Discrete-time adaptive state tracking control schemes using gradient algorithms

This paper revisits a classical adaptive control problem: adaptive state tracking control of a state-space plant model, and solves the open discrete-time state tracking model reference adaptive control problem. Adaptive state tracking control schemes for continuous-time systems have been reported in the literature, using a Lyapunov-algorithm based design and analysis procedure. Such a procedure has not been successfully applied to the discrete-time adaptive state tracking control problem which has remained open. In this paper, new adaptive state tracking control schemes are developed for discrete-time systems, using gradient algorithms for updating the controller parameters. Both direct and indirect adaptive designs are derived, which have the desired parameter adaptation properties and closed-loop system stability and state tracking properties. Such a new gradient-algorithm based framework is also applicable to the continuous-time adaptive state tracking control problem to develop new solutions, as compared with the traditional Lyapunov-algorithm based solutions.