Equation-Based Object-Oriented Modeling Languages and Tools 

Abstract: Ptolemy is an open-source and extensible modeling and simulation framework. It offers heterogeneous modeling capabilities by allowing different models of computation to be composed hierarchically in an arbitrary fashion. This paper describes modal models, which allow to hierarchically compose finite-state machines with other models of computation, both untimed and timed. The semantics of modal models in Ptolemy are defined in a modular manner.

Abstract: The current development towards multiple processor cores in personal computers is making distribution and parallelization of simulation software increasingly important. The possible speedups from parallelism are however often limited with the current centralized solver algorithms, which are commonly used in today’s simulation environments. An alternative method investigated in this work utilizes distributed solver algorithms using the transmission line modeling (TLM) method. Creation of models using TLM elements to separate model components makes them very suitable for computation in parallel because larger models can be partitioned into smaller independent submodels. The computation time can also be decreased by using small numerical solver step sizes only on those few submodels that need this for numerical stability. This is especially relevant for large and demanding models. In this paper we present work in how to combine TLM and solver inlining techniques in the Modelica equation-based language, giving the potential for efficient distributed simulation of model components over several processors.

Abstract: The Directed Acyclic Graph (DAG), which can be generated by object oriented modelling languages, is often the most natural way of representing and manipulating a dynamic optimization problem. With this representation, it is possible to step-by-step reformulate an (infinite dimensional) dynamic optimization problem into a (finite dimensional) non-linear program (NLP) by parametrizing the state and control trajectories. We introduce CasADi, a minimalistic computer algebra system written in completely self-contained C++. The aim of the tool is to offer the benifits of a computer algebra to developers of C++ code, without the overhead usually associated with such systems. In particular, we use the tool to implement automatic differentiation, AD. For maximum efficiency, CasADi works with two different graph representations interchangeably: One supporting only scalar-valued, built-in unary and binary operations and no branching, similar to the representation used by today’s tools for automatic differentiation by operator overloading. Secondly, a representation supporting matrixvalued operations, branchings such as if-statements as well as function calls to arbitrary functions (e.g. ODE/DAE integrators). We show that the tool performs favorably compared to CppAD and ADOL-C, two state-of-the-art tools for AD by operator overloading. We also show how the tool can be used to solve a simple optimal control problem, minimal fuel rocket flight, by implementing a simple ODE integrator with sensitivity capabilities and solving the probl em with the NLP solver IPOPT. In the last example, we show how we can use the tool to couple the modelling tool JModelica with the optimal control software ACADO Toolkit.

Abstract: This contribution outlines an XML format for representation of differential-algebraic equations (DAE) models obtained from continuous time Modelica models and possibly also from other equation-based modeling languages. The purpose is to offer a standardized model exchange format which is based on the DAE formalism and which is neutral with respect to model usage. Many usages of models go beyond what can be obtained from an execution interface offering evaluation of the model equations for simulation purposes. Several such usages arise in the area of control engineering, where dynamic optimization, Linear Fractional Transformations (LFTs), derivation of robotic controllers, model order reduction, and real time code generation are some examples. The choice of XML is motivated by its de facto standard status and the availability of free and efficient tools. Also, the XSLT language enables a convenient specification of the transformation of the XML model representation into other formats.