Diffedge: Differentiation, analysis of sensitivity, and identification of hybrid modes described under Simulink
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Diffedge is a new methodology that eliminates the drawbacks of finite-difference approximations and the complexity to use the automatic differentiation. It combines the powerful of computer algebra system and block diagram structures for computing the derivative of a Simulink model with respect to the independent parameters. Diffedge calculates the symbolic derivative of the mathematical models described in the form of block diagram. The obtained symbolic derivative is also represented in graphic form (block diagrams) and can be used like any Simulink model. The benefits for the user are numerous. We remain in the Simulink environment. Diffedge does not require any task of programming and modification of the model. The visualisation of the partial derivatives is possible for any coordinates of the model. This presentation illustrates the capabilities of Diffedge, its implementation in the Matlab environment and some applications.
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... The output sensitivity functions are computed by the software Diffedge c which enables the sensitivity analysis of block diagrams by computer algebra [18]. 5) In the next step, the practically identifiable parameters Θ are selected according to numerical properties of an empirical Fisher information Matrix. ...
Photodynamic therapy (PDT) is an alternative treatment for cancer that involves the administration of a photosensitizing agent, which is activated by light at a specific wavelength. This illumination causes a sequence of photoreactions, which - in the presence of molecular oxygen - is supposed to be responsible for the death of the tumor cells. The PDT efficiency stems from the optimal interaction between these three factors (light, drug and oxygen). In this paper, a new approach is proposed to estimate photophysical parameters which characterize the ability of a photosensitizing drug to produce singlet oxygen. This approach is based on system identification techniques. This model-based method would allow biologists to estimate all the photophysical parameters from spectro-fluorescence data generated by only one experiment. Secondly, contrary to usual techniques which are restricted to in vitro studies, this approach can be directly applied to in vivo data.
This communication deals with model calibration, i.e. the parameter estimation of large and complex simulation models, from imposed experimental data. A calibra-tion methodology including practical identifiability, parameter selection and parameter estimation is proposed. The estimation of the sensitivity functions of the model outputs is performed by a new software : Diffedge® that enables us to symbolically derive a mathematical model described by a block diagram implemented in Simulink®. A case study of a winding system is detailed to illustrate the ‘applicability’ of such an approach in practice.
Contributions presented in this document deal with the development of methods and tools for the experimental modeling of interconnected systems by modular representations. Contrary to black-box descriptions, the modular modeling approaches not only aim at describing the dynamical behavior of the whole system but also to depict its physical structure in terms of components and interactions. Problems associated with the experimental modeling of interconnected systems are multiple : mathematical formulation of modular representations, practical identifiability, parameter estimation and uncertainty description.
The proposed research project is concerned with the systems biology in engineering. It is focused on the experimental modeling of interconnected systems in biology and more precisely in cancerology. Two applications domains are developed : the experimental of photodynamic therapy and the identification of metabolic networks. Photodynamic therapy is an example of interconnected systems in which three system identification problems are investigated. The two final objectives are (i) to better control the reproducibility of the therapeutic outcomes and (ii) to mathematically characterize the efficacy of new photosensitizing agents. These two questions may be described as problems concerning parameter identifiability, parameter estimation and system control. Classical and modern methods of experiment design are proposed to solve these problems.
This paper deals with parameter selection and estimation of large and complex simulation models. This estimation problem is addressed in the case of passive observation, i.e. when no controlled experiment is possible. Given the lack of information in the data, an appropriate methodology is proposed to select and estimate some physical parameters of the model. Its implementation is based on a new software: Diffedge© which makes it possible to symbolically determine model output sensitivity functions of block diagrams. An application to a winding prototype is developed to illustrate the effectiveness of such an approach in practice.
The following questions are often encountered in system and control theory. Given an algebraic model of a physical process, which variables can be, in theory, deduced from the input-output behavior of an experiment? How many of the remaining variables should we assume to be known in order to determine all the others? These questions are parts of the \emph{local algebraic observability} problem which is concerned with the existence of a non trivial Lie subalgebra of the symmetries of the model letting the inputs and the outputs invariant. We present a \emph{probabilistic seminumerical} algorithm that proposes a solution to this problem in \emph{polynomial time}. A bound for the necessary number of arithmetic operations on the rational field is presented. This bound is polynomial in the \emph{complexity of evaluation} of the model and in the number of variables. Furthermore, we show that the \emph{size} of the integers involved in the computations is polynomial in the number of variables and in the degree of the differential system. Last, we estimate the probability of success of our algorithm and we present some benchmarks from our Maple implementation.
A new approach to time-critical optimisation in the context of identication and control is presented. Symbolic algebra is used to provide the equations for computing the sensitivity functions of a system relevant to provide rapid computation of gradient information. It is veried that the resultant gradientbased optimisation is substantially faster than the corresponding non-gradient method. An inverted pendulum example illustrates the approach. 1 Introduction Model based optimisation is fundamental to a number of control-relevant issues including model-based predictive control and system identication. For realtime applications, the time taken for such optimisation is crucial. As will be seen, each iteration of an optimisation in this context requires computation of the solution of a non-linear ordinary dierential equation (simulation of the system model) and this is computationally expensive. Therefore we seek optimisation algorithms which require few evaluations of the ordinary ...
Diffedge user manual
- J Masse
J. Masse. Diffedge user manual 2003 v2. Technical report, 2000.