A Newton-type method and optimality test for problems with bang-singular-bang optimal control
- In the paper, a second-order method is investigated for control problems
where the control has bang-singular-bang structure.
To start with, the first-order system is formulated as a variational
inequality including a differential equation for the switching function.
For this system, a certain inexact Josephy-Newton method is considered.
Under strong second-order sufficient conditions obtained via Goh's
transformation of control and state-adjoint data, the local solvability
is proved for the iterative problems. For so-called semilinear
problems, locally the state and adjoint iterates converge superlinearly.
The paper is completed by a Riccati test approach for verifying
second-order optimality.