Mathematical Sciences: Stochastic Adaptive Control

本课题将研究随机自适应控制中的一系列问题。随机自适应控制是对未知系统的最优遍历控制，包括辨识和控制。对于有限维、连续时间、未知的线性随机系统，该研究将改进完全观测系统的现有结果，并对部分观测系统有更好的概念理解。对于未知的随机线性分布参数系统，将具有边界或点控制的解析半群描述的系统的自适应控制的初始工作扩展到随机双曲型系统。对于未知的有限维非线性随机系统，几乎自最优性和自最优性的结果将得到改善。本文将针对具有圆柱噪声的半线性方程组族，研究未知随机分布参数系统的自适应控制。大多数物理系统需要控制机制的干预才能达到最佳性能。通常，系统不是完全已知的，并且经常包含随机和未知的扰动。受未知随机扰动影响的未知系统的控制称为随机自适应控制。大多数被控系统需要随机自适应控制以满足系统性能要求。该项目将研究随机自适应控制中的问题，这些问题是由物理系统的潜在应用所驱动的。预计将在自适应随机控制过程及其应用的概念理解方面取得重大进展。

A collection of problems in stochastic adaptive control will be investigated in this project. Stochastic adaptive control is the optimal ergodic control of an unknown system and includes identification and control. For finite dimensional, continuous time, unknown linear stochastic systems the research will improve existing results for completely observed systems and result in a better conceptual understanding of partially observed systems. For unknown stochastic linear distributed parameter systems the initial work on adaptive control of systems described by analytic semigroups with boundary or point control will be expanded to stochastic hyperbolic systems. For unknown, finite dimensional nonlinear stochastic systems the results for almost self- optimality and self-optimality will be improved. The adaptive control of unknown stochastic distributed parameter systems will be initiated for families of semilinear equations with cylindrical noise. Most physical systems require the intervention of control mechanisms for their optimal performance. Typically the system is not completely known and often contains random and unknown perturbations. The control of an unknown system subject to unknown random perturbations is called stochastic adaptive control. Most controlled systems require stochastic adaptive control in order to meet system performance criteria. This project will investigate problems in stochastic adaptive control that are motivated by potential applications to physical systems. It is anticipated that significant improvements in the conceptual understanding of adaptive stochastic control processes and their applications will be obtained .