Use of prior bounds on time constants and steady‐state gain in recursive parameter bounding

Abstract

AbstractComputation of parameter bounds of a linear dynamical system, given input–output observations and bounds on model‐output error, has been developed as an alternative to classical parameter estimation using least squares, maximum likelihood or the prediction error method. When bounds on time‐domain plant behaviour are known in advance, they can be used to develop prior parameter bounds for discrete‐time rational transfer‐function parameters. These bounds can be used to initialize standard parameter‐bounding algorithms which process input–output observations to update the exact polytope feasible set or one of its outer bounding approximations such as an ellipsoid, orthotope or parallelotope. This paper presents a method to compute such prior bounds from bounds on time constants and steady‐state (dc) gain, often available from the physics of the system or from previous experience. The method finds subsets making up the prior feasible parameter set, recursively in model order, for any configuration of the pole ranges. An analysis leading to measures of the value of prior bounds, in terms of their chances of remaining active when new bounds derived from observations are imposed, is presented. A simulation study compares polytope updating with and without such initial bounds. The simulations investigate the influence of the tightness of time‐constant and steady‐state‐gain bounds in reducing the volume of the feasible sets obtained as observations are processed. The effects of initial bound tightness and signal‐to‐noise ratio on survival time of the prior bounds are also examined. Copyright © 2002 John Wiley & Sons, Ltd.