A model checking framework for linear time invariant switching systems using structural systems analysis

Abstract

This paper introduces the concept of structural hybrid systems to address, as a particular case, the model checking problem of switching (possible large scale) linear time invariant systems. Within the proposed setup, we provide necessary conditions to ensure properties such as controllability, at each time. We show that such model checking controllability properties can be implemented using efficient algorithms (with polynomial complexity). An example, based on the IEEE 5-bus power system, is presented which illustrates our model checking and design methodologies. This work was partially supported by grant SFRH/BD/33779/2009, from Fundac ¸ão para a Ciência e a Tecnologia (FCT) and the CMU-Portugal (ICTI) program, and by projects CONAV/FCT-PT (PTDC/EEACRO/113820/2009), FCT (PEst-OE/EEI/LA0008/2013) and MORPH (EU FP7 No. 288704).

Analysis and design of electric power grids with p-robustness guarantees using a structural hybrid system approach

“…Theorem 1 ( [5], [15]): Let D(Ā) = (X , E X ,X ) be the state digraph and its DAG representation with k SCCs, de- Finally, we present some additional concepts necessary to study the structure of the network topology constraints and its robustness to transmission line failures in Section IV. For both directed and undirected graph, with some abuse of notation, we denote an edge from vertex…”

“…Nevertheless, to preclude the system to lose structural controllability, two strategies are possible: (i) reallocate resources such as inputs to ensure that the dynamical system associated with islands formed after transmission line failures is structurally controllable, see [5] for details; or (ii) redesign the network topology, by adding transmission lines, to ensure that the structural switching system representing the dynamics of the electric power grid has a pre-specified level of robustness. In the next subsection, we explore the latter scenario in further detail.…”

“…Motivated by the uncertainties in the models' parameters and/or floating point approximations, we resort to structural systems [4], where only the location of the zero/nonzero entries of the system plant matrices is considered. In the context of switching systems, we obtain the so-called structural switching systems, a subclass of structural hybrid systems introduced in [5]. One of the distinct characteristics of structural systems is the capability of inferring controllability properties that hold almost always.…”

“…In this paper, the proposed approach and design scenarios ensure that the system is always structurally controllable and, therefore, capable of maintaining the operation standards. Additional references about structural hybrid systems can be found in [5], and applications of structural switching systems can be found, for instance, in [13], [14].…”

Structural minimum controllability problem for switched linear continuous-time systems

“…The current work also differs from [23], [24], where the structural minimum controllability problem aimed to ensure structural controllability for each mode of the switched continuoustime linear system; note that this conservative notion contrasts with the controllability definition considered in the present manuscript. In [20] the structural minimal controllability problem for linear time-invariant systems was considered under heterogenous cost, i.e., the variables actuated can incur in different costs.…”