Control Theory and Systems Biology by Pablo A. Iglesias, Brian P. Ingalls

By Pablo A. Iglesias, Brian P. Ingalls

A survey of ways engineering recommendations from keep watch over and structures thought can be utilized to aid biologists comprehend the habit of mobile platforms.

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Alternatively, when the control depends only on the system output: uðtÞ ¼ ky ð yðtÞÞ; the feedback is known as static output feedback. In contrast to static feedback, the controller may itself involve an auxiliary dynamic system, which allows it to take into account past behavior of the system (as opposed to only acting on current system values). In this case, the feedback system is described by a vector of control states rðtÞ. When such a feedback depends on output values, it takes the form d rðtÞ ¼ gð yðtÞÞ; dt ð1:11aÞ uðtÞ ¼ lðrðtÞ; yðtÞÞ ð1:11bÞ and is referred to as dynamic output feedback.

The frequency response of the system is the restriction of the transfer function to arguments of the form s ¼ jo. The complex-valued frequency response Gð joÞ ¼ AðoÞe jfðoÞ can be plotted in a number of ways. Perhaps the most useful of these visualizations is the Bode plot, in which the magnitude and argument of the frequency response are plotted separately (Bode, 1945). The magnitude AðoÞ, the system gain, is plotted on a log-log scale, where the gain is measured in decibels (dB) (defined by x dB ¼ 20 log10 x).

7 7 yðtÞ ¼ 6 4 .. 5: yp ðtÞ The choice of output might be dictated by available experimental assays or by which components of the system interact with processes external to the network of interest. An alternative role for the output yðtÞ is to allow the analysis to focus on a particular aspect of system behavior. That might be the concentration of a particular component species or some function of overall behavior, for example, the flux through a metabolic pathway. For the simplest input-output systems, referred to as 20 Brian P.

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