Ito-Volterra Integral Approach to Optimal Filtering and Control of Processes with Continuous, Discrete and Delayed Measurements

本研究主要关注具有任意时变先验未知时滞的连续系统的基于连续和离散测量的最优状态估计问题。允许离散测量的采样率以先验未知的方式随时间变化。在这种情况下，最佳过滤方程必须是连续的，以反映过程的连续性质，并考虑连续的测量。当离散测量变得可用时，这个最佳滤波器将受到不连续输入的影响。该研究的创新之处在于：(1)将问题直接视为具有不连续的连续问题，而不简化假设；(2)研究离散和连续测量中最一般的时变和先验未知延迟情况。提出的研究目的是：1。发展了具有离散和连续测量的连续系统的最优状态估计理论；2 .将已有的理论推广到离散测量的采样率未知且时变的情况；3 .将已开发的理论扩展到离散和连续测量均受任意时变和先验未知时滞影响的情况；4 .将整体方法的一般理论结果简化为实际重要情况下的状态空间系统和具有植物和测量记忆的系统；开发实现所开发方法的软件；通过仿真和实验研究测试和比较所开发的方法。其他目标是为在工厂结构和参数、限制和投入不连续的情况下扩展拟议的综合方法奠定基础；将结果推广到非线性系统；并研究了所提出的滤波方法在对偶控制问题中的应用。这项研究将包括国际和工业合作。在过程和系统动态运行过程中，基于现有测量对表征变量的估计是各种工程和科学领域的基本问题。估计问题的一个特殊情况是，当需要估计不能直接测量的变量时，我们需要在估计过程中使用过程的模型。对于具有时变和通常未知延迟的离散和连续测量，基于模型的估计方法的一个特别重要的情况是所提出的方法的主题。本项目开发的方法将适用于人工采样过程的状态和参数估计、人为触发的数据采集以及由数据网络中信息传输的不确定性特性引入的测量和驱动时间延迟的远程过程的状态估计等领域。在本研究过程中发展的理论基础将与具有任意时变时滞的任意离散和连续测量组合的线性动态系统的实际相关案例相关。对非线性系统也作了推广。

This research is mostly concerned with the problem of the optimal state estimation of continuous systems based on continuous and discrete measurements, subject to arbitrary, time-varying and a priori unknown time delays. The sampling rate of discrete measurements is allowed to vary in time in a priori unknown way. The optimal filter equation in this case must be continuous to reflect the continuous nature of the process, and to account for continuous measurements. This optimal filter will be subject to discontinuous inputs at the moment when discrete measurements become available. The innovation of the research is that (1) the problem is approached directly as a continuous problem with discontinuities without simplifying assumptions, and (2) the most general case of time-varying and a priori unknown delays in discrete and continuous measurements is studies. The aims of the proposed research are to:1. Develop the theory of optimal state estimation for continuous systems with discrete and continuous measurements;2. Extend the developed theory for the case when sampling rates of the discrete measurements are unknown and time varying;3. Extend the developed theory to include the case when both discrete and continuous measurements are subject to arbitrary, time varying and a priori unknown time delays;4. Reduce the general theoretical results of an integral approach to practically important cases of state space systems and systems with plant and measurement memory;5. Develop the software that implements the developed methods, and6. Test and compare the developed methods using simulation and experimental studies.Additional objectives are to lay the foundation for extending the proposed integral approach for the case of discontinuities of plant structure and parameters, constraints and inputs; to extend the results on nonlinear systems; and to study the application of the developed filtering methods to dual control problems.The research will include international and industrial collaboration.The estimation, based on available measurements, of variables characterizing processes and systems during their dynamic operation, is the fundamental problem in the variety of engineering and science areas. A special case of the estimation problem when it is desirable to estimate variables that are not directly measurable requires that we use the model of the process in the estimation procedure. A particular important case of the model-based estimation methods for the case of discrete and continuous measurements with time varying and generally unknown delays is the subject of the proposed approach. The method developed during this project will be applicable in such areas as state and parameter estimation for processes with manual sampling, human-triggered data acquisition and state estimation of remote processes with time delays in measurements and actuation introduced by non-deterministic properties of the information transport through the data network. The theoretical foundation developed in the course of this research will be relevant to practically relevant cases of linear dynamic systems with any combination of discrete and continuous measurements subject to arbitrary and time-varying time delays. The extension on the case of non-linear systems is also proposed.