Feasibility and stability results for constrained stable generalized predictive control (Q1898491)

The problem of predictive control for discrete-time, autonomous dynamical systems with bounded both controls and outputs is studied. The system is described (using the \(z\)-transform) in terms of a transfer function with possible zeros and poles outside the unit circle. The problem is to predict, over a given finite horizon, the vector of future tracking errors and to minimize its norm over a given number of future control moves such that the norm of the control is as small as possible. Necessary and sufficient conditions for the existence of stabilizing feedback controls which satisfy the constraints is proved in the following cases: 1 unstable pole, 1 unstable zero or two unstable poles of the denominator of the transfer function. Two illustrative examples are presented. At the end, one algorithm for constrained predictive control with guaranteed stability and asymptotic tracking is presented and illustrated by two examples.