Lyapunov-based adaptive state estimation for a class of nonlinear stochastic systems
Lyapunov-based adaptive state estimation for a class of nonlinear stochastic systems
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DOI：
10.1016/j.automatica.2012.05.002
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发表时间：
2012-07
期刊：
影响因子：
--
通讯作者：
Li Xie;P. Khargonekar
中科院分区：
文献类型：
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作者：
Li Xie;P. Khargonekar
研究一类具有未知常数参数的非线性随机系统的自适应状态估计问题。这些非线性系统具有线性参数结构，并且假定非线性以类lipschitz方式有界。利用Lyapunov稳定性理论的随机对应物，我们给出了连续时间和离散时间非线性随机系统在均方意义上具有最终指数有界估计误差的自适应状态估计和参数估计。给出了lmi的可解性的充分条件。此外，我们还引入了一种次优设计方法来优化参数估计均方误差的上界。这种次优设计过程也通过LMI计算实现。通过鞅方法，我们还证明了相关的Lyapunov函数具有非负的Lyapunov指数。
This paper is concerned with an adaptive state estimation problem for a class of nonlinear stochastic systems with unknown constant parameters. These nonlinear systems have a linear-in-parameter structure, and the nonlinearity is assumed to be bounded in a Lipschitz-like manner. Using stochastic counterparts of Lyapunov stability theory, we present adaptive state and parameter estimators with ultimately exponentially bounded estimator errors in the sense of mean square for both continuous-time and discrete-time nonlinear stochastic systems. Sufficient conditions are given in terms of the solvability of LMIs. Moreover, we also introduce a suboptimal design approach to optimizing the upper bound of the mean-square error of parameter estimation. This suboptimal design procedure is also realized by LMI computations. By a martingale method, we also show that the related Lyapunov function has a non-negative Lyapunov exponent.