A quantitative study of the trade-offs between the tasks of control law design and plant identification 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 minimizes the objective function. The optimization problem together with the energy constraint is formulated by using an augmented state vector. This results in a nonlinear two-point boundary value problem and eliminates the need for using a trial and error approach to satisfy the energy constraint. An example of a single-degree-of-freedom oscillator is used to illustrate the basic concepts underlying the proposed approach. Significant trade-offs between identification and control tasks are observed, the trade-offs becoming increasingly important for increasing levels of input energy.

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