Estimation and Identification of Nonlinear Systems

9970998Krener这个研究项目的重点是使用非线性和可能有噪声的观测值来估计非线性系统的状态和参数。 第一个问题是利用广义李雅普诺夫函数证明非线性观测器的存在性和收敛性。 我们还解决了非线性滤波和平滑的高效计算方案的发展。 本计画的另一半是针对非线性系统，特别是多项式非线性系统，发展有效的参数估计方法。 我们将集中在识别系统中的一些模型类，如反馈线性化系统。 我们将使用非线性系统特有的性质，如分叉和谐波相互作用的存在，以帮助它们的识别。在整个科学和工程中，动力系统的模型被用来描述真实的世界过程的演变。 在小的偏移上，线性模型可以相当准确，但在较大的运动上，通常必须依赖于非线性模型。 从线性观测值估计线性系统的状态是一个发展良好的领域，并且有效且计算上可行的方法是众所周知的。但是，非线性系统状态估计的理论和方法虽然相当广泛，但并不完全令人满意。对于大多数非线性系统，确实存在全局收敛的、计算上可行的技术。 类似地，线性系统的参数识别是一个成熟的领域，但非线性系统的参数识别却发展得很少。我们提出的研究，估计状态和识别参数的非线性系统，使用各种新的方法，表现出相当大的承诺。

9970998KrenerThis research project focuses on the estimation of states and parameters of nonlinear systems using nonlinear and possibly noisy observations. The first question addressed is the existence and convergence of nonlinear observers using a generalization of Lyapunov functions. We also address the development of efficient computational schemes for nonlinear filtering and smoothing. The other half of the project is to develop effective parameter estimation schemes for nonlinear systems, particularly, systems with polynomial nonlinearities. We will focus on identifying systems within some model class such as the feedback linearizable systems. We shall use the properties particular to nonlinear systems such as the presence of bifurcations and harmonic interactions to assist in their identification.Throughout science and engineering, models of dynamical systems are used to describe the evolution of real world processes. Over small excursions, linear models can be quite accurate but over larger motions one generally must rely on nonlinear models. The estimation of the state of a linear system from linear observations is a well developed area and effective and computationally feasible methods are well-known. But the theory and methodology for estimating the state of a nonlinear system while quite extensive is not completely satisfactory. There do exist globally convergent, computationally feasible techniques for most nonlinear systems. Similarly the identification of the parameters of a linear system is a mature field but the identification of the parameters of a nonlinear system is much less developed. We are proposing research in estimating the state and identifying the parameters of nonlinear systems using a variety of new methods that show considerable promise.