Abstract

This mini-course presents a formulation of the hierarchical control design problem for nonlinear systems. The idea in hierarchical control design is to “divide and conquer” a complex control specification by decomposing it into a hierarchy of sub-specifications, each one typically easier to enforce than the original specification. The backstepping technique for equilibrium stabilization is a popular example of hierarchical control design.

Hierarchical control specifications arise naturally in modern robotics applications. To illustrate, the path following problem for vehicle formations involves a hierarchy of two specifications: first enforce the desired formation, then make the formation follow a pre-specified path in three-space. Enforcing the formation corresponds to stabilizing a subset $\Gamma_1$ of the vehicles’ state space; making the formation follow the path corresponds to stabilizing a second subset, $\Gamma_2$, contained in $\Gamma_1$. Thus in this context, hierarchical control design corresponds to the simultaneous stabilization of two nested invariant sets $\Gamma_2 \subset \Gamma_1$.

In this mini-course a framework is proposed in which hierarchical control design amounts to the simultaneous stabilization of a finite collection of nested controlled invariant sets. I will discuss so-called reduction principles as tools to address this stabilization problem. The theory will be used to solve two problems: the design of distributed controllers solving the circular formation stabilization problem for nonholonomic vehicles, and the design of almost-global position controllers for thrust-propelled underactuated vehicles. In the context of equilibrium stabilization of lower-triangular control systems, I will show that reduction principles allow one to improve the classical backstepping technique.

Biography

Manfredi Maggiore was born in Genoa, Italy. He received the Laurea degree in Electrical Engineering in 1996 from the University of Genoa and the PhD degree in Electrical Engineering from the Ohio State University, USA, in 2000. Since 2000 he has been with the Edward S. Rogers Sr. Department of Electrical and Computer Engineering, University of Toronto, Canada, where he is currently Professor. He has been a Visiting Professor at the University of Roma Tor Vergata (2001) and the University of Bologna (2007-2008). His research focuses on mathematical nonlinear control, and relies on methods from dynamical systems theory and differential geometry.