Abstract
This paper equivalence of control and convergence of control are defined. We first introduce new notions of J-equivalence and ɛ-J equivalence where J is a performance index. Then we given a definition of a new convergence based the above notions. According to these equivalence it is easier to find a control which make the error between the performance index and optimal performance index decrease as time increases. In addition, it is convenient to carry out theoretical analysis to some of known systems. Besides a series of results are given the properties of J-equivalence. One of which is that the control of self tuning regulator will be convergent to minimum variance control in terms of J-equivalence only if closed loop output of the system is bounded uniformaly, the estimation of parameters converget in quadric mean.
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