The Delayed Doubly Stochastic Linear Quadratic Optimal Control Problem

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...

Optimal Linear Quadratic Control

Linear Quadratic Optimal Control

In previous lectures, we discussed the design of state feedback controllers using using eigenvalue (pole) placement algorithms. For single input systems, given a set of desired eigenvalues, the feedback gain to achieve this is unique (as long as the system is controllable). For multi-input systems, the feedback gain is not unique, so there is additional design freedom. How does one utilize this...

Characterization 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...