Output regulation for linear distributed parameter systems

This dissertation is concerned with the solvability of the output regulation problem for infinite-dimensional linear control systems with bounded control and observation operators. By output regulation we mean a control design problem in which the objective is to achieve tracking, disturbance rejection and internal stability. Two versions of output regulation are considered: the state feedback regulator problem, in which we look for a static state feedback control law and the error feedback regulator problem in which a dynamical controller is sought for which only the tracking error is available to the controller. Under the standard assumption of stabilizability necessary and sufficient conditions are given for the solvability of the state feedback problem and under the additional assumption of detectability necessary and sufficient conditions are given for the solvability of the error feedback problem. The solvability of both problems are characterized in terms of the solvability of a pair of linear regulator equations. This characterization represents an extension of the results obtained by B. Francis for multivariable linear control systems. The approach follows the lines of the geometric theory of output regulation developed by C. I. Byrnes and A. Isidori for finite-dimensional nonlinear systems. The solvability of the regulator equations is shown to be equivalent to the property that the zero dynamics of the composite, formed from the plant and the exosystem, contains isomorphic copies of the exosystem and the plants' zero dynamics. Examples of periodic tracking are presented for parabolic and hyperbolic systems.