摘要
超稳定性理论是自适应控制稳定性证明的有力工具,但至今它只限于确定性系统。通过对超稳定性理论进一步研究和算法结构变化,本文给出了利用超稳定性理论证明随机自适应控制(特别是Goodwin的随机逼近法)的稳定性。结果表明,与目前的证明方法——Martingale函数法和Ljung的ODE法相比,超稳定性方法有相当的优越性。它不需要象Martingale函数法那样去构造一个相当困难的随机Lyapunov函数,也可放松ODE法所必需的系统噪声平稳的条件。
Hyperstability theory is a significant tool for stability proofs of adaptive control, but so far it is only used for deterministic systems. Based on a further study of hypestability theory and a suitable conversion of the adaptive control construction, hyperstability theory are used for the stability proofs of stochastic adaptive control. It is shown that hyperstability theory can be used in stochastic case and has advantages over the previous Martingale function method and Ljung's ODE method. Comparing with the Martingale method, it does not require to build sedulously a stochastic Lyapunov function, which is usually very difficult to do. And it also omits the condition of stationary process of system noise, which is necessary in Ljung's ODE method.
出处
《自动化学报》
EI
CSCD
北大核心
1990年第1期66-70,共5页
Acta Automatica Sinica
关键词
自适应控制
超稳定性
正实函数
Hyperstabitity
positive real function
adaptive control.
