Optimal control and disturbance damping for a class of nonlinear systems with time-delay

This note presents a feedforward and feedback optimal control (FFOC) law for a class of nonlinear time-delay systems affected by external disturbances. A sequence of inhomogeneous linear non-delay state and adjoint vector equations are constructed to approximate to the original two-point boundary value (TPBV) problems from the original optimal control problem. The convergence of the sequences is proved. The FFOC law obtained consists of analytical linear feedforward and feedback terms and the limit of a compensation sequence. By using the finite-time iteration of the compensation sequence, a suboptimal control law is obtained. A disturbance observer is introduced to obtain a physically realizable feedforward controller. Simulation results demonstrate the validity of this method.