Analysis of the error in an iterative algorithm for solution of regulator problems for linear distributed parameter control systems



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This work is based on the classical geometric method, for solving problems of regulation involving asymptotic tracking and disturbance rejection for linear distributed parameter systems. The classical geometric method is based on the solution of a coupled pair of operator equations referred to as Regulator Equations. In general it is not easy to solve the Regulator Equations or even obtain accurate numerical solution for simple control problems. %In fact, most of the time the classical geometric method gives the solvability conditions of the regulator problem, instead the actual solution.

In this thesis, we present a methodology for tracking and disturbance rejection, which is more general than the one based on the Regulator Equations, and applies to general smooth signals.
This methodology is based on an iterative algorithm known as the \b-iterative algorithm for obtaining approximate solution for regulator problems for a class of infinite dimensional linear control systems. This thesis describes the error analysis for this iterative method regarding more general references and disturbances. In this work we consider bounded input operators and both bounded and unbounded output operators. In particular, we obtain estimates showing geometric convergence of the error, controlled by the parameter β. In addition, we demonstrate our estimates on a variety of control problems in multi-physics applications by numerically solving the \b-iterative algorithm using the finite element software ``COMSOL" .



Regulator problems, Linear distributed, Parameter systems, Iterative algorithm, Error estimates, Geometric control