Mathematical Sciences: Stochastic Adaptive Control

随机自适应控制中的一系列问题将 在这个项目中进行调查。随机自适应控制 未知系统的最优遍历控制，包括 识别和控制。对于有限维，连续 时，未知线性随机系统的研究将提高 完全观测系统的现有结果，并导致一个 更好地理解部分观测系统的概念。 对于未知随机线性分布参数系统， 解析描述系统自适应控制初步研究 具有边界或点控制的半群将被扩展为 随机双曲系统对于未知的有限维 非线性随机系统的结果几乎自 最优性和自最优性将得到改善。自适应 未知随机分布参数系统的控制 对于半线性方程族， 圆柱形噪声 大多数物理系统需要控制的干预 以实现最佳性能。该系统通常 不完全已知，通常包含随机和未知 扰动控制一个未知的系统， 未知的随机扰动称为随机自适应 控制大多数受控系统要求随机自适应 控制，以满足系统性能标准。这 项目将研究随机自适应控制问题 这是由物理系统的潜在应用所激发的。 预计概念方面的重大改进 了解自适应随机控制过程及其 将收到申请。

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 .