Necessary conditions for optimal control problems with and without state constraints: a comparative study

  • Authors:

  • Md. Haider Ali Biswas;Maria Do Rosario De Pinho

  • Affiliations:

  • Department of Electrical and Computer Engineering, Faculty of Engineering, University of Porto, Portugal;Department of Electrical and Computer Engineering, Faculty of Engineering, University of Porto, Portugal

  • Venue:
  • WSEAS Transactions on Systems and Control
  • Year:
  • 2011

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Abstract

It is commonly accepted that optimal control theory was born with the publication of a seminal paper by Pontryagin and collaborates last century, at the end of 50's. Since then optimal control theory has played a relevant role not only in the dynamic optimization but also in the control and system engineering. Another crucial moment in this theory is closely related with the development of nonsmooth analysis during the 70's and 80's. Nonsmooth analysis has triggered a renew interest in optimal control problems and brought new solutions to old problems. Nowadays optimal control theory is essential to different areas like system engineering, economics and biology since many problems are modelled as optimal control problems. A challenging area of study in this theory remains that of state constraints. In this paper we review the very basic notions of optimal control problems with and without state constraints focussing on necessary conditions of optimality for state constrained problems.