# A fully unconstrained interior point algorithm for multivariable state and input constrained optimal control problems

September 2012 Category : Optimal control | All

**Authors**: P. Malisani, F. Chaplais, N. Petit, 6th European Congress on Computational Methods in Applied Sciences and Engineering (ECCOMAS 2012), September 10-14 2012, Vienna, Austria.

This paper exposes a methodology to solve constrained optimal control problems for non linear systems using 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 this choice allows one to approach a 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 single input single output systems.

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**BibTeX**:

@Proceedings{,

author = {P. Malisani, F. Chaplais, N. Petit},

editor = {Eberhardsteiner J., Böhm, H.J., Rammerstorfer F.G},

title = {A fully unconstrained interior point algorithm for multivariable state and input constrained optimal control problems},

booktitle = {6th European Congress on Computational Methods in Applied Sciences and Engineering (ECCOMAS 2012)},

volume = {},

publisher = {Vienna University of Technology},

address = {Vienna},

pages = {1-17},

year = {2012},

abstract = {This paper exposes a methodology to solve constrained optimal control problems for non linear systems using 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 this choice allows one to approach a 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 single input single output systems.},

keywords = {state constrained optimal control, interior point methods, penalty functions}}