Local optimization of dynamic programs with guaranteed satisfaction of path constraints

• Jun Fu ^[1] ; Johannes M.M. Faust ^[2] ; Benoît Chachuat ^[3] ; Alexander Mitsos ^[2]
  1. [1] Massachusetts Institute of Technology

     Massachusetts Institute of Technology

     City of Cambridge, Estados Unidos

     
  2. [2] Rheinisch-Westfälische Technische Hochschule Aachen University

     Rheinisch-Westfälische Technische Hochschule Aachen University

     Städteregion Aachen, Alemania

     
  3. [3] Imperial College, London, UK

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• Localización: Automatica: A journal of IFAC the International Federation of Automatic Control, ISSN 0005-1098, Vol. 62, 2015, págs. 184-192
• Idioma: inglés
• Texto completo no disponible (Saber más ...)
• Resumen

  • An algorithm is proposed for locating a feasible point satisfying the KKT conditions to a specified tolerance of feasible inequality-path-constrained dynamic programs (PCDP) within a finite number of iterations. The algorithm is based on iteratively approximating the PCDP by restricting the right-hand side of the path constraints and enforcing the path constraints at finitely many time points. The main contribution of this article is an adaptation of the semi-infinite program (SIP) algorithm proposed in Mitsos (2011) to PCDP. It is proved that the algorithm terminates finitely with a guaranteed feasible point which satisfies the first-order KKT conditions of the PCDP to a specified tolerance. The main assumptions are: (i) availability of a nonlinear program (NLP) local solver that generates a KKT point of the constructed approximation to PCDP at each iteration if this problem is indeed feasible; (ii) existence of a Slater point of the PCDP that also satisfies the first-order KKT conditions of the PCDP to a specified tolerance; (iii) all KKT multipliers are nonnegative and uniformly bounded with respect to all iterations. The performance of the algorithm is analyzed through two numerical case studies.