Controller synthesis for infinite-state systems / synthese de controleurs pour des systemes a espace d'états infini

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``Software must run closed loop.'' This statement from Robert Laddaga emerges from thinking about software agent evolution from conventional programs. Software agents require more monitoring and control because of their greater degree of autonomy, adaptation and mobility. The control of dynamic systems is a discipline that is born at the beginning of last century. Many solutions founded on powerful mathematical theories have been proposed for continuous systems and more recently for discrete event systems as programs or software agents. In the last case, the real impact is less significant, although several efforts have been made to elaborate a substantial theory called Supervisory Control Theory. Controlling programs during their execution implies, amongst other, solving fundamental problems related to their representation in a mathematical form. A natural way to represent a program is to use an automaton with a stack of unlimited size as well parameters that symbolize unbounded values. It results from this modelling pushdown systems and parameterized systems with infinitely many reachable states. Therefore, the control of infinite-state systems raises new important issues, which have been study very little in the past in the context of the Supervisory Control Theory, and constitutes the main subject of the present research program.