Manuel Lanchares
(Advisor: Professor Wassim M. Haddad)
will defend a doctoral dissertation entitled,
Stochastic Nonlinear Control for Continuous and Discrete Time
Systems: Stability, Dissipativity, and Optimality
on
Tuesday, April 9 at 12:00 p.m.
Lyman Hall, Room 307
Abstract
In this dissertation, we provide a unified framework to address the problems of stability,
dissipativity, and optimality for stochastic dynamical systems. Here, we consider both
continuous-time and discrete-time stochastic dynamical systems. For each of this class of systems,
we start by using supermartingale theory to develop theorems concerning Lyapunov,
asymptotic, and exponential stability in probability. We also provide essential generalizations
of the Krasovskii-LaSalle invariant set theorem for stochastic dynamical systems. Next, we
introduce the concept of stochastic dissipativity through an energetic supermartingale condition.
We continue by formulating various necessary and sufficient conditions for stochastic
dissipativity. Additionally, we derive extended Kalman-Yakubovich-Popov conditions and
utilize dissipativity principles to establish stability criteria for feedback interconnections of
stochastic dynamical systems. Moreover, we investigate applications to thermodynamic models.
Finally, we present a unified approach to optimal nonlinear analysis and feedback control
within nonlinear stochastic dynamical systems by leveraging the insights on stability and dissipativity
previously developed. Our focus lies on offering a framework that guarantees both
stochastic stability and optimality. Moreover, we devise optimal feedback controllers for
affine nonlinear systems through an inverse optimal control problem and determine stability
margins.
Committee
Dr. Wassim M. Haddad, Chairman - School of Aerospace Engineering
Dr. Yongxin Chen - School of Aerospace Engineering
Dr. Kyriakos G. Vamvoudakis - School of Aerospace Engineering
Dr. George Kardomateas - School of Aerospace Engineering
Dr. Chaouki T. Abdallah - School of Electrical and Computer Engineering