratic Control

Abstract. In this paper, we formulate a general time-inconsistent stochastic linear–quadratic (LQ) control problem. The time-inconsistency arises from the presence of a quadratic term of the expected state as well as a state-dependent term in the objective functional. We define an equilibrium, instead of optimal, solution within the class of open-loop controls, and derive a sufficient condition...

Linear-quadratic control problem with a linear term on semiinfinite interval: theory and applications∗

We describe a complete solution of the linear-quadratic control problem on a semiinfinite interval with the linear term in the objective function. Some applications are considered.