טכניון מכון טכנולוגי לישראל
הטכניון מכון טכנולוגי לישראל - בית הספר ללימודי מוסמכים  
M.Sc Thesis
M.Sc StudentYuri Dolgin
SubjectModel Order Reduction for Uncertain Systems
DepartmentDepartment of Electrical Engineering
Supervisors Professor Emeritus Feuer Arie
Professor Emeritus Zeheb Ezra


Abstract

This research deals with model order reduction of uncertain discrete-time SISO systems. Model reduction is well studied and its use is very common for fixed-coefficients systems. Physical world however poses more sophisticated kind of problems: uncertainties in physical parameters and unmodeled dynamics cause the original model to have uncertain parameters. Then, the question is: how would we cope with model reduction for such systems and, even more basic question is: what is the meaning of model reduction for systems with uncertain parameters?

    Four main directions of our investigation were:
  •  approximation of the value set of original uncertain high-order system by the fixed-coefficients low-order system
  • approximation of the amplitude value set of original uncertain high-order system by the amplitude of a fixed-coefficients low-order system
  • approximation of the value set of original uncertain high-order system by the value set of uncertain low-order system
  •  approximation of the amplitude value set of original uncertain high-order system by the amplitude value set of uncertain low-order system.

One of the applications of the first two kinds of model reduction is finding a nominal system of reduced order. An interesting point here is that the model simplification of the original system includes also the reduction

(removal) of the system’s uncertainty.


The last two kinds of model reduction pertain to applications performing worst-case analysis, where it is vital to get maximally similar uncertainty structure after model reduction. These kinds of model reduction may be viewed as a “full extension” of the concepts of classical model reduction to the case of uncertain systems.


Solution of the above problems is based on semi-infinite programming. The original problems are brought to the form of linear programming problems with infinite number of constraints and are solved by known methods for solution of linear semi-infinite programming problems. The solution also makes use of an algorithm for efficient calculation of frequency response envelopes of an uncertain discrete-time system.


All of the above algorithms were implemented in MATLAB and were used for reduction of several high-order systems.