Optimal control problems with a continuous inequality constraint on the state and the control

R. C. Loxton, K. L. Teo, V. Rehbock, Ka Fai Cedric Yiu

Research output: Journal article publicationJournal articleAcademic researchpeer-review

144 Citations (Scopus)


We consider an optimal control problem with a nonlinear continuous inequality constraint. Both the state and the control are allowed to appear explicitly in this constraint. By discretizing the control space and applying a novel transformation, a corresponding class of semi-infinite programming problems is derived. A solution of each problem in this class furnishes a suboptimal control for the original problem. Furthermore, we show that such a solution can be computed efficiently using a penalty function method. On the basis of these two ideas, an algorithm that computes a sequence of suboptimal controls for the original problem is proposed. Our main result shows that the cost of these suboptimal controls converges to the minimum cost. For illustration, an example problem is solved.
Original languageEnglish
Pages (from-to)2250-2257
Number of pages8
Issue number10
Publication statusPublished - 1 Oct 2009


  • Constraints
  • Nonlinear control systems
  • Nonlinear programming
  • Optimal control

ASJC Scopus subject areas

  • Control and Systems Engineering
  • Electrical and Electronic Engineering


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