Advanced Topics in Control and Estimation of State-Multiplicative Noisy Systems

Abstract

In this paper, we will first derive a general synthesis condition for the output-feedback H∞ control of smooth nonlinear systems. Computationally efficient H∞ 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 nonlinearH∞ 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∞ and optimal control problems. The proposed nonlinearH∞ control approach has been applied to several examples to demonstrate its advantages over existing nonlinear control techniques and its usefulness to engineering problems.