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Loop variants are used to guarantee that loops will terminate. A loop invariant is an assertion which must be true before the first loop iteration and remain true after each iteration. This implies that when a loop terminates correctly, both the exit condition and the loop invariant are satisfied.
On some systems, this loop will execute ten times as expected, but on other systems it will never terminate. The problem is that the loop terminating condition (x != 1.1) tests for exact equality of two floating point values, and the way floating point values are represented in many computers will make this test fail, because they cannot ...
The closed-loop transfer function is measured at the output. The output signal can be calculated from the closed-loop transfer function and the input signal. Signals may be waveforms, images, or other types of data streams. An example of a closed-loop block diagram, from which a transfer function may be computed, is shown below:
A method might look at how variables change with respect to some loop condition (possibly showing termination for that loop), other methods might try to transform the program's calculation to some mathematical construct and work on that, possibly getting information about the termination behaviour out of some properties of this mathematical model.
The loop counter is used to decide when the loop should terminate and for the program flow to continue to the next instruction after the loop. A common identifier naming convention is for the loop counter to use the variable names i , j , and k (and so on if needed), where i would be the most outer loop, j the next inner loop, etc.
After completing all the statements in the loop body, the condition, (x < 5), is checked again, and the loop is executed again, this process repeating until the variable x has the value 5. It is possible, and in some cases desirable, for the condition to always evaluate to true, creating an infinite loop .
The control action is the switching on/off of the boiler, but the controlled variable should be the building temperature, but is not because this is open-loop control of the boiler, which does not give closed-loop control of the temperature. In closed loop control, the control action from the controller is dependent on the process output.
The loop invariants will be true on entry into a loop and following each iteration, so that on exit from the loop both the loop invariants and the loop termination condition can be guaranteed. From a programming methodology viewpoint, the loop invariant can be viewed as a more abstract specification of the loop, which characterizes the deeper ...