Lipschitz Stability of Broken Extremals in Bang-Bang Control Problems

  • Ursula Felgenhauer
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4818)


Optimal bang-bang controls appear in problems where the system dynamics linearly depends on the control input. The principal control structure as well as switching points localization are essential solution characteristics. Under rather strong optimality and regularity conditions, for so-called simple switches of (only) one control component, the switching points had been shown being differentiable w.r.t. problem parameters. In case that multiple (or: simultaneous) switches occur, the differentiability is lost but Lipschitz continuous behavior can be observed e.g. for double switches. The proof of local structural stability is based on parametrizations of broken extremals via certain backward shooting approach. In a second step, the Lipschitz property is derived by means of nonsmooth Implicit Function Theorems.


Switching Point Control Component Multiple Switch Simple Switch Bang Control 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  • Ursula Felgenhauer
    • 1
  1. 1.Institut für MathematikBrandenburgische Technische Universität CottbusCottbusGermany

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