The effect of controlling to reduce complexity

VitaliV's Via-Art John Lennon
VitaliV's Via-Art John Lennon (Photo credit: Wikipedia)

Any control mechanism usually is a complex system but the effect on the system is to make it more stable. This is due to feedback. In terms of complexity, if we measure the complexity of a controlled system with feedback we will find a lower value. It is possible visualize this easily through classic control theory for a system with only an output variable.

When we are analyzing complex systems, the problem is made more difficult because a complex system has a huge number of state variables, but conceptually we can understand that feedback of variables can be used to stabilize a system (and reduce its complexity), although the control mechanisms are complex systems themself. That is the reason because we say that we only can manage what we can measure. The assertion is an important truth, but it is true too that a measure is not a control action is only a part of it.

In a typical complex system, the inputs and outputs can define badly a whole set of state variables, and it is possible that we cannot define a perfect control system when the observable subspace does not match the controllable one. Measuring a single output and using it to feedback an input does not make more stable a system necessarily, even this can make more unstable the selected output. But we can use a complexity measure to analyze if a control activity is being positive (is stabilizing our system) or negative.

It is very interesting to analyze what happens when we start to establish wrong connections between output variables and input ones without a proper control device that guarantees a more stable system. Back to a system with a single variable, a control system tries to cancel poles that makes the system unstable with zeros, but if our control system introduces more unstable poles instead of the needed zeros the controller turns the system into a more unstable one.

Although we can see this discussion as excessively technical, we can think about daily matters:

First of all, imagine there’s no heaven (although this sentence belongs to John Lenon); imagine a large company without managers, an enterprise where all workers did what all they wanted. I’m sure that it does not work very well although all workers know the final benefit of the company. Feedback does not provide more stability without a control system.

Then, imagine there are no countries (as John Lennon proposed too), imagine a global economy where we cannot find a direct way to reduce complexity because there is no government. Things will be more difficult to be done every time. But, fortunately, we can measure the complexity of our business and analyze it when we do some action to improve, then we will be able to know if our actions have provided more stability or not.

Finally, imagine no possessions (following John Lennon again); imagine a world where national states are an instrument to control the society that increasing its debt are limiting the financial resources that enterprises and people need to make operative the productive part of the economy.

If you have been able to imagine all this, you will have visualized the future or the world if we do not think in terms of reducing complexity through technical mechanisms instead of increasing connections between different agents of the economy that only increases bureaucracy instead of stabilizing the productive part of the economy.


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