Correlation Method for Computing Sensitivity Functions on a High-Speed Iterative Analog Computer

During successive high-speed iterative-analog-computer runs, the parameters a1, a2, . . ., am of a simulated dynamical system are perturbed by mutually orthogonal binary sequences of perturbations ¿ai = ±¿a. Each parameter perturbation remains constant during a full 1-ms analog-computer run. Simple correlation of the perturbed solution-sample sequences x(tk)+¿x(tk) with each parameter-perturbation sequence simultaneously produces approximations ¿x(tk)/¿ai to all the system sensitivity coefficients ¿x(t)/¿ai as the sampling time tkis automatically stepped. Note that correlation with binary variables requires no multipliers. The new technique is compared to the conventional method requiring separate sensitivity-equation setups for each sensitivity coefficient, and a simple example is presented.