Study On Sensitivity Parameter Method Of Optimal Control For Linear Discrete Large-Scale Systems With Time-Delay

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 shipborne towed vehicles. This paper proposed a sensitivity parameter method for the optimal control problem of linear discrete large-scale systems with time-delay.For time-delay systems, the optimal control problems on quadratic performance indexes are usually transformed to two-point boundary value problems with both time-delay terms and time-advance terms. Therefore, to solve these optimal control problems is very difficult, no mater for exact solutions or numerical solutions. As for large-scale systems, the optimal control problems are especially difficult. Because the subsystems are often interconnected, and the resulting two-point boundary value problems have not only time-delay terms and time-advance terms but also coupling terms.In this paper, a sensitivity method based new approach to the optimal control problems of linear discrete large-scale systems with state time-delay is thoroughly studied:1. To eliminate the time-delay, time-advance and coupling terms, a sensitivity parameter is introduced to the original two-point boundary value problems. The problems are further transformed, and then decomposed to series ofnew two-point boundary value problems. These series of new problems are relatively simple and easy to solve.2. By solving the new problems order by order, their time-delay, time-advance, and coupling terms can be solved one by one. Based on this fact, the detailed algorithms to sovle these series of new two-point boundary value problems are proposed. By solving these problems, the optimal control law of the large-scale system is obtained.3. And an accelerated algorithm for linear discrete large-scale systems with small time-delay is further introduced.4. In real applications, the exact solutions of the optimal control problems are very hard to get. An eclectic way is to find a suboptimal control law according to certain precision demand. For easy use in real applications, the suboptimal approach is also studied.