(Advisor: Prof. W. M. Haddad]
will propose a doctoral thesis entitled,
Finite-Time Stability, Semistability, and Optimality of Discrete-Time Nonlinear Dynamical Systems with Application to Network Consensus
Friday, April 30 at 2:00 p.m.
In this work, we study finite time stability for discrete-time dynamical systems. In particular, we address finite time stability of the discrete autonomous systems by providing Lyapunov and converse Lyapunov theorems for finite-time stability, and show that the settling-time function capturing the finite settling time behavior of the dynamical system and the regularity properties of the Lyapunov function are related. Then, we develop a framework for optimal nonlinear feedback control for finite time stability and stabilization for nonlinear discrete-time controlled dynamical systems based on steady-state form of the Bellman equation and inverse optimal control. Next, we propose a finite-time stability and stabilization framework for state dependent nonlinear impulsive systems by developing sufficient Lyapunov conditions for finite time stability of impulsive dynamical systems. Moreover, we use our stability results to design hybrid finite time stabilizing control laws for impulsive dynamical systems. Next, we develop a framework on semistability and finite-time semistability of discrete-time systems, which involves a continuum of equilibria. Specifically, we develop Lyapunov and converse Lyapunov theorems for semistability and finite time semistability, and show that the regularity properties of the Lyapunov function is related to the settling time function that captures the finite settling time behavior of the dynamical system. Moreover, we use the results to design semistable and finite time semistable consensus protocols for discrete dynamical networks consensus based on basic discrete-time thermodynamic principles. Finally, we propose Lyapunov and converse Lyapunov theorems for discrete-time stochastic semistable nonlinear dynamical systems. In particular, we provide necessary and sufficient Lyapunov conditions for stochastic semistability by using the difference operator of the Lyapunov function, which is an analog of the infinitesimal generator for continuous-time stochastic dynamical system. Then we use the results to develop semistable consensus protocols for discrete-time networks with communication uncertainty that involves the exchange of information between agents based on basic discrete-time thermodynamic principles.
- Prof. W. M. Haddad – School of Aerospace Engineering (advisor)
- Prof. J. V. R. Prasad – School of Aerospace Engineering
- Prof. K. Vamvoudakis – School of Aerospace Engineering