Linear Quadratic Optimal Control Problem for Linear Stochastic Generalized System in Hilbert Spaces

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...

Indefinite 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...