Positive definite performance functions for parameter adaptive control problems

The formulation of a class of parameter adaptive control problems, including plant parameter identification, is developed for deterministic linear systems which leads to a positive definite performance index J(??) with the properties: (i) J(??) and its derivatives can be computed at the end of each observation time interval using only input-output data, i.e., no state estimation is employed, (ii) a minimal value J(??*), computed by the use of any suitable gradient Type algorithm, is known to be optimal provided J(??*) = 0 and some other nondegeneracy conditions involving the input-output data are upheld, (iii) unknown disturbance inputs can be incorporated.