Variable gain linear quadratic regulator and its application

A variable gain linear quadratic regulator(VGLQR) for stabilizing a class of multivariable nonlinear control system is proposed. The VGLQR method is derived by using the Lyapunov function approach. This control scheme can be viewed as a novel gain scheduling controller, and the feedback gain obtained by solving algebraic Riccati equation online is changing with state. In addition, a fast algorithm based on Schur method for the solution of algebraic Riccati equations online is discussed and a software package was developed during the present research. In this paper, the VGLQR control method is applied to a general nonlinear system, also the effectiveness of the proposed method is verified by stabilization of triple inverted pendulum system. Simulation and physical experiment results demonstrate that the VGLQR is of good stability and adaptability, which are distinctly better than that of classical LQR controller.