Reaserch Into Optimal Tracking Control For Nonlinear Time-Delay Systems With Persistent Disturbances

As we all know, almost all actual control systems are affected by external disturbances inevitably. Except for stochastic disturbances, there are external deterministic disturbances which widely exist in practical processes. So the systems with deterministic disturbances are widely applied to many application areas, such as aerospace, industry, mechanical engineering and ocean engineering. The vibration which is from external disturbances impacts the performance of control systems, so the design of controller to eliminating or reducing the external disturbances affecting to system is very important. Therefore, the analysis of the optimal control for nonlinear systems with external disturbances is appropriate for actual systems, and is one of the important control problems both in theory and in practice. On the other hand, nonlinear and time-delay are widely exist in practical systems. For example, the scale of machine vibration signal and the transform delay of the control signal in offshore platform shock absorption control system, etc. Theoretically, nonlinear and time-delay systems are infinite dimension systems which are described by functional differential equation, the problem which coming down to nonlinear or time-delay systems are hard to solve. The integration of stability analysis of nonlinear or time-delay systems and control algorithm is a important task.In this paper, the phenomena of disturbances are analyzed in brief firstly. Then, the relative studies on the optimal tracking control problem for nonlinear and time-delay systems up to now are given in detail.The optimal tracking control problem for nonlinear systems, linear time-delay systems, nonlinear time-delay systems with persistent disturbances are considered.Base on the internal model principle, the disturbance compensator is constructed. The system with persistent disturbances is transformed into an augmented system without persistent disturbances. Then,a nondelay sequence solutions which uniformly converges original time-delay systems is constructed by sensitivity approach,the optimal tracking control law of the argument system is obtained by calculating the sequence . By intercepting the finite terms of optimal control sequence, the suboptimal tracking control law of augment systems and original systems is obtained. The algorithm of obtaining the optimal tracking control law is designed and simulations demonstrate the validity of the designed approach. The proposed algorithm avoids solving the Riccati equation basing on state vector or the Hamilton-Jacobi-Bellman (HJB) equation and has low computational complexity. Since a problem of physical realization arises by this method, the disturbance observer and reference input observer are constructed to make the state of exosystems to be accessible. At last, the simulation examples demonstrate the validity of the designed approach.