Approximate optimal tracking control for a class of nonlinear systems

The optimal tracking control (OTC) problem for a class of nonlinear systems with a quadratic performance index is studied. By introducing a sensitivity parameter and expanding the power series around it, the original OTC problem is transformed into a sequence of nonhomogeneous linear two-point boundary value problems. The OTC law obtained consists of an analytic linear feedback term, an analytic linear feedforward term, and a nonlinear compensation term, which is the series sum of the adjoint vector sequence. A reduced-order reference input observer is constructed to make the feedforward term physically realizable. A simulation example is employed to test the validity of the sensitivity approach.