Mixed Deterministic/Randomized Methods for Fixed Order Controller Design

In this paper, we propose a general methodology for designing fixed order controllers for single-input single-output plants. The controller parameters are classified into two classes: randomized and deterministically designed. For the first class, we study randomized algorithms. In particular, we pr...

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Bibliographic Details
Published in:IEEE Transactions on Automatic Control Vol. 53; no. 9; pp. 2033 - 2047
Main Authors: Fujisaki, Y., Oishi, Y., Tempo, R.
Format: Journal Article
Language:English
Published: New York, NY IEEE 01.10.2008
Institute of Electrical and Electronics Engineers (IEEE)
Institute of Electrical and Electronics Engineers
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subjects:
Algorithm design and analysis
Algorithms
Applied sciences
Automatic control
Computation
Computer science
Computer science; control theory; systems
Control system synthesis
Control systems
Control theory. Systems
Critical frequencies
Design engineering
Design methodology
Equations
Exact sciences and technology
Fixed order controller design
Fixed order controller design; H(infinity) performance; interval plants; randomized algorithms; stabilization
Frequency
H_\infty performance
interval plants
Intervals
Inversions
Linear programming
Optimization
Output feedback
randomized algorithms
Stabilization
Studies
Three-term control
Stabilization
Fixed order control
interval plants
H infinite control
Control synthesis
Linear programming
Randomized algorithm
Mixed method
Interval arithmetic
Optimization
Fixed order controller design
Randomization
Linear equation
Matrix inversion
H∞ performance
randomized algorithms
Algorithm complexity
Matrix method
SISO system
Deterministic approach
ISSN:0018-9286, 1558-2523
Online Access:Get full text
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Summary:In this paper, we propose a general methodology for designing fixed order controllers for single-input single-output plants. The controller parameters are classified into two classes: randomized and deterministically designed. For the first class, we study randomized algorithms. In particular, we present two low-complexity algorithms based on the Chernoff bound and on a related bound (often called ldquolog-over-logrdquo bound) which is generally used for optimization problems. Secondly, for the deterministically designed parameters, we reformulate the original problem as a set of linear equations. Then, we develop a technique which efficiently solves it using a combination of matrix inversions and sensitivity methods. A detailed complexity analysis of this technique is carried on, showing its superiority (from the computational point of view) to existing algorithms based on linear programming. In the second part of the paper, these results are extended to H infin performance. One of the contributions is to prove that the deterministically designed parameters enjoy a special convex characterization. This characterization is then exploited in order to design fixed order controllers efficiently. We then show further extensions of these methods for stabilization of interval plants. In particular, we derive a simple one-parameter formula for computing the so-called critical frequencies which are required by the algorithms.
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ISSN:0018-9286
1558-2523
DOI:10.1109/TAC.2008.929397