模型不确定非线性随机系统的鲁棒性能准则设计

对于一类模型不确定非线性随机系统,用耗散性的观点发展了鲁棒性能准则理论.特别地,将确定性非线性系统理论中的耗散性概念引入到模型不确定随机非线性系统中,并以此作为基础来发展H∞理论.在精确模型随机非线性系统H∞基础上,建立了模型不确定系统L2增益和HJI不等式的可解性的关系.由于HJI偏微分方程难于求解,考虑模型参数满足某种适当匹配条件的系统的鲁棒性能准则问题,我们不需要通过求解HJI方程就可以得到此类系统的H∞控制律.

Robust Performance Rule Design for Stochastic Nonlinear Systemswith Model Uncertainty

This paper deals with the theory of Robust performance rule from the view of dissipation for a large class of stochastic nonlinear systems with model uncertainty. In particular, the notion of dissipation associated with deterministic nonlinear systems is introduced for the uncertain stochastic nonlinear systems, and is used to study $H_\infty$ control. On the basis of exact stochastic nonlinear systems, the connection between the $L_2$-gain of the uncertain stochastic nonlinear systems and the solution to a certain HJI inequality is established. In general, it is difficult to solve the HJI partial differential equation, by using the Robust performance rule problem of the model satisfying some proper matching condition, the $H_\infty$ control law of the system is obtained without solving the HJI equation.