A constructive interior penalty method for optimal control problems with state and input constraints

This paper exposes a methodology which allows us to address constrained optimal control of non linear systems by interior penalty methods. A constructive choice for the penalty functions that are introduced to account for the constraints is established in the article. It is shown that it allows us to approach the solution of the non linear optimal control problem using a sequence of unconstrained problems, whose solutions are readily characterized by the simple calculus of variations. An illustrative example is given. The paper extends recent contributions, originally focused on linear dynamics.