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JModelica.org
JModelica.org is a commercial software platform based on the Modelica modeling language for modeling, simulating, optimizing and analyzing complex dynamic systems. The platform is maintained and developed by Modelon AB in collaboration with academic and industrial institutions, notably Lund University and the Lund Center for Control of Complex Systems (LCCC). The platform has been used in industrial projects with applications in robotics, vehicle systems, energy systems, separation and polyethylene production. The key components of the platform are: * A Modelica compiler for translating Modelica source code into C or XML code. The compiler also generates models compliant with the Functional Mock-up Interface standard. * A Python package for simulation of dynamic models, Assimulo. Assimulo provides interfaces to several state of the art integrators and is used as a simulation engine in JModelica.org. * Algorithms for solving large scale dynamic optimization problems implementing l ...
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Modelica
Modelica is an object-oriented, declarative, multi-domain modeling language for component-oriented modeling of complex systems, e.g., systems containing mechanical, electrical, electronic, hydraulic, thermal, control, electric power or process-oriented subcomponents. The free Modelica language is developed by the non-profit Modelica Association. The Modelica Association also develops the free Modelica Standard Library that contains about 1400 generic model components and 1200 functions in various domains, as of version 4.0.0. Characteristics While Modelica resembles object-oriented programming languages, such as C++ or Java, it differs in two important respects. First, Modelica is a modeling language rather than a conventional ''programming'' language. Modelica classes are not compiled in the usual sense, but they are translated into objects which are then exercised by a simulation engine. The simulation engine is not specified by the language, although certain required capabil ...
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Wolfram SystemModeler
Wolfram System Modeler, developed by Wolfram MathCore, is a platform for engineering as well as life-science modeling and simulation based on the Modelica language. It provides an interactive graphical modeling and simulation environment and a customizable set of component libraries. Interface Wolfram System Modeler's primary interface, Model Center, is an interactive graphical environment including a customizable set of component libraries. Models developed in Model Center can be simulated in the Simulation Center. The software also provides a tight integration with the Mathematica environment. Users can develop, simulate, document, and analyze their Wolfram System Modeler models within Mathematica notebooks. The software is used in the engineering field as well as in the life sciences. Editions Originally developed by MathCore Engineering as MathModelica, it was acquired by Wolfram Research on March 30, 2011. It was then re-released as Wolfram SystemModeler on May 23, 2012 ...
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CasADi
CasADi is a free and open source symbolic framework for automatic differentiation and optimal control.Joel Andersson, Johan Åkesson, Moritz Diehl: "CasADi - A symbolic package for automatic differentiation and optimal control". Recent Advances in Algorithmic Differentiation. 2012. See also *Automatic differentiation *JModelica.org JModelica.org is a commercial software platform based on the Modelica modeling language for modeling, simulating, optimizing and analyzing complex dynamic systems. The platform is maintained and developed by Modelon AB in collaboration with academi ... References {{Reflist Mathematical optimization software Free software programmed in Python ...
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Optimal Control
Optimal control theory is a branch of mathematical optimization that deals with finding a control for a dynamical system over a period of time such that an objective function is optimized. It has numerous applications in science, engineering and operations research. For example, the dynamical system might be a spacecraft with controls corresponding to rocket thrusters, and the objective might be to reach the moon with minimum fuel expenditure. Or the dynamical system could be a nation's economy, with the objective to minimize unemployment; the controls in this case could be fiscal and monetary policy. A dynamical system may also be introduced to embed operations research problems within the framework of optimal control theory. Optimal control is an extension of the calculus of variations, and is a mathematical optimization method for deriving control policies. The method is largely due to the work of Lev Pontryagin and Richard Bellman in the 1950s, after contributions to calcu ...
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Gauss Pseudospectral Method
The Gauss pseudospectral method (GPM), one of many topics named after Carl Friedrich Gauss, is a direct transcription method for discretizing a continuous optimal control problem into a nonlinear program (NLP). The Gauss pseudospectral method differs from several other pseudospectral methods in that the dynamics are not collocated at either endpoint of the time interval. This collocation, in conjunction with the proper approximation to the costate, leads to a set of KKT conditions that are identical to the discretized form of the first-order optimality conditions. This equivalence between the KKT conditions and the discretized first-order optimality conditions leads to an accurate costate estimate using the KKT multipliers of the NLP. Description The method is based on the theory of orthogonal collocation where the collocation points (i.e., the points at which the optimal control problem is discretized) are the Legendre–Gauss (LG) points. The approach used in the GP ...
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ASCEND
ASCEND is an open source, mathematical modelling chemical process modelling system developed at Carnegie Mellon University since late 1978. ASCEND is an acronym which stands for Advanced System for Computations in Engineering Design. Its main uses have been in the field of chemical process modelling although its capabilities are general. ASCEND includes nonlinear algebraic solvers, differential/algebraic equation solvers, nonlinear optimization and modelling of multi-region 'conditional models'. Its matrix operations are supported by an efficient sparse matrix solver called ''mtx''. ASCEND differs from earlier modelling systems because it separates the solving strategy from model building. So domain experts (people writing the models) and computational engineers (people writing the solver code) can work separately in developing ASCEND. Together with a number of other early modelling tools, its architecture helped to inspire newer languages such as Modelica. It was recognised f ...
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Openmodelica
OpenModelica is a free and open source environment based on the Modelica modeling language for modeling, simulating, optimizing and analyzing complex dynamic systems. This software is actively developed by Open Source Modelica Consortium, a non-profit, non-governmental organization. The Open Source Modelica Consortium is run as a project oRISE SICS East AB in collaboration with Linköping University. OpenModelica is used in academic and industrial environments. Industrial applications include the use of OpenModelica along with proprietary software in the fields of power plant optimization, automotive and water treatment. Tools and Applications OpenModelica Compiler (OMC)OpenModelica Compiler
(OMC) is a

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C (programming Language)
C (''pronounced like the letter c'') is a General-purpose language, general-purpose computer programming language. It was created in the 1970s by Dennis Ritchie, and remains very widely used and influential. By design, C's features cleanly reflect the capabilities of the targeted CPUs. It has found lasting use in operating systems, device drivers, protocol stacks, though decreasingly for application software. C is commonly used on computer architectures that range from the largest supercomputers to the smallest microcontrollers and embedded systems. A successor to the programming language B (programming language), B, C was originally developed at Bell Labs by Ritchie between 1972 and 1973 to construct utilities running on Unix. It was applied to re-implementing the kernel of the Unix operating system. During the 1980s, C gradually gained popularity. It has become one of the measuring programming language popularity, most widely used programming languages, with C compilers avail ...
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MapleSim
MapleSim is a Modelica-based, multi-domain modeling and simulation tool developed by Maplesoft. MapleSim generates model equations, runs simulations, and performs analyses using the symbolic and numeric mathematical engine of Maple. Models are created by dragging-and-dropping components from a library into a central workspace, resulting in a model that represents the physical system in a graphical form. Maplesoft began development of MapleSim partly in response to a request from Toyota to produce physical modeling tools to aid in their new model-based development process. The MapleSim library includes many components that can be connected together to model a system. These components are from areas of science and engineering such as electrical, mechanical, and thermal engineering fields. MapleSim also includes traditional signal flow components that can be combined with other physical components in the workspace. Thus, MapleSim is able to combine causal modeling methods with acau ...
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SimulationX
SimulationX is a CAE software application running on Microsoft Windows for the physical simulation of technical systems. It is developed and sold by ESI Group. History In the mid 1980s, VEB Mikromat in Dresden (Germany) developed a program for DOS to design controlled feed axis systems and to perform hydraulic calculations. In 1993, ITI GmbH, founded by former Mikromat employees in 1990, introduced a simulation tool for Microsoft Windows designed for dynamic calculations of drive systems: ITI-SIM 1. With the release of ITI-SIM 2 in 1995, the software also allowed for fluid simulations. In 2002, the newly developed application SimulationX, based on the object-oriented description language Modelica, was introduced to the market. By the year 2007, ITI-SIM (then in version 3.8) had been completely replaced by SimulationX. Since the beginning of 2016, ITI belongs to the ESI Group and now operates under the name ESI ITI GmbH. Modeling and Functionality Simulation models are ...
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PROPT
The PROPT MATLAB Optimal Control Software is a new generation platform for solving applied optimal control (with ODE or DAE formulation) and parameters estimation problems. The platform was developed by MATLAB Programming Contest WinnerPer Rutquistin 2008. The most recent version has support for binary and integer variables as well as an automated scaling module. Description PROPT is a combined modeling, compilation and solver engine, built upon the TomSym modeling class, for generation of highly complex optimal control problems. PROPT uses a pseudospectral Collocation method (with Gauss or Chebyshev points) for solving optimal control problems. This means that the solution takes the form of a Polynomial, and this polynomial satisfies the DAE and the path constraints at the collocation points. In general PROPT has the following main functions: * Computation of the constant matrices used for the differentiation and integration of the polynomials used to approximate the ...
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