Compositional abstraction and safety synthesis using overlapping symbolic models

In this paper, we develop a compositional approach to abstraction and safety synthesis for a general class of discrete time nonlinear systems. Our approach makes it possible to define a symbolic abstraction by composing a set of symbolic subsystems that are overlapping in the sense that they can share some common state variables. We develop compositional safety synthesis techniques using such overlapping symbolic subsystems. Comparisons, in terms of conservativeness and of computational complexity, between abstractions and controllers obtained from different system decompositions are provided. Numerical experiments show that the proposed approach for symbolic control synthesis enables a significant complexity reduction with respect to the centralized approach, while reducing the conservatism with respect to compositional approaches using non-overlapping subsystems

Reachability-based Identification, Analysis, and Control Synthesis of Robot Systems

We introduce reachability analysis for the formal examination of robots. We propose a novel identification method, which preserves reachset conformance of linear systems. We additionally propose a simultaneous identification and control synthesis scheme to obtain optimal controllers with formal guarantees. In a case study, we examine the effectiveness of using reachability analysis to synthesize a state-feedback controller, a velocity observer, and an output feedback controller.Comment: This work has been submitted to the IEEE for possible publication. Copyright may be transferred without notice, after which this version may no longer be accessibl

Online Abstractions for Interconnected Multi-Agent Control Systems

In this report, we aim at the development of an online abstraction framework for multi-agent systems under coupled constraints. The motion capabilities of each agent are abstracted through a finite state transition system in order to capture reachability properties of the coupled multi-agent system over a finite time horizon in a decentralized manner. In the first part of this work, we define online abstractions by discretizing an overapproximation of the agents' reachable sets over the horizon. Then, sufficient conditions relating the discretization and the agent's dynamics properties are provided, in order to quantify the transition possibilities of each agent.Comment: 22 pages. arXiv admin note: text overlap with arXiv:1603.0478

Compositional Synthesis of Finite Abstractions for Networks of Systems: A Small-Gain Approach

In this paper, we introduce a compositional scheme for the construction of �nite abstractions (a.k.a. symbolic models) of interconnected discrete-time control systems. The compositional scheme is based on small-gain type reasoning. In particular, we use a notion of so-called alternating simulation functions as a relation between each subsystem and its symbolic model. Assuming some small-gain type conditions, we construct compositionally an overall alternating simulation function as a relation between an interconnection of symbolic models and that of original control subsystems. In such compositionality reasoning, the gains associated with the alternating simulation functions of the subsystems satisfy a certain \small-gain" condition. In addition, we introduce a technique to construct symbolic models together with their corresponding alternating simulation functions for discrete-time control subsystems under some stability property. Finally, we apply our results to the temperature regulation in a circular building by constructing compositionally a �nite abstraction of a network containing N rooms for any N � 3. We use the constructed symbolic models as substitutes to synthesize controllers compositionally maintaining room temperatures in a comfort zone. We choose N = 1000 for the sake of illustrating the results. We also apply our proposed techniques to a nonlinear example of a fully connected network in which the compositionality condition still holds for any number of components. In these case studies, we show the e�ectiveness of the proposed results in comparison with the existing compositionality technique in the literature using a dissipativity-type reasoning.</p