Dynamical systems with binary-valued observations are widely used in information industry, technology of biological pharmacy and other fields. Though there have been much efforts devoted to the identification of such systems, most of the previous investigations are based on first-order gradient algorithm which usually has much slower convergence rate than the Quasi-Newton algorithm. Moreover, persistence of excitation(PE) conditions are usually required to guarantee consistent parameter estimates in the existing literature, which are hard to be verified or guaranteed for feedback control systems. In this paper, we propose an online projected Quasi-Newton type algorithm for parameter estimation of stochastic regression models with binary-valued observations and varying thresholds. By using both the stochastic Lyapunov function and martingale estimation methods, we establish the strong consistency of the estimation algorithm and provide the convergence rate, under a signal condition which is considerably weaker than the traditional PE condition and coincides with the weakest possible excitation known for the classical least square algorithm of stochastic regression models. Convergence of adaptive predictors and their applications in adaptive control are also discussed.
翻译:信息产业、生物药店技术和其他领域广泛使用具有二元价值的动态观测系统,尽管在识别这类系统方面已作出大量努力,但以往的调查大多以一级梯度算法为基础,这种梯度算法通常比Quasi-Newton算法的趋同率慢得多,此外,通常需要持续的引力条件,以保证现有文献中一致的参数估计值,这些参数估计很难核实或保证反馈控制系统。在本文件中,我们提议采用在线预测的Quasi-Newton型算法,用二元值观察和不同阈值来估算随机回归模型的参数。我们通过使用Stochatic Lyapunov 函数和马丁瓜估计方法,建立估算算法的高度一致性,并在比传统的PE条件严重弱得多的信号条件下提供趋同率,与已知的典型的随机回归模型最小值算法中最弱的可能引力相一致。还讨论适应预测器及其在适应性控制中的应用。