Stochastic Adaptive Control of Distributed Parameter Systemswith Boundary Control

线性偏微分算子或线性时滞系统是许多物理现象的有效模型。这些系统的扰动通常可以用白噪声来建模。通常，这些模型具有未知的参数，并且系统必须被控制，因此线性随机分布参数系统存在随机自适应控制问题。在许多分布式系统中，存在边界控制。在该方案中，描述了线性随机分布参数系统边界控制的一些自适应控制问题。显然没有关于这个话题的结果。这类系统的随机自适应控制问题包括给出未知参数的相容估计族，Riccati方程解关于参数的连续性，推广了Ito公式，并验证了一类自适应控制的自寻优性。在此基础上，提出了随机半线性抛物方程自适应控制的研究方向。

Linear partial differential operators or linear delay time systems are effective models for many physical phenomena. Perturbations of these systems can often be modelled by white noise. Typically these models have unknown parameters and the systems must be controlled so there is the problem of stochastic adaptive control for linear, stochastic distributed parameter systems. In many distributed systems there is boundary control. In this proposal some problems of adaptive control for linear, stochastic distributed parameter systems with boundary control are described for investigation. Apparently no results are available on this topic. The problem of stochastic adaptive control for these systems include the exhibition of a consistent family of estimates of the unknown parameters, the continuity of the solution of a Riccati equation with respect to parameters, a generalization of the Ito formula and the verification of the self-optimizing property of a family of adaptive controls. Furthermore the initiation of an investigation of adaptive control for stochastic semilinear parabolic equations is proposed.