Design of Optimal Tracking Controller for Systems with Control-Affine Form

This paper deals with the optimal tracking control (OTC) problem for a class of nonlinear system with control- affine form. The feedforward compensation technique is used in order to make the system's output asymptotically track the desired trajectory. An adjoint vector is introduced to compensate the control-affine nonlinearity of the dynamic system. The compensation term is obtained by introducing an iterative procedure for solving a sequence of linear inhomogeneous two- point boundary value (TPBV) problems using the successive approximation approach (SAA). The OTC law obtained consists of an accurate state feedback term, a feedforward term and a compensation term which is the limit of the adjoint vector sequence. Using a finite-time iteration of the adjoint vector among optimal solution sequence, we can obtain a suboptimal tracking control (STC) law. An aircraft model is employed to test the validity of this method.