Generalized nonlinear H-infinity synthesis condition with its numerically efficient solution

作者：Zheng Qian; Wu Fen^*

来源：International Journal of Robust and Nonlinear Control, 2011, 21(18): 2079-2100.

DOI：10.1002/rnc.1682

• nonlinear H-infinity control
• output feedback
• polynomial nonlinear systems
• SOS programming

In this paper, we will first derive a general synthesis condition for the output-feedback H-infinity control of smooth nonlinear systems. Computationally efficient H-infinity control design procedure for a subclass of smooth nonlinear systems with polynomial vector field is then proposed by converting the resulting Hamilton-Jacobi-Isaacs inequalities from rational forms to their equivalent polynomial forms. Using quadratic Lyapunov functions, both the state-feedback and output-feedback problems will be reformulated as semi-definite optimization conditions and locally tractable solutions can be obtained through sum-of-squares (SOS) programming. The proposed nonlinear H-infinity design approach achieves significant relaxations on the plant structure compared with existing results in the literature. Moreover, the SOS-based solution algorithm provides an effective computational scheme to break the bottleneck in solving nonlinear H-infinity and optimal control problems. The proposed nonlinear H-infinity control approach has been applied to several examples to demonstrate its advantages over existing nonlinear control techniques and its usefulness to engineering problems.

• 出版日期2011-12