Dynamics, Perturbations, and Control
The core model of control theory and perturbation theory starts from a nominal dynamical system, with additional terms describing the control input and/or the influence of the perturbation. Open loop control and time-varying perturbations have the common feature that they are expressed as time-varying functions that, in general, have their own dynamics. The difference is that in the context of perturbations one studies the system behavior under all possible perturbation functions and often tries to understand the “worst-case scenario.” In control theory, after analyzing the possible system behavior under the influence of the admissible control functions, one tries to find a control (open or closed loop) that, when applied to the system, results in a desired response. But, in any case, one first needs to study the possible system behaviors under a given class of control and/or perturbation functions.
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