Adjoint sensitivity analysis for hybrid systems and its application to identification of biological systems

Krzysztof Fujarewicz
2010 Procedia - Social and Behavioral Sciences  
Many practical problems of identification, parameter estimation and optimization of dynamical systems have dual, continuousdiscrete nature. For example the task of parameter estimation for continuous-time model when discrete-time measurements are given has such a form. The gradient-based optimization of a performance index may use the gradient obtained by both forward or adjoint sensitivity analysis. Here we present a structural approach to construction of the adjoint system for any hybrid
more » ... m given as a block diagram. The method specifies a set of simple rules. In particular it explains how to handle two elements interfacing between discrete and continuous parts of the hybrid system: ideal AD and DA samplers. As an illustration we present an application of the method to estimation of parameters of models of cell signaling pathways. Open access under CC BY-NC-ND license. Krzysztof Fujarewicz / Procedia Social and Behavioral Sciences 2 (2010) 7652-7653 7653 Rules of construction of the sensitivity and the adjoint systems In order to build the sensitivity model (tangent-linearized) all elements should be replaced by corresponding elements from the second column of Table 1 . Similarly, the so-called modified adjoint system (adjoint system "reversed" in time) can be built using elements from the third column.
doi:10.1016/j.sbspro.2010.05.162 fatcat:i7f6psz54nhodkzmr3rs4rabny