Stochastic Adaptive Control and Related Topics

本提案描述了用于调查的各种随机问题。这些问题与随机自适应控制有关，随机自适应控制是对不完全已知的随机系统的控制。通常，为了解决自适应控制问题，需要辨识系统的未知参数，同时构造控制器。控制问题的成本泛函通常是遍历的(单位时间的平均成本)。通过扩展随机演算并将其用于自适应控制问题，提出了一类过程，即分数布朗运动。这一系列流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组。研究连续时间分支过程的自适应控制，是因为这些过程是重要的，而且对这些过程的控制应用很少。对风险敏感的控制问题对金融模型特别有用。提出了对这些问题进行自适应控制的研究。这项建议中的工作应该适用于具有受控随机模型的物理系统。用数学模型来描述物理系统，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，模型不是完全指定的，因此有必要从系统的演化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态，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。提出了研究随机自适应控制中的各种问题。这些问题包括集中系统和分布式系统。我们还将研究一些新的利用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.