Question

For minimizing the transfer function the condition is :

(a) Second differentiation of the function must be zero

(b) Second differentiation of the function must be positive

(c) Second differentiation of the function must be negative

(d) Second differentiation of the function must be complex

I have been asked this question in exam.

This interesting question is from Optimal Control Problems-2 in portion Optimal Control Systems of Control Systems

Answer 1

The correct answer is:

(b) Second differentiation of the function must be positive

Explanation:

In optimal control problems, minimizing a transfer function often involves finding the condition for a minimum by analyzing the second derivative of the cost function or objective function. The key principle in optimization is that:

• If the second derivative of a function is positive, the function is concave up, indicating a minimum.
• If the second derivative is negative, the function is concave down, indicating a maximum.
• If the second derivative is zero, further analysis is needed to determine whether it is a maximum, minimum, or saddle point.

Thus, for minimizing a function, the condition is that the second derivative must be positive, confirming the presence of a local minimum.