Does a system need to be completely identified? (Q1974983)

The paper deals with the design of an identification-based adaptive control law for linear dynamical systems. A recursive least-squares method is used for the identification of system parameters in the presence of zero mean white noise random disturbances and for the design of the adaptive control system. It is shown that the design of an adaptive locally optimal control algorithm does not require consistent estimates of system parameters and hence may be based on pure least-squares, without applying additional signals in the scheme. Such a property holds true if the adaptive controller parameters are specific functions of the current least-squares system parameter estimates. Proper conditions for self-tuning controllers based on recursive least-squares estimates, guaranteeing local optimality of the adaptive system, are given. Decomposition of the estimate space into orthogonal subspaces and the averaging method are applied in the deterministic and the stochastic case, respectively, to prove invariance of the parameters of locally optimal control laws for the quadratic objective function (with respect to the reference path tracking error). The behaviour of the predictor error, tracking error and system parameter estimates in the adaptive system is considered and appropriate convergence conditions are established.