Study On Optimal External Disturbances Rejection Control For Singularly Perturbed Systems With Time-Delay

Almost all practical control systems are affected by external disturbances. For instances, fully-submerged hydrofoil craft, off-shore platform and ships locate in hostile marine environment and undergo excessive vibrations due to wave loads and wind. The vibrations derived from the external disturbances make the system performances and working environment bad to some extent. It is significant to design controller to eliminate or rejection the external disturbances. On the other hand, time-delay is a common phenomenon in real control system, such as measurement and transformation delay of control signal in ocean platform vibration rejection control systems. In the sense of the theoretical analysis, time-delay system is an infinite-dimension system described by the functional differential equations, and it is very difficult to study generally. The stability analysis and control algorithms design for time-system is an important issue in control research community.In many practical engineering problems, such as aeronautics and astronautics, ocean engineering, electric power systems and robot systems, there often exist two or even more time constant with different time-scales. This kind of problem can be modeled as singularly perturbed systems. The analysis and design for singularly perturbed systems has been of considerable concern, and well-developed. Because of the perturbation property of the singularly perturbed system, the optimal control problem based on the linear quadratic cost functional will lead to solve a Hamilton-Jacobi partial differential equations with multi-time scale or a high order singularly perturbed two-point boundary value (TPBV) problem with small perturbation parameter, which is almost impossible to obtain its exact analytic solutions except for the simplest cases. So looking for an approximate solution to obtain a near optimal control law is one of the important aims of researchers. In resent years, a bulk of research results for singularly perturbed continuous or discrete time systems without time-delay have been obtained in both theory and application fields. However, for the case of the singularly perturbed time-delay system affected by...