Research Into Optimal Tracking Control For Nonlinear Time-delay Large-scale 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 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 disturbance affecting to system is very important. Therefore, the analysis of the optimal control for systems with external disturbances is appropriate for actual systems in practice. Nonlinear and time-delay systems 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 systems, etc.In the ocean engineering area, many systems can be considered as complex large-scale systems with time-delay, such as the vibration control systems for large-scale offshore structures, and the attitude control systems for ship borne towed vehicles. The problem which coming down to nonlinear or time-delay systems are hard to solve .For time-delay systems ,the optimal control problems on quadratic performance indexes are usually transformed to two-point boundary value problems with both time-advance terms and time-delay terms. Therefore, it is very difficult to solve these optimal control problems, no mater for exact solutions or numerical solutions.In this paper, a sensitivity method is used to study the optimal tracking control problem, and an approximate optimal tracking control approach which is based on the sensitivity approach is proposed. In first section, optimal control theory of time-delay systems and nonlinear systems and the development and main result of large-scale systems are discussed. Then the sensitivity approach is studied detailed.In second section, the sensitivity parameterεis introduced into the two-point boundary value problem which is obtained by the optimal tracking control problem of time-delay nonlinear system. By sensitivity approach, the time-delay item, the time-advance item and the nonlinear item which are unknown is transformed into items which are known. Then, the forgoing two-point boundary value problem is transformed into a series two-point boundary value problem without time-delay item, time-advance item and nonlinear item. The relation of them is demonstrated.The optimal tracking problem of nonlinear large-scale system is considered by the sensitivity approach. Based on the internal principle, the subsystem of nonlinear large-scale system which is affect by the disturbances is transformed into the augmented subsystem without disturbances. By sensitivity approach the nonlinear item is transformed into known item, the optimal tracking control of nonlinear large-scale system is obtained. Then, the optimal tracking control law of original system can be obtained. Simulations demonstrate the validity of the designed approach.The optimal tracking control problem of nonlinear time-delay large-scale system is considered based on the third section. By sensitivity approach, the algorithm which is appropriate for these kinds of systems can be obtained. Simulations demonstrate the validity of the designed approach.In real applications, because of the complexity of the problem, it is hard to obtain the exact solutions. An eclectic way is to find a suboptimal control law according to certain precision demand. So the suboptimal approach is also studied.