  This paper develops an adaptive state tracking control scheme for
discrete-time systems, using the least-squares algorithm, as the new solution
to the long-standing discrete-time adaptive state tracking control problem to
which the Lyapunov method (well-developed for the continuous-time adaptive
state tracking problem) is not applicable. The new adaptive state tracking
scheme is based on a recently-developed new discrete-time error model which has
been used for gradient algorithm based state tracking control schemes, and uses
the least-squares algorithm for parameter adaptation. The new least-squares
algorithm is derived to minimize an accumulative estimation error, to ensure
certain optimality for parameter estimation. The system stability and output
tracking properties are studied. Technical results are presented in terms of
plant-model matching, error model, adaptive law, optimality formulation, and
stability and tracking analysis. The developed adaptive control scheme is
applied to a discrete-time multiple mobile robot system to meet an adaptive
state tracking objective. In addition, a collision avoidance mechanism is
proposed to prevent collisions in the whole tracking process. Simulation
results are presented, which verify the desired system state tracking
properties under the developed least-squares algorithm based adaptive control
scheme.
