Adaptive control of discrete-time strict-feedback nonlinear systems

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. We propose an 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 online estimation and control, we adopt a two-phase control strategy. First, in the nonlinearity basis 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 for this phase which guarantees that its duration is finite and that at its end we will be able to compute future values of the system state. 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