非線性控制系統， 採用“狀態相關(微分形式)Riccati 方程式”設計

Abstract

In the area of nonlinear control systems, recently the easy-to-implement state-dependent Riccati equation (SDRE) strategy has been shown to be effective by numerous practical applications, possessing collectively many of the capabilities and overcoming many of the difficulties of other nonlinear control methods. Its diverse fields of applications include missiles, aircrafts, satellites, ships, unmanned aerial vehicles (UAV), biomedical systems analysis, industrial electronics, process control, autonomous maneuver of underwater vehicles, and robotics. Due to the great similarity to SDRE, the newly emerged state-dependent differential Riccati equation (SDDRE) approach exhibits great potential from both the analytical and practical viewpoints, and shares most of the benefits of SDRE while differing mainly in the time horizon considered (i.e. finite for SDDRE and infinite for SDRE). However, there is a significant lack of theoretical fundamentals to support all the successful implementations, especially the feasible choice of the possessed design flexibility (namely, iv the infinitely many factorizations of the state-dependent coefficient matrix) with predictable performance is still under development for both schemes. In this thesis, considering the general finite-order nonlinear time-variant systems, several problems related to the design flexibility are investigated and solved, which appear at the very beginning of the implementation of both schemes. Finally, connections to the literature in various topics of research are established, and the proposed scheme is demonstrated via examples, including real-world applications.