Tracking with asymptotic sliding mode and adaptive input delay effect compensation of nonlinearly perturbed delayed systems applied to traffic feedback control

Asymptotical sliding mode-model reference adaptive control design for a class of systems with parametric uncertainty, unknown nonlinear perturbation and external disturbance, and with known input and state delays is proposed. To overcome the difficulty to directly predict the plant state under uncertainties, a control design is based on a developed decomposition procedure, where a ‘generalised error’ in conjunction with auxiliary linear dynamic blocks with adjustable gains is introduced and the sliding variable is formed on the basis of this error. The effect of such a decomposition is to pull the input delay out of first step of the design procedure. As a result, similarly to the classical Smith predictor, the adaptive control architecture based only on the lumped-delays, i.e. without conventional in such cases difficult-implemented distributed-delay blocks. Two new adaptive control schemes are proposed. A linearisation-based control design is constructed for feedback control of an urban traffic region model with uncertain dynamics. Simulation results demonstrate the effectiveness of the developed adaptive control method.