Related papers: Bisimulation equivalence of DAE systems
The controller design of the so-called "difference algebraic equation" (DAE) systems that are frequently shown in industrial processes, tend to be challenging because of the combination of algebraic equations and high state dimensions. In…
We investigate how various forms of bisimulation can be characterised using the technology of logical relations. The approach taken is that each form of bisimulation corresponds to an algebraic structure derived from a transition system,…
For nonlinear differential-algebraic equations (DAEs), we define two kinds of equivalences, namely, the external and internal equivalence. Roughly speaking, the word "external" means that we consider a DAE (locally) everywhere and…
We consider linear differential-algebraic equations DAEs and the Kronecker canonical form KCF of the corresponding matrix pencils. We also consider linear control systems and their Morse canonical form MCF. For a linear DAE, a procedure…
We consider reasoning and minimization in systems of polynomial ordinary differential equations (ode's). The ring of multivariate polynomials is employed as a syntax for denoting system behaviours. We endow this set with a transition system…
In this paper we propose definitions of equivalence via stochastic bisimulation and of equivalence of stochastic external behavior for the class of discrete-time stochastic linear control systems with possibly degenerate normally…
The category of presheaves on a (small) category is a suitable semantic universe to study behaviour of various dynamical systems. In particular, presheaves can be used to record the executions of a system and their morphisms correspond to…
This paper introduces a new behavioral system model with distinct external and internal signals possibly evolving on different time scales. This allows to capture abstraction processes or signal aggregation in the context of control and…
Control systems are usually modeled by differential equations describing how physical phenomena can be influenced by certain control parameters or inputs. Although these models are very powerful when dealing with physical phenomena, they…
Bilinear systems emerge in a wide variety of fields as natural models for dynamical systems ranging from robotics to quantum dots. Analyzing controllability of such systems is of fundamental and practical importance, for example, for the…
The theory of coalgebras, for an endofunctor on a category, has been proposed as a general theory of transition systems. We investigate and relate four generalizations of bisimulation to this setting, providing conditions under which the…
We develop a new bisimulation (pseudo)metric for weighted finite automata (WFA) that generalizes Boreale's linear bisimulation relation. Our metrics are induced by seminorms on the state space of WFA. Our development is based on spectral…
This paper introduces the counterpart of strong bisimilarity for labelled transition systems extended with time-out transitions. It supports this concept through a modal characterisation, congruence results for a standard process algebra…
Different representations of dissipative Hamiltonian and port-Hamiltonian differential-algebraic equations (DAE) systems are presented and compared. Using global geometric and algebraic points of view, translations between the different…
This paper formulates and studies the concepts of approximate (alternating) bisimulation relations characterizing equivalence relations between interconnected systems and their abstractions. These equivalence relations guarantee that the…
Port-Hamiltonian systems theory provides a systematic methodology for the modeling, simulation and control of multi-physics systems. The incorporation of algebraic constraints has led to a multitude of definitions of port-Hamiltonian…
The Kripke semantics of various logics arises via categorical dualities between a category of relational frames and their maps, and a category of algebras and logical homomorphisms. When the relational frames are considered as computational…
A biform theory is a combination of an axiomatic theory and an algorithmic theory that supports the integration of reasoning and computation. These are ideal for specifying and reasoning about algorithms that manipulate mathematical…
The "bisimulation problem" for equational graphs of finite out-degree is shown to be decidable. We reduce this problem to the bisimulation problem for deterministic rational (vectors of) boolean series on the alphabet of a dpda M. We then…
We consider a class of systems over finite alphabets, namely discrete-time systems with linear dynamics and a finite input alphabet. We formulate a notion of finite uniform bisimulation, and motivate and propose a notion of regular finite…