Adaptive constrained control subject to both input-amplitude and input-velocity constraints

An adaptive constrained one-step-ahead controller is presented, which is appropriate for the case where the input steady-state value u _r, corresponding to a desirable set-point y_r, is known a priori. Specifically, it is the deterministic version of the generalized minimum variance controller, designed in such a way as to handle two kinds of constraints, namely, |u_r(k)|⩽c and |u _r(k)-u(k-1)|⩽w. It is shown that for a stable, discrete-time, either minimum or nonminimum phase system, this can be achieved by making a suitable online choice of the quantities l and Q(q ^-1). Apart from the well-known RLS and projection algorithms, any other recursive parameter estimation scheme can be applied, as far as it shares some of the basic properties of the above algorithms. The performance of the proposed controller is demonstrated by means of simulation