An Approximate Optimal Damping Control Method for Nonlinear Time-delay Systems with Disturbances

The optimal damping control for nonlinear time-delay systems with persistent disturbances is considered. Based on successive approximation approach (SAA), the optimal damping control (ODC) law is achieved by solving a decoupled sequence of inhomogeneous linear two-point boundary value (TPBV) problems without time-delay and time-advance terms. The ODC law of the original problem consists of accurate state feedback term, disturbance rejection term and a nonlinear time-delay compensation term, which is the limit of the adjoint vector sequence. By using the finite-time iteration of the compensation sequence, we can obtain an approximate optimal disturbance rejection control law. The proposed algorithms not only solve optimal control problems in the nonlinear time-delay system but also reduce the computation time and improve the precision. Numerical examples are included to illustrate the procedures. Keywordsnonlinear time-delay systems; optimal damping control; persistent disturbances; successive approximation approach