On the SQH method for solving optimal control problems with non-smooth state cost functionals or constraints

In this study, we discuss how the sequential quadratic Hamiltonian (SQH) scheme can be used to solve optimal control problems with non-smooth state constraints or non-smooth state cost terms. Theoretical and numerical aspects are both considered. Further, we connect to other recent techniques to solve such optimal control problems. The capability to handle non-smooth state terms extends the possibilities of modeling costs of the state and the dynamics of a system, e.g. to weight the deviation of the state from a desired state in an L1-norm. In this work, the non-smooth state terms are transformed into a bilinear structure on which the SQH scheme proved to solve optimal control problems fast promising an efficient numerical solution also in the non-smooth case. The novelty of the presented approach is that the non-smoothness is transformed into a bilinear structure. It is proved that the SQH method, which is based on the Pontryagin maximum principle, converges to an optimal solution of the corresponding transformed optimal control problem without any globalization techniques.