Series-based approximate approach of optimal tracking control for nonlinear systems with time-delay

The optimal output tracking control (OTC) problem for nonlinear systems with time-delay is considered. Using a series-based approximate approach, the original OTC problem is transformed into iteration solving linear two-point boundary value problems without time-delay. The OTC law obtained consists of analytical linear feedback and feedforward terms and a nonlinear compensation term with an infinite series of the adjoint vectors. By truncating a finite sum of the adjoint vector series, an approximate optimal tracking control law is obtained. A reduced-order reference input observer is constructed to make the feedforward term physically realizable. Simulation examples are used to test the validity of the series-based approximate approach.