Quantized State System Simulation

FRANÇOIS CELLIER; ERNESTO KOFMAN; GUSTAVO MIGONI; MARIO BORTOLOTTO

Edimburgo, Escocia

Conferencia; 2008 International Simulation Multi-conference; 2008

The Society for Modeling and Simulation International

The paper introduces a new family of numerical ODE solvers called Quantized State System (QSS) methods. Given a set of ODEs in its state-space representation, the QSS methods replace the classic time slicing by a quantization of the states, leading to an asynchronousdiscrete-event simulation model instead of a discrete time difference equation model.QSS methods applied to stable linear time-invariant systems give always practically stable numerical results, irrespective of the quantization adopted. Taking into account that the QSS methods are explicit algorithms, this property has strong theoretical implications and offers a promising perspective for applications such as real-time simulation of stiff systems, where implicitsolutions are usually unacceptable. Also discussed are the main properties of the methodsin the context of simulating discontinuous systems (the asynchronous nature of these algorithmsgives them important advantages for discontinuity handling). Another class of systems that can be simulated by means of these algorithms are marginally stable (Hamiltonian) systems.