I am relatively new to this topic. I understand the basics of optimization of control systems using a cost function and constraints and solve it as a minimization or maximization problem. I also understand that the cost function should be expressed as a function of parameters that I can change or control [for optimal output]. All the examples i have gone through in the theory take a simplistic control system like an inverted pendulum and come up with cost function for example as a function of initial position based on simple physics equations.
My question here is how can this be done for complex control systems like a Braking control systems in a vehicle. If braking distance is considered as a performance metric to be optimized to be as minimum as possible. How to come up with a cost function for this as a function of some input parameter? Is there a formal mathematical way of doing it?
Dear Bhargav Kinnal :
See if this can answer your question:
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Regards,
Jai
There is no formal mathematical way to derive cost functions, but there are principles one should follow. For example, framing the problem probabilistically, one could seek to minimize the probability of an accident resulting from a braking policy. This would require estimating probabilities of braking within various distances, which would vary tremendously on various covariates such a weather conditions, vehicle speed, etc. Or one could pursue a simpler strategy of minimizing the (cost =) probability of a worst case scenario. But one could also frame the problem economically - the penalty for a collision is $x and one would seek to miminize the expected value that quantity. (Incidentally, such metrics have been used since the 1950's to estimate the damage from a nuclear accident, and they implicitly place a value on human life.) It should be realized that the choice of cost functions when human life is an issue is essentially a moral, not mathematical, issue.
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