Adaptive Set-Point Regulation Using Multiple Estimators

Mohamad Shahab1, Daniel E. Miller2

  • 1KAUST
  • 2University of Waterloo

Details

10:40 - 11:00 | Wed 11 Dec | Méditerranée 5 | WeA03.3

Session: Adaptive Control I

Abstract

In this paper, we consider the problem of step-tracking for an nth-order discrete-time plant with unknown plant parameters belonging to a closed and bounded uncertainty set; we naturally assume that the plant does not have a zero at z = 1. We carry out parameter estimation for a slightly modified plant; indeed, we cover the set of admissible parameters by a finite set of compact and convex sets, and use an original-projection-algorithm based estimator for each. At each point in time, a switching algorithm is used to determine which estimates are used in the pole-placement-based controller; our approach does not assume that the switching stops at any point in time. We prove that this adaptive controller guarantees desirable linear-like closed-loop behavior (exponential stability and a bounded noise gain), as well as asymptotic tracking when the noise is constant.