Contribución al control geométrico de sistemas de eventos discretos en el álgebra max-plus

Abstract : This work is in the context of the theory of linear Systems in the dioids. The initial motivation of this study was to contribute to the analysis and control of max-plus linear systems, specifically using a geometric approach. The contribution of this thesis focuses on two issues. The first part is dedicated to study of the relationship between the concepts of controlled invariance and dynamic state feedback controlled invariance in a semi-ring. This relationship allows us to show the equivalence of these two concepts. The second part relates to a new problem in the theory of max-plus linear systems, it is the synthesis, with a geometric approach, of a static state feedback control law, in order to satisfy a set of specifications that apply to the state space of the system. This is specifically to control of discrete event systems described by a linear model in max-plus. We define and characterize the set of admissible initial conditions, which are the cause of non-decreasing solutions. Temporal restrictions on the system state space are described by the semi-module defined by the image of the Kleene star of the matrix associated with time restrictions. The geometric properties of this semi-module are studied. Sufficient conditions for the existence of a causal control law by static feedback are presented. Calculating causal control laws is also presented. To illustrate the application of this approach, two control problems are presented.
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Carolina Cardenas Lucena. Contribución al control geométrico de sistemas de eventos discretos en el álgebra max-plus. Automatic. École centrale de Nantes; Universidad de los Andes (Mérida, Venezuela), 2016. Español. ⟨NNT : 2016ECDN0004⟩. ⟨tel-02185328⟩

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