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Register a new userCompositional Construction of Abstractions for Infinite Networks of Discrete-Time Switched Systems
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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.
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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 undesirable inputs over which the controller has real-time readings but no control. By definition, a system is resilient if it can still reach a target after a loss of control authority. However, after a malfunction a resilient system might be significantly slower to reach a target compared to its initial capabilities. We quantify this loss of performance through the new concept of quantitative resilience. We define this metric as the maximal ratio of the minimal times required to reach any target for the initial and malfunctioning systems. Naive computation of quantitative resilience directly from the definition is a time-consuming task as it requires solving four nested, possibly nonlinear, optimization problems. The main technical contribution of this work is to provide an efficient method to compute quantitative resilience. Relying on control theory and on three novel geometric results we reduce the computation of quantitative resilience to a single linear optimization problem. We illustrate our method on two numerical examples: an opinion dynamics scenario and a trajectory controller for low-thrust spacecrafts.
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 individual agents. In this report, we extend supervisor localization to study the distributed control of DES with infinite behavior. Specifically, we first employ Thistle and Wonhams supervisory control theory for DES with infinite behavior to compute a safety supervisor (for safety specifications) and a liveness supervisor (for liveness specifications), and then design a suitable localization procedure to decompose the safety supervisor into a set of safety local controllers, one for each controllable event, and decompose the liveness supervisor into a set of liveness local controllers, two for each controllable event. The localization procedure for decomposing the liveness supervisor is novel; in particular, a local controller is responsible for disabling the corresponding controllable event on only part of the states of the liveness supervisor, and consequently, the derived local controller in general has states number no more than that computed by considering the disablement on all the states. Moreover, we prove that the derived local controllers achieve the same controlled behavior with the safety and liveness supervisors. We finally illustrate the result by a Small Factory example.
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 proposes a framework that, by making use of linear models of the frequency response of different types of power plants, including also grid--forming and grid-following converters, is capable to infer a numerically tractable dynamical model to be used in frequency stability assessment. Furthermore, the proposed framework makes use of models defined in a way such that their parameters can be inferred from real-time measurements feeding a classical least squares estimator. The paper validates the proposed framework using a full-replica of the dynamical model of the IEEE 39 bus system simulated in a real-time platform.
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 proposed approach is based on the notion of alternating simulation functions. This notion relates a concrete network to its symbolic model with guaranteed mismatch bounds between their output behaviors. We propose a compositional approach to construct a symbolic model for an infinite network, together with an alternating simulation function, by composing symbolic models and alternating simulation functions constructed for subsystems. Assuming that each subsystem is incrementally input-to-state stable and under some small-gain type conditions, we present an algorithm for orderly constructing local symbolic models with properly designed quantization parameters. In this way, the proposed compositional approach can provide us a guideline for constructing an overall symbolic model with any desired approximation accuracy. A compositional controller synthesis scheme is also provided to enforce safety properties on the infinite network in a decentralized fashion. The effectiveness of our result is illustrated through a road traffic network consisting of infinitely many road cells.
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 that characterize the distance between control systems while preserving opacity properties across them. Instead of treating large-scale systems in a monolithic manner, we develop a compositional scheme to construct the interconnected finite abstractions together with the overall opacity-preserving simulation functions. For a network of incrementally input-to-state stable control systems and under some small-gain type condition, an algorithm for designing local quantization parameters is presented to orderly build the local symbolic models of subsystems such that the network of symbolic models simulates the original network for an a-priori defined accuracy while preserving its opacity properties.
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