Tracking Control for Nonlinear Systems with State and Control Constraints:

A Nee Reference Governor Approach

 

Professor Elmer Gilbert

 

Department of Aerospace Engineering

University of Michigan

 

 

Using various methodologies such as linear-system design techniques and gain scheduling, it is often possible to implement feedback controllers that provide accurate tracking performance over a wide range of operating conditions.  However, rapid transitions in reference commands often cause violation of crucial constraints on state and control variables.  In this talk I present a reference governor approach for avoiding such violations when there are significant nonlinearities in the descriptions of the closed-loop system and constraints.

A reference governor is a nonlinear precompensator that modifies the time evolution of reference commands in a constraint-admissible way.  The approach described here differs from others in how potential constraint violation is anticipated.  There is no need to characterize certain, difficult-to-determine positively invariant sets.  This significantly broadens the class of methods available for finding a suitable function V, the main computational element needed in the implementation of the reference governor.  It also permits the treatment of certain types of uncertainties.

Theory of the new approach is reviewed, including the statement of very basic conditions that assure that the reference governor has nice properties such as finite settling time.  Several specific methods for obtaining V are discussed.  One promising approach is the use off-line system simulation and machine learning.  An example application is described.

 
Friday, January 18, 2002

3:30 - 5:00 p.m.

1500 EECS