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A Weak Maximum Principle for Optimal Control Problems with Nonsmooth Mixed Constraints

Abstract

We derive a weak Maximum Principle for nonsmooth optimal control problem involving mixed constraints under some convexity assumptions. Notably we consider problems with possibly nonsmooth mixed constraints. A nonsmooth version of the positive linear independence of the gradients with respect to the control of the mixed constraints plays a key role in validation of our main result.

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Author information

Correspondence to M. d. R. de Pinho.

Additional information

Dedicated to Boris Mordukhovich on his 60th birthday.

The first author was support by FEDER and FCT-Portugal, grants POSC/EEA/SRI/61831/2004 and SFRH/BSAB/781/2008. G.N. Silva thanks the financial support of CNPq grant 200875/06-0 and FAPESP grant 07-5226-6.

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de Pinho, M.d.R., Loewen, P. & Silva, G.N. A Weak Maximum Principle for Optimal Control Problems with Nonsmooth Mixed Constraints. Set-Valued Anal 17, 203–221 (2009). https://doi.org/10.1007/s11228-009-0108-1

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Keywords

  • Optimal control
  • Maximum principle
  • Nonsmooth analysis

Mathematics Subject Classification (2000)

  • 49K15