Control Theory and Biological Systems

Control Theory and Biological Systems

Control Theory and Biological Systems

Control Theory and Biological Systems

Excerpt

Although physiologists have realized since the time of Claude Bernard that they deal with a collection of complex, interrelated biological regulators, the application of control-system theory to biological systems has only just begun. This is partly because the theory itself is of relatively recent origin and was first developed for physical systems by mathematicians, physicists, and engineers whose language is often unfamiliar to biologists. This communication barrier has served to conceal the beautiful generality of systems theory. It does not matter in principle whether the system is a physical one built by man or whether it is that most complex and marvelous system of all, man himself. This does not mean that all of the theoretical tools necessary for the analysis of biological systems are already available, for biological systems are much more complex than physical systems. Thus, existing control-system theory is largely a theory of linear systems but almost all biological systems contain essential nonlinearities. Although a complete analytical theory exists for linear differential equations, no comparable general treatment is yet available for nonlinear ones. However, for particular cases, solutions can now be obtained by computer techniques.

But the important point is that whatever form the equations may take for a particular system, the general approach is the same for all systems. This is the theme that I will emphasize in this book. The very act of formulating the problem in terms of block diagrams and mathematical relationships, requiring as it does the precise identification and rigorous definition of previously vague concepts, provides insight and clarification obtainable in no other way. In this sense, the details of the mathematical manipulations required to solve the particular equations so obtained are of secondary importance.

We would be unrealistic if we did not recognize a traditional . . .

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