Adaptive Control of Nonlinear Time-Delay Systems with Application to a Two-Stage Chemical Reactor

Global adaptive regulation of general strict feedback system with unknown time-delay by state feedback is a long-standing problem. This note provides, for the first time, a solution to this problem by introducing a novel dynamic gain-based adaptive backstepping approach. A key feature of the developed approach is that the Lyapunov function and the adaptive law are chosen in a new recursive manner. With the help of appropriate Lyapunov-Krasovskii functionals, a memoryless state feedback controller is explicitly constructed. It is shown that global adaptive regulation can be achieved for the nonlinear time-delay system. Finally, we use a two-stage chemical reactor to demonstrate the application of the proposed scheme.