Three-dimensional nonlinear H₂/H_∞ guidance law based upon approach of solving the state feedback Nash balance point

SANG Bao-hua^1,2, JIANG Chang-sheng²

1.College of Aviation Technology,Nanjing University of Aeronautics and Astronautics,Nanjing 210016,China;2.Dept. of Automation Engineering,Nanjing University of Aeronautics and Astronautics,Nanjing 210016,China



Abstract:

Based upon the theory of the nonlinear quadric two-person nonzero-sum differential game,the fact that the time-limited mixed H2/H∞ control problem can be turned into the problem of solving the state feedback Nash balance point is mentioned. Upon this,a theorem about the solution of the state feedback control is given,the Lyapunov stabilization of the nonlinear system under this control is proved,too. At the same time,this solution is used to design the nonlinear H2/H∞ guidance law of the relative motion between the missile and the target in three-dimensional(3D) space. By solving two coupled Hamilton-Jacobi partial differential inequalities(HJPDI),a control with more robust stabilities and more robust performances is obtained. With different H∞ performance indexes,the correlative weighting factors of the control are analytically designed. At last,simulations under different robust performance indexes and under different initial conditions and under the cases of intercepting different maneuvering targets are carried out. All results indicate that the designed law is valid.

Key words:  nonlinear system,mixed H2/H∞ control  state feedback Nash balance point  two-person nonzero-sum differential game  three-dimensional guidance law

DOI：10.11916/j.issn.1005-9113.2010.03.016

Clc Number:V249.3

Fund: