THE EFFECTS OF COMPUTATIONAL DELAY IN DESCRIPTOR-BASED TRAJECTORY TRACKING CONTROL

Descriptor Predictive Control (DPC) has been shown to be a useful meth od for solving nonlinear tracking problems. A rigorous analysis of loc al stability and performance characteristics of this method has been a chieved previously by studying the linear plant under the assumption t hat the delay introduced in the control due to numerical computation c an be neglected. It was shown that, if the plant is controllable and m inimum phase, stability is guaranteed and tracking is achieved exponen tially with any desired rate of convergence. It was also shown that so metimes DPC must include a specially designed preliminary feedback. In this paper, we carry out a similar analysis by taking into account co mputational delay, which is unavoidable in actual implementation of DP C. We show, in particular, that under the same assumptions, and provid ed the special preliminary feedback is used, that the closed loop syst em remains stable as long as the delay is smaller than a threshold and that exponential tracking is achieved. However, the rate of convergen ce of the tracking error cannot be chosen arbitrarily because it is co nstrained by the plant zeros. The delay analysis is used to explain ex perimental observations in the literature about the occasional failure of previous implementations of the DPC approach at small sampling per iods. A nonlinear robotics problem is worked in detail.