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Optimality: Minimum-Time for Linear Systems

  • Eduardo D. Sontag
Part of the Texts in Applied Mathematics book series (TAM, volume 6)

Abstract

We consider time-invariant continuous-time linear systems
(10.1)
with the control-value set U being a compact convex subset of ℝ m . As usual, a control is a measurable map ω: [0,T] → ℝ m so that ω(t) ∈ U for almost all t ∈ [0,T]. We denote by L m (0,T) the set consisting of measurable essentially bounded maps from [0,T] into ℝ m (when m = 1, just L (0,T)) and view the set of all controls as a subset L U (0,T) ⊆ L m (0,T). In this chapter, we write simply L U instead of L U , because, U being compact, all maps into U are essentially bounded.

Keywords

Maximum Principle Nonzero Vector Supporting Hyperplane Matrix Pair Minimal Time Function 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer Science+Business Media New York 1998

Authors and Affiliations

  • Eduardo D. Sontag
    • 1
  1. 1.Department of MathematicsRutgers UniversityNew BrunswickUSA

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