ABSTRACT
This chapter introduces a different class of numerical ordinary differential equations (ODE) solvers that discretize the state variables, while keeping the time variable continuous. It shows that continuous-time systems described by sets of ODEs can be conveniently converted to equivalent discrete-event descriptions under the Discrete EVent system Specification (DEVS) formalism. The chapter also shows that the numerical properties of the approximations can be analyzed as rigorously as is the case with the classical numerical ODE solvers. It looks at an important application of quantized state methodology; namely, the systematic design of digital controllers for continuous plants using a new approach to digital redesign involving a Quantized State Control (QSC) architecture. The aforementioned real-time version of PowerDEVS allows easy implementation of QSC strategies on normal PCs. Timed Graph Transformation, as proposed by S. Gyapay et al., integrates time in only one particular theoretical foundation of graph transformation: the double push-out approach.
