Manuel Lanchares
Advisor: Prof. Wassim M. Haddad

will propose a doctoral thesis entitled,

Stochastic Nonlinear Discrete-Time and Hybrid Control:
Stability, Dissipativity, and Optimality

On

Thursday, May 25 at 12:00 p.m.
Montgomery Knight Building 317

Abstract
In this research, we develop dissipativity theory and optimal control for stochastic dynamical systems. In particular, we address the problem of stochastic dissipativity for both continuous-time and discrete-time stochastic dynamical systems. We provide an equivalence between the sample path dependent energetic (i.e., supermartingale) and the power balance (i.e., algebraic) forms for characterizing stochastic dissipativity for continuous-time and discrete-time stochastic dynamical systems. For discrete-time systems, the results are then used to derive extended Kalman–Yakubovich–Popov conditions for characterizing stochastic dissipativity and losslessness in terms of the nonlinear system functions. Moreover, feedback interconnection stability in probability results are also developed. Next, we investigate the role of Lyapunov functions in evaluating nonlinear-nonquadratic cost functionals for nonlinear stochastic difference equations. Furthermore, a stochastic optimal control framework is developed by exploiting connections between stochastic Lyapunov theory and stochastic Bellman theory. Next, we derive stability margins for optimal and inverse optimal stochastic feedback regulators. Specifically, gain, sector, and disk margin guarantees are obtained for discrete-time nonlinear stochastic dynamical systems controlled by nonlinear optimal and inverse optimal controllers that minimize a nonlinear-nonquadratic performance criterion. Finally, we develop a nonlinear stochastic port-Hamiltonian system model characterized by energy conservation and entropy nonconservation laws that are consistent with statistical thermodynamic principles.

Committee

• Prof. Wassim M. Haddad – School of Aerospace Engineering (advisor)
• Prof. Yongxin Chen – School of Aerospace Engineering
• Prof. Kyriakos G. Vamvoudakis – School of Mechanical Engineering