Reasoning about Discontinuous Change

Nishida, Toyoaki; Doshita, Shuji

doi:10.1016/b978-1-4832-1447-4.50022-5

Cited by 18 publications

(14 citation statements)

References 7 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…So the consecutive mode switch to α 11 has to occur before the state vector is updated to its a posteriori values, x = x + . Mathematically, this can be represented as where α 2 is a so-called mythical mode [5,13].…”

Section: Parameter Abstractionmentioning

confidence: 99%

A Hybrid Modeling and Simulation Methodology for Dynamic Physical Systems

Mosterman¹,

Biswas

2002

SIMULATION

View full text Add to dashboard Cite

This article presents the design and implementation of a robust simulation methodology for hybrid models of physical systems that encompasses behavior patterns that undergo discrete transitions between modes of continuous behavior evolution. This methodology is based on a mathematical framework that captures time scale and parameter abstractions in modeling complex physical phenomena. The formal semantics for characterizing hybrid behaviors is defined in terms of three distinct modes of system operation: (1) continuous, (2) pinnacles, and (3) mythical. A key link is established between the switching transitions and the a priori and a posteriori state vector values, which defines the recursive mode switching functions that govern the interactions between the continuous and discrete components of the system models. The effectiveness of the approach is demonstrated by examples of physical system models that are presented along with a simulator to handle these.

show abstract

Section: Parameter Abstractionmentioning

confidence: 99%

A Hybrid Modeling and Simulation Methodology for Dynamic Physical Systems

Mosterman¹,

Biswas

2002

SIMULATION

View full text Add to dashboard Cite

show abstract

“…However, the resulting superdense time [21], R×N is insufficient to precisely describe the intricate behavior of discontinuities in physical system models [31]. In particular, an ontology of hybrid dynamics in physical system models that was developed in previous work [34] includes a class of behaviors referred to as mythical modes [35] that can be well formalized in superdense time. The ontology also includes a class of behaviors called pinnacles, though, which requires a time advance during discontinuous change, and, therefore, cannot be formalized by the integer dimensions of superdense time.…”

Section: Introductionmentioning

confidence: 99%

A hyperdense semantic domain for hybrid dynamic systems to model different classes of discontinuities

Mosterman

Simko

Zander³

et al. 2014

Proceedings of the 17th International Conference on Hybrid Systems: Computation and Control

View full text Add to dashboard Cite

The physics of technical systems, such as embedded and cyber-physical systems, is frequently modeled using the notion of continuous time. The underlying continuous phenomena may, however, occur at a time scale much faster than the system behavior of interest. In such situations, it is desirable to approximate the detailed continuous-time behavior by discontinuous change. Two classes of discontinuous change can be identified: pinnacles and mythical modes. This work shows how pinnacles are well modeled using a hyperreal notion of time while a superdense notion of time applies well to mythical modes. Thus, the combination, called hyperdense time, is proposed to allow for the expression of the semantics of both pinnacles and mythical modes. Further, the hyperdense semantic domain is translated into a computational representation as a three-dimensional model of time. In particular, continuous-time behavior is mapped onto floating point numbers, while the mythical mode and pinnacle event iterations each map onto an integer dimension. A modified Newton's cradle is used as a case study and to illustrate the computational implementation.

show abstract

“…They are used for the computation of the contact forces for each contact combination. This type of locations are inspired by the well-known mythical modes, originally proposed in Nishida and Doshita (1987) and later expanded to hybrid systems by Mosterman andBiswas (1998, 2000). The computation nodes have to be understood in this sense, just a set of transition intermediate states associated to a discontinuous change.…”

Section: Ifac Adhs 12mentioning

confidence: 99%

“…The collection of this new type of discrete locations and the resets between them is called a computation node. The computation nodes are inspired by the well-known mythical modes, originally proposed in Nishida and Doshita (1987) and later expanded to hybrid systems by Mosterman andBiswas (1998, 2000).…”

Section: Introductionmentioning

confidence: 99%

A Hybrid Automaton for a Class of Multi-Contact Rigid-Body Systems with Friction and Impacts*

O’Toole

Navarro-López

2012

IFAC Proceedings Volumes

View full text Add to dashboard Cite

Hybrid automata is a powerful framework for representing the dynamics of rigid-body mechanical systems. Thus far however, work has mainly focused on examples with only single points of contact. Consider for instance, the ubiquitous bouncing-ball example. The case of multiple contacts is much more complex. An event at one contact can affect the other contacts even when there is no apparent transmission mechanism. In this paper, we present a general hybrid automaton for systems consisting of multiple rigid-bodies with convex differentiable surfaces. The hybrid automaton assumes that Newton's impact law (restitution) and Coulomb friction are acting at the points of contact. Multiple contacts are addressed by introducing computational nodes which can be considered as the well-known mythical modes in the discontinuous systems' literature. These nodes consist of non-dynamical discrete states and reset operations which find valid combinations of contact forces. In this manner, they will guide the executions of the hybrid automaton to the relevant hybrid discrete locations.

show abstract

Reasoning about Discontinuous Change

Cited by 18 publications

References 7 publications

A Hybrid Modeling and Simulation Methodology for Dynamic Physical Systems

A Hybrid Modeling and Simulation Methodology for Dynamic Physical Systems

A hyperdense semantic domain for hybrid dynamic systems to model different classes of discontinuities

A Hybrid Automaton for a Class of Multi-Contact Rigid-Body Systems with Friction and Impacts*

Contact Info

Product

Resources

About