This paper is concerned with an application of optimal regulator to control for mechanical systems. The properties of limiting form is discussed in detail, which is derived by letting the weighting ...matrix of state vector tend to infinity in standard optimal regulator problem. In this study, the limiting form is derived under the general initial conditions. Then it is shown that the limiting form includes delta functions and its derivatives. Further, it is pointed out that the limiting form leads to the solution for the output zeroing problem. Control inputs are bounded in some initial conditions, although the feedback gain increases with the weighting matrix. This clarifies the reason why the linear regulator can be applied to the control for certain mechanical systems with a constraint. A simulation is carried out to evaluate the effectiveness of this control method.
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