Abstract
In section 1.2, we presented a factorization of problem P0 in a cylinder involving a Riccati equation. This equation is reminiscent of the equation that yields the optimal feedback for a control problem with linear dynamics and quadratic cost. We also studied this equation by adapting the method developed by J.-L. Lions to solve closed-loop optimal control problems in systems determined by parabolic equations. In this chapter, we will give an equivalent formulation of problem P0 in terms of an optimal control problem. We will show that decoupling this control problem produces the same decoupled system as. This approach provides a different kind of insight into the analytical difficulties posed by the Riccati due to the unboundedness of the operator P. However, note that this approach of reformulating the problem in terms of optimal control is limited to self-adjoint boundary value problems.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callMore From: Factorization of Boundary Value Problems Using the Invariant Embedding Method
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
