Optimization and systems theory
Optimization and systems theory is a discipline in applied mathematics primarily devoted to methods of optimization, including mathematical programming and optimal control, and systems theoretic aspects of control and signal processing. In addition, attention is given to applied problems in operations research, systems engineering and control engineering.
Research performed at the division of optimization and systems theory has a wide span encompassing theory as well as applications. It concerns various topics in mathematical systems theory, with particular emphasis on stochastic systems, filtering, identification and robust and nonlinear control; mathematical programming, with large-scale nonlinear programming, structural optimization; and a wide range of applications. The nature of the research is such that the division acts as a bridge between the department of mathematics and many applied disciplines.
Examples of applications include autonomous systems, optimization of radiation therapy, telecommunications and structural optimization. The applied projects are often carried out in close cooperation with industrial partners and experts from the applied areas of study. Our research therefore gives a close interaction between fundamental research in our fields and more applied areas. The division is active in several research centers at KTH.
My present research is mainly in two different directons: (i) moment problems for rational positive measures and (ii) stochastic systems theory. Direction (i) deals with a class of nonclassical moment problems that are motivated by engineering applications, in which certain conditions of bounded complexity (rank, degree), reflecting physical realizability by a finite-dimensional device, are required. Moment problems are typically underdetermined, and in this new setting they give rise to finite-dimensional manifolds of solutions. Thus, a global-analysis approach, where one studies the manifold of solutions as a whole, can provide the basis for parameterizing, comparing, and selecting particular solutions based on additional design criteria. Applications to spectral estimation, robust control theory, system identification and image processing are considered. In direction (ii) we develop a geometric theory for stochastic systems and study certain problems in stochastic control theory.
Svanberg's main area of research is theory and methods for nonlinear optimization, in particular so called "structural optimization" which is an application area dealing with optimal design of load-carrying structures.
He has developed a numerical optimization method (for inequality-constrained problems) called "method of moving asymptotes" and corresponding computer codes in Fortran and Matlab. These codes, which are freely available for academic usage, are today frequently used tools for structural optimization.
Since January 2011, he is the academic advisor for the industrial doctoral student project "Topology optimization of fatigue-constrained structures", financed by VR and SCANIA.