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Hybrid Dynamic Systems

Critical infrastructure systems (CIS) of interest are composed of two fundamentally different, yet joined systems: the network of interconnected dynamic components and the logical switching designed to maintain a desired level of performance.  This structure permits CIS to be modeled within a well-defined Hybrid Dynamical Systems (HDS) framework1. The significance of the HDS model is not only in the definitions, but also in the implications for organization of associated computer simulations and applicability of analysis tools.

In general, HDS are those systems with interacting continuous and discrete system dynamics (1).  A common HDS example is one composed of a finite-state machine (the discrete system) that selects from a set of right-hand sides for ordinary differential equations (the continuous system).  This structure is shown conceptually in figure 1 with {A, B, C} the states of the discrete system, y the (measured) output of the continuous system compared with critical thresholds ycr1 and ycr2, u the system input, and x the state of the continuous system with behavior governed by the multi-valued right-hand side fi(x,u) where iÎ{A, B, C}.

Conceptual diagram of HDS structure


1.  Matveev, A. S. and A.V. Savkin, Qualitative Theory of Hybrid Dynamical Systems, Birkhäuser Boston, 2000.

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