Control algorithm for unknown time-varying systems†

A simple algorithm is briefly described for the control of rapidly time-varying unknown systems and its performance is illustrated by several linear and non-linear examples, including plants with unstable input zeros. The algorithm uses local flow behaviour and exhibits ‘one-step-adaptive model reference-like’ performance. The algorithm requires no prior knowledge of the plant except that it is linear in the control. The performance of the algorithm depends on its ability to make local predictions of plant behaviour and consequently the order of the controller is determined by the local curvature of the desired trajectories, the natural curvature of the plant trajectories, and the controller sampling rate.