The problem of adaptive control design for discrete-time nonlinear systems with unknown parameters has been solved only for very special cases; in particular, to guarantee global stability, existing solutions impose growth restrictions on the nonlinearities. In this talk we propose a novel approach which removes this obstacle and yields global stability and tracking for systems in the strict-feedback form. Instead of the traditional structure of concurrent on-line estimation and control, we adopt a two-phase control strategy: First, in the active identification phase, we use the control input to drive the system state to points in the state space which provide us with information about the unknown parameters. We develop an algorithm which guarantees that the duration of this phase is finite and that at its end we will be able to compute future values of the system states. Then, in the look-ahead control phase, we use this prediction capability to treat the system as completely known and to drive it to its desired state in finite time.
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