Linear Systems with Hard Constraints and Disturbances: An Extended Command Governor with Large Domain of Attraction

The talk considers a nonlinear control policy that is an extension of those provided by command governors and reference governors. As in these traditional governors it applies to discrete-time linear systems with hard constraints and set bounded disturbances. The corresponding extended command governor preserves the main properties of the traditional governors, such as straightforward online implementation and finite settling time response to arbitrarily specified set points. The principal advantage over traditional governors is significantly larger domains of attraction that may be comparable in size with those obtained by dynamic programming. An important procedure for reducing the number of online computations is given that applies to both command governors and extended command governors. Connections to an interesting model predictive control strategy are made. An example compares the domain of attraction for the extended command governor with those generated by prior control schemes. Results in a recent paper by Kolmanovsky, Gilbert, and Tseng are reviewed. They concern a fourth order lateral dynamics model of a 4-wheel vehicle, where the control is wheel steering angle and the hard constraint guarantees both right-side and left-side tire loads are positive.