Optimal Output Tracking Control for Nonlinear Time-Delay Systems

This note focuses on the optimal output tracking control (OOTC) problem of a class of nonlinear systems with state time-delay. By using a successive approximation approach (SAA), the OOTC problem is transformed into a sequence of linear inhomogeneous two-point boundary value (TPBV) problems including adjoint vector differential equations. An iterative procedure is presented to solve the adjoint vector sequence. The OOTC 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 output tracking control (SOTC) law. A simulation example is employed to test the validity of the SAA