  A novel method of an adaptive linear quadratic (LQ) regulation of uncertain
continuous linear time-invariant systems is proposed. Such an approach is based
on the direct self-tuning regulators design framework and the exponentially
stable adaptive control technique developed earlier by the authors. Unlike the
known solutions, a procedure is proposed to obtain a non-overparametrized
regression equation (RE) with respect to the unknown controller parameters from
an initial RE of the LQ-based reference tracking control system. On the basis
of such result, an adaptive law is proposed, which under mild regressor finite
excitation condition provides monotonous convergence of the LQ-controller
parameters to an adjustable set of their true values, which bound is defined
only by the machine precision. Using the Lyapunov-based analysis, it is proved
that the mentioned law guarantees the exponential stability of the closed-loop
adaptive optimal control system. The simulation examples are provided to
validate the theoretical contributions.
