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

本文主要研究具有任意、时变和先验未知时滞的连续系统基于连续和离散观测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，最优过滤方程必须是连续的，以反映过程的连续性质，并考虑到连续测量。当离散测量变得可用时，该最优滤波器将受到不连续输入的影响。研究的创新之处在于：(1)在不简化假设的情况下，直接将问题归结为具有不连续性的连续问题；(2)研究了离散和连续测量中最一般的时变和先验未知时滞的情况。研究的目的是：1.发展离散和连续观测连续系统的最优状态估计理论；2.将所发展的理论推广到离散观测的采样率未知和时变的情况；3.将所发展的理论扩展到包括离散和连续观测都受到任意、时变和先验未知时滞的情况；4.将积分方法的一般理论结果简化到实际重要的状态空间系统和具有被控对象和测量记忆的系统；5.开发实现所述方法的软件。利用仿真和实验研究对所开发的方法进行测试和比较。另外的目标是为将所提出的积分方法推广到对象结构和参数、约束和输入不连续的情况奠定基础；推广关于非线性系统的结果；以及研究所开发的滤波方法在双重控制问题中的应用。研究将包括国际和工业合作。基于可用测量对表征过程和系统动态运行的变量的估计是各种工程和科学领域的基本问题。当需要估计不可直接测量的变量时，估计问题的一个特例要求我们在估计过程中使用该过程的模型。对于离散和连续测量具有时变和一般未知延迟的情况，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。在本项目期间开发的方法将适用于手动采样过程的状态和参数估计、人为触发的数据采集以及由于数据网络中信息传输的不确定性而引入的测量和执行时延的远程过程的状态估计。在本研究过程中形成的理论基础将适用于具有任意和时变时滞的离散和连续测量的任意组合的线性动态系统的实际相关情况。文中还提出了对非线性系统的推广。

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.