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

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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.