Ph.D. Defense

Luke Somers

(Advisor: Prof. Wassim M. Haddad)

Feedback Interconnection of Dissipative Systems and Accelerated Learning for Adaptive Control

Friday, November 22

1:00 p.m.

Montgomery Knight Building 317

Abstract

In this research, we develop partial stability theorems for nonlinear continuous-time and discrete-time dissipative feedback systems. Specifically, by invoking additional structural constraints on the forward and feedback loop system storage functions, we develop feedback interconnection partial stability results for dissipative nonlinear dynamical systems. Our results provide extensions of the positivity and small gain theorems for guaranteeing partial stability of feedback interconnected systems. Moreover, we introduce the notion of strongly dissipative dynamical systems. In particular, we construct a stronger version of the dissipation inequality that implies system dissipativity and generalizes the notion of strict dissipativity but unlike strict dissipativity, which for a closed dynamical system implies asymptotic stability, the closed dynamical system possesses the property that system trajectories converge to a Lyapunov stable equilibrium state in finite time. Next, we develop new continuous-time, momentum-based adaptive laws for identification and control by augmenting higher-order tuners into the integral gradient and recursive least squares algorithms. In addition, we develop an online learning algorithm for solving the Bellman equation for affine in the control discrete-time nonlinear uncertain dynamical systems. To ensure accelerated learning of our algorithm in generating optimal control policies, we use an actor-critic structure predicated on higher-order tuner laws. Finally, we merge our strong dissipativity framework with our momentum-based adaptive control architecture to develop adaptive controllers with finite time guarantees. 

Committee

 • Prof. Wassim M. Haddad– School of Aerospace Engineering (advisor) 

• Prof. Kyriakos G. Vamvoudakis– School of Aerospace Engineering

• Prof. Jonnalagadda V.R. Prasad– School of Aerospace Engineering 

• Dr. Cedric Justin – School of Aerospace Engineering • Prof. Junsoo Lee– University of South Carolina