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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| Vydané v: | IEEE Transactions on Automatic Control Ročník 53; číslo 9; s. 2033 - 2047 |
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| Hlavní autori: | , , |
| Médium: | Journal Article |
| Jazyk: | English |
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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) |
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| ISSN: | 0018-9286, 1558-2523 |
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| Abstract | 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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| AbstractList | 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 "log-over-log" 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 @@iH@ @@dinfin@ 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. 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. [...] for the deterministically designed parameters, we reformulate the original problem as a set of linear equations. 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 "log-over-log" 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 sub(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. |
| Author | Oishi, Y. Fujisaki, Y. Tempo, R. |
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| Cites_doi | 10.1080/00207178708933889 10.1007/978-1-4471-3651-4 10.1007/10997703_3 10.1002/rnc.618 10.1109/TAC.1980.1102505 10.1214/aoms/1177729330 10.1007/b137802 10.1002/(SICI)1099-1239(200002)10:2<83::AID-RNC464>3.0.CO;2-L 10.1016/j.automatica.2005.08.010 10.1016/S0005-1098(03)00034-7 10.1109/TAC.2008.927790 10.1002/(SICI)1099-1239(199611)6:9/10<1079::AID-RNC270>3.0.CO;2-# 10.1109/TAC.2004.829632 10.1109/TAC.2004.825961 10.1109/9.16420 10.1016/j.automatica.2006.06.006 10.1016/S0005-1098(03)00108-0 10.1016/S0167-6911(97)00005-4 10.1109/TAC.2005.860290 10.1007/978-1-4471-3748-1 10.1109/TAC.2005.849187 10.1016/S0005-1098(02)00180-2 10.1109/TAC.2008.2007535 10.1016/j.sysconle.2006.11.002 10.1016/S0005-1098(03)00078-5 10.1016/S0005-1098(96)00141-0 10.1016/j.automatica.2006.09.020 10.1109/TAC.2003.814103 10.1016/S0167-6911(97)00014-5 10.1017/CBO9780511814075 10.1016/S0005-1098(01)00089-9 |
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| Keywords | 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 |
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| SubjectTerms | 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 |
| Title | Mixed Deterministic/Randomized Methods for Fixed Order Controller Design |
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