Stochastic Adaptive Control and Related Topics

[9971790 .邓肯]这个建议描述了各种用于调查的随机问题。这些问题与随机自适应控制有关，它是对一个不完全已知的随机系统的控制。通常，要解决自适应控制问题，需要识别系统的未知参数并同时构造控制。控制问题的成本函数通常是遍历的（单位时间的平均成本）。一族过程，分数布朗运动，提出了发展的随机微积分和使用这些过程的自适应控制问题。这一系列过程似乎具有广泛的适用性。考虑部分已知的半线性系统，提出了随机分布参数系统的自适应控制。这类系统包括一些随机偏微分方程。由于连续时间分支过程是一个重要的过程，而对这些过程的控制很少使用，因此提出了对连续时间分支过程的自适应控制进行研究。风险敏感控制问题对金融模型特别有用。针对这些问题，提出了研究自适应控制的方法。本建议中的工作应适用于具有受控随机模型的物理系统。它应该加强对这些物理系统的理解。数学模型用于描述物理系统，并对这些数学模型进行分析。通常需要控制物理系统，以便在数学模型中引入控制。通常情况下，模型是不完全确定的，因此有必要从系统的演化过程中识别模型的一些参数。为了描述系统中的扰动或未建模的动力学，在模型中引入了噪声。对带有噪声的不完全指定系统的控制称为随机自适应控制。提出研究随机自适应控制中的各种各样的问题。这些问题包括集总和分布式系统。本文还将研究一些新的基于分数布朗运动的噪声模型。

9971790DuncanThis proposal describes a variety of stochastic problems for investigation. These problems are associated with stochastic adaptive control which is the control of an incompletely known stochastic system. Typically to solve an adaptive control problem it is necessary to identify the unknown parameter of the system and simultaneously to construct a control. The cost functionals for the control problems are typically ergodic (average cost per unit time). A family of processes, fractional Brownian motion, is proposed for development by extending a stochastic calculus and using these processes for adaptive control problems. This family of processes seems to have wide applicability. Adaptive control for stochastic distributed parameter systems is proposed by considering partially known semilinear systems. This family of systems includes some stochastic partial differential equations. The adaptive control of continuous time branching processes is proposed for investigation because these processes are important and little use of control has been made for these processes. Risk sensitive control problems are especially useful for financial models. It is proposed to study adaptive control for these problems. The work in this proposal should be applicable to physical systems that have stochastic models that are controlled. It should enhance the understanding of these physical systems.Mathematical models are used to describe physical systems and analysis is performed on these mathematical models. Typically it is required to control the physical systems so that control is introduced in the mathematical models. Usually the models are not completely specified so it is necessary to identify some parameters of the model from the evolution of the system. To describe perturbations or unmodelled dynamics in a system, noise is introduced in the model. The control of an incompletely specified system with noise is called stochastic adaptive control. It is proposed to investigate a wide variety of problems in stochastic adaptive control. These problems include lumped and distributed systems. Some new noise models using fractional Brownian motion will also be investigated.