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Set-Valued Maps

  • Randy A. Freeman
  • Petar Kokotović
Part of the Modern Birkhäuser Classics book series (MBC)

Abstract

In robust control theory, an uncertain dynamical system is described by a set of models rather than a single model. For example, a system with an unknown parameter generates a set of models, one for each possible value of the parameter; likewise for a system with an unknown disturbance (which can be a function of time as well as state variables and control inputs). As a result, any map one might define for a single model becomes a set-valued map. Such is the case with an input/output map, a map from initial states to final states, or a map from disturbances to values of cost functionals. It is therefore natural that, in our study of robust nonlinear control, we use the language and mathematical apparatus of set-valued maps. In doing so, we follow the tradition started in the optimal control literature in the early sixties [27, 153] and continued in the control-related fields of nonsmooth analysis, game theory, differential inclusions, and viability theory [21, 127, 128, 5, 79].

Keywords

Neighborhood Versus Continuity Property Steiner Point Closed Unit Ball Selection Theorem 
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

© Birkhäuser Boston 2008

Authors and Affiliations

  • Randy A. Freeman
    • 1
  • Petar Kokotović
    • 2
  1. 1.Department of Electrical and Computer EngineeringNorthwestern UniversityEvanstonUSA
  2. 2.Department of Electrical and Computer EngineeringUniversity of CaliforniaSanta BarbaraUSA

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