Tradeoffs between Identification and Control in Dynamic Systems

A quantitative study of the tradeoffs between the tasks of control law design and plant identifcation for linear dynamic systems is presented. The problem is formulated in the context of optimal control and optimal identification through the intermediary concept of an optimal input. The duality between identification and control is quantified by optimal inputs, which have a specified amount of energy, and which minimize the objective function. An example of a single degree-of-freedom oscillator is used to illustrate the basic concepts underlying the proposed approach. Significant tradeoffs between identification and control tasks are observed, the tradeoffs becoming increasingly important for increasing levels of input energy.