Asymptotic Regulation of Time-Delay Nonlinear Systems With Unknown Control Directions

This paper studies the problem of global state regulation with stability for time-delay nonlinear systems with unknown control directions. Using a dynamic gain-based method for counteracting time-delay nonlinearity and the Nussbaum-gain function for dealing with unknown control directions, we develop a dynamic state feedback control strategy that solves the problem. A novel construction of Lyapunov-Krasovskii functionals is presented and plays a key role in handling nonlinearity with delayed states and unknown control directions simultaneously. The proposed dynamic state feedback compensators are shown to guarantee 1) global asymptotic convergence of the system state to the origin and 2) global boundedness of the resulting closed-loop systems.