RISE-based adaptive control of an uncertain nonlinear system with unknown state delays

A continuous robust adaptive control method is designed for a class of uncertain nonlinear systems with unknown constant time-delays in the states. Specifically, a robust adaptive control method, a gradient-based desired compensation adaptation law (DCAL), and a Lyapunov-Kravoskii (LK) functional-based delay control term are utilized to compensate for unknown time-delays, linearly parameterizable uncertainties, and additive bounded disturbances for a general nonlinear system. Despite these disturbances, a Lyapunov-based analysis is used to conclude that the system output asymptotically tracks a desired time varying bounded trajectory.