The paper considers some control problems for systems described on infinite-dimensional spaces. A mathematical framework in terms of semigroups is developed which enables the generalisation of the finite-dimensional results to infinite dimensions, and which includes partial differential equations and delay equations as special cases. After first surveying some finite-dimensional results, abstract dynamical systems are introduced and the systems theory concepts of stability, controllability, observabiity and the linear quadratic problem are analysed. Throughout the paper the abstract theory is applied to a number of examples to obtain specific results.

Infinite-Dimensional Linear Systems Theory

In this paper, we consider new regularization methods for linear inverse problems of dynamic type. These methods are based on dynamic programming techniques for linear quadratic optimal control problems. Two different approaches are followed: a continuous and a discrete one. We prove regularization properties and also obtain rates of convergence for the methods derived from both approaches. A numerical example concerning the dynamic EIT problem is used to illustrate the theoretical results.

/pdf/on-regularization-methods-for-inverse-problems-of-dynamic-1nu7cmylma.pdf

On regularization methods for inverse problems of dynamic type

In this article, we investigate the connection between regularization theory for inverse problems and dynamic programming theory. This is done by developing two new regularization methods, based on dynamic programming techniques. The aim of these methods is to obtain stable approximations to the solution of linear inverse ill-posed problems. We follow two different approaches and derive a continuous and a discrete regularization method. Regularization properties for both methods are proved as well as rates of convergence. A numerical benchmark problem concerning integral operators with convolution kernels is used to illustrate the theoretical results.

/pdf/on-regularization-methods-based-on-dynamic-programming-42a3rh3jk3.pdf

On regularization methods based on dynamic programming techniques

We investigate continuous regularization methods for linear inverse problems of static and dynamic type. These methods are based on dynamic programming approaches for linear quadratic optimal control problems. We prove regularization properties and also obtain rates of convergence for our methods. A numerical example concerning a dynamical electrical impedance tomogra- phy (EIT) problem is used to illustrate the theoretical results.

/pdf/regularization-by-dynamic-programming-4iho7rj3yd.pdf

Regularization by dynamic programming

The paper treats an inverse problem of source identification in systems modeled by partial differential equations (PDEs) of parabolic type. Assuming the locations of all sources are known, regularization procedures and recursive estimation algorithms are developed to estimate the intensity of each of the multiple sources.

http://ieeexplore.ieee.org/iel5/7965/22015/01023236.pdf

A.B. Kurzhanskii

Papers

Dynamic programming in problems of identifying distributed parameter systems