Output feedback adaptive stabilization and command following for minimum phase dynamical systems with unmatched uncertainties and disturbances

Abstract

In this article, we develop an output feedback adaptive control framework for continuous-time minimum phase multivariable dynamical systems for output stabilisation and command following. The approach is based on a nonminimal state-space realisation that generates an expanded set of states using the filtered inputs and filtered outputs and their derivatives of the original system. Specifically, a direct adaptive controller for the nonminimal state-space model is constructed using the expanded states of the nonminimal realisation and is shown to be effective for multi-input, multi-output linear dynamical systems with unmatched disturbances, unmatched uncertainties and unstable dynamics. The proposed adaptive control architecture requires only knowledge of the open-loop system's relative degree as well as a bound on the system's order. Several illustrative numerical examples are provided to demonstrate the efficacy of the proposed approach.

Keywords:

• output feedback
• direct adaptive control
• minimum phase systems
• unmatched disturbances
• unmatched uncertainty
• nonminimal state-space realisation
• stabilisation
• command following

Acknowledgements

This research was supported in part by the Air Force Office of Scientific Research under Grant FA9550-09-1-0429.