• Jean-Pierre Aubin
Part of the Systems & Control: Foundations & Applications book series (MBC)


Consider the evolution of a control system with (multivalued) feedbacks:
where the state x(·) ranges over a finite dimensional vector-space X and the control u(·) ranges over another finite dimensional vector-space Z. Here, the first equation describes how the control — regarded as an input to the system — yields the state of the system1 — regarded as an output — whereas the second inclusion shows how the state-output “feeds back” to the control-input. The set-valued map U : XZ may be called an “a priori feedback”. It describes the state-dependent constraints on the controls. A solution to this system is a function tx(t) satisfying this system for some control tu(t).


General Equilibrium Theory Contingent Derivative Viability Kernel Cultural Code Viability Constraint 
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Copyright information

© Springer Science+Business Media New York 2009

Authors and Affiliations

  • Jean-Pierre Aubin
    • 1
  1. 1.EDOMADE (Ecole Doctorale de Mathématique de la Décision)Université de Paris-DauphineParis cedex 16France

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