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In this paper, we develop a compositional scheme for the construction of continuous approximations for interconnections of infinitely many discrete-time switched systems. An approximation (also known as abstraction) is itself a continuous-space system, which can be used as a replacement of the original (also known as concrete) system in a controller design process. Having designed a controller for the abstract system, it is refined to a more detailed one for the concrete system. We use the notion of so-called simulation functions to quantify the mismatch between the original system and its approximation. In particular, each subsystem in the concrete network and its corresponding one in the abstract network are related through a notion of local simulation functions. We show that if the local simulation functions satisfy certain small-gain type conditions developed for a network containing infinitely many subsystems, then the aggregation of the individual simulation functions provides an overall simulation function quantifying the error between the overall abstraction network and the concrete one. In addition, we show that our methodology results in a scale-free compositional approach for any finite-but-arbitrarily large networks obtained from truncation of an infinite network. We provide a systematic approach to construct local abstractions and simulation functions for networks of linear switched systems. The required conditions are expressed in terms of linear matrix inequalities that can be efficiently computed. We illustrate the effectiveness of our approach through an application to AC islanded microgirds.
This paper introduces the notion of quantitative resilience of a control system. Following prior work, we study systems enduring a loss of control authority over some of their actuators. Such a malfunction results in actuators producing possibly unde
Recently we developed supervisor localization, a top-down approach to distributed control of discrete-event systems (DES) with finite behavior. Its essence is the allocation of monolithic (global) control action among the local control strategies of
One of the fundamental concerns in the operation of modern power systems is the assessment of their frequency stability in case of inertia-reduction induced by the large share of power electronic interfaced resources. Within this context, the paper p
This paper presents a compositional framework for the construction of symbolic models for a network composed of a countably infinite number of finite-dimensional discrete-time control subsystems. We refer to such a network as infinite network. The pr
In this paper, we propose a compositional approach to construct opacity-preserving finite abstractions (a.k.a symbolic models) for networks of discrete-time nonlinear control systems. Particularly, we introduce new notions of simulation functions tha