| 内容提要: |
Optimal control is an important branch of the modern control theory, in the last decades, optimal control problems of first-order descriptor systems have been studied extensively, many significant results have been achieved. As the research moves along, many scholars find that in practical applications, a large number of physical systems are more suitable to model by second-order or higher-order differential algebraic equations. Inspired by the optimal control theory for linear systems via analyzing a Riccati matrix equation, the optimal control problem of second-order descriptor systems based on Riccati matrix equation is still open and has not been deeply investigated. In the present work, we try to solve the optimal control problem for second-order systems with singular mass matrix by applying the general Riccati matrix equation method, so that the determined feedback controller can stabilize the closed-loop system and minimize a given performance index. |