Optimal control of DAEs with unconstrained terminal costs

Paul Wijnbergen*, Stephan Trenn

*Corresponding author for this work

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This paper is concerned with the linear quadratic optimal control problem for impulse controllable differential algebraic equations on a bounded half open interval. Regarding the cost functional, a general positive semi-definite weight matrix is considered in the terminal cost. It is shown that for this problem, there generally does not exist an input that minimizes the cost functional. First it is shown that the problem can be reduced to finding an input to an index-1 DAE that minimizes a different quadratic cost functional. Second, necessary and sufficient conditions in terms of matrix equations are given for the existence of an optimal control.
Original languageEnglish
Title of host publication2021 60th IEEE Conference on Decision and Control (CDC)
Number of pages6
ISBN (Print)978-1-6654-3660-1
Publication statusPublished - 17-Dec-2021
Event2021 60th IEEE Conference on Decision and Control (CDC) - Austin, TX, United States
Duration: 14-Dec-202117-Dec-2021


Conference2021 60th IEEE Conference on Decision and Control (CDC)
Country/TerritoryUnited States
City Austin, TX


  • Sufficient conditions
  • Costs
  • Conferences
  • Optimal control
  • Differential algebraic equations
  • Switches

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