Robust Estimation and Control of Infinite Dimensional Systems (RECIDS)

Automation and control have become an indispensable part of modern life. Using cruise control to set the speed of a car, landing a rover on Mars, or forecasting the weather, are all accomplished using tools from the field of automation and control systems theory. The successful development of automatic control algorithms requires a mathematical description of the relevant process. Most existing tools are limited in application to a specific kind of mathematical description, namely that of Ordinary Differential Equations (ODE) of finite order. However, systems that are characterized by delays and transport phenomena, such as petroleum exploration and production and stability of large power transmission networks, requires a different kind of description known as infinite dimensional systems. To enable the effective use of automatic algorithms to these kinds of systems requires us to modify existing and develop new mathematical tools to handle the particular behavior of infinite dimensional systems. This will enable new, and enhance the existing, capabilities of monitoring, optimizing and controlling drilling and production processes, and provide tools and theory to deal with the stability of large distributed power system grids directly as infinite dimensional systems.

In the field of control of infinite dimensional systems the main impacts was on proving that a large class of existing results yield controller with arbitrarily small delay robustness, which makes them infeasible for industrial application. Based on this we proposed modifications which avoids this problem for interconnected systems of the ODE-PDE, ODE-PDE-ODE, and PDE-ODE-PDE type. Furthermore we derived a stabilizing controller for a new class of PDE-ODE-PDE systems and showed that there is sub-class of these which are under-actuated and cannot be controlled. This theoretical insight lead to a practical result on the control and estimation of axial and torsional behavior of drill strings which is a system of the ODE-PDE-DOE type, and resulted in the submission of an American patent on a new method for estimating drill string behavior.

Modern approaches to process monitoring, optimization and control promise to enhance robustness and performance of automation through the merger of process knowledge encoded in mathematical models with real-time measurements from the process. Such approaches, known as 'model based estimation and control', require a mathematical model of the process, and existing results are mostly limited to models described by Ordinary Differential Equations (ODEs) of finite order. However, a broad spectrum of engineering systems, such as petroleum exploration and production and stability of large power transmission networks, are characterized by delays and transport phenomena which requires infinite dimensional model. On these systems established results using ODEs exhibit a limited range of applicability and subpar performance. There has recently been significant theoretical progress on the control of infinite dimensional systems, however, to enable application of these emerging results to industrial control-problems, greater maturity of the design paradigm must be achieved through the explicit introduction of classical design concepts in feedback control. Our approach is to enable this by extending results on multi-objective controller synthesis using Linear Matrix Inequalities (LMIs) to handle a broad class of infinite dimensional. This will enable the extension of applicability of some of the most sophisticated tools for controller design to that of a very general class of infinite dimensional systems, and pave the way for a wide range of application of infinite dimensional controllers to industrial problems. By explicitly addresses the distributed nature of the control and estimation problems, these results will enable new, and enhance the existing, capabilities of monitoring, optimizing and controlling drilling and production processes, and provide tools and theory to deal with the stability of large distributed power system grids directly as infinite dimensional systems.