Bisimilar Finite Abstractions of Interconnected Systems

Approximately bisimilar finite-state modeling of interconnected systems

“…If one knows the internal interconnection structure of a complex system, it is natural to take advantage of such knowledge to reduce the complexity of the computation of the abstraction process and that of the resultant abstraction itself. In [6], it was shown that the conventional approximate bisimulation is not preserved under interconnection. moreover, in the same work, the notion of interconnection-compatible (IC-)approximate bisimulation has been presented.…”

“…Once a finite abstraction of each subsystem is designed based on IC-approximate bisimulation and a certain compatibility criteria is fulfilled, we can simply interconnect subsystems to form a finite abstraction of the entire concrete system. However, an analytical condition on a quantizer derived in [6] has some limitations. First, it is based on infinite-horizon approximate bisimulation.…”

“…In Section 2, we define finite-step approximate bisimulation of discrete-time systems. In Section 3, we briefly review the discussion given in [6]. Here, we make some minor modifications for adopting to finite-step formulation.…”

Stabilization of Finite Automata with Application to Hybrid Systems Control

“…To overcome the hardness of analysis/synthesis of complex systems, recently, there have been several works on finite-state approximations such as (bi)simulation relations (e.g., Girard et al 2008;Tazaki and Imura 2008) and qualitative models (e.g., Batt et al 2005;Chaves et al 2009). In these approaches, dynamical systems are approximated by finite automata (directed graphs), and the analysis/control problems of them are in general reduced to a kind of search problems on graphs.…”

Online Abstractions for Interconnected Multi-Agent Control Systems

“…Abstractions for nonlinear systems include (Reissig, 2011), which is focused on general discrete time systems and (Abate et al, 2009), where box abstractions are derived for polynomial and other classes of systems. Furthermore, abstractions for interconnected systems have been recently developed in (Tazaki and Imura, 2008;Pola et al, 2014Pola et al, , 2016Rungger and Zamani, 2015;Meyer et al, 2015;Dallal and Tabuada, 2015) and are primarily based on small gain criteria. In this work we consider multi-agent systems and provide an online abstraction methodology which enables the exploitation of the system's dynamic properties over bounded reachable sets.…”