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Optimal Control via Factorization and Model Matching

Encyclopedia of Systems and Control

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Abstract

One approach to linear control system design involves the matching of certain input-output models with respect to a quantification of closed-loop performance. The approach is based on a parametrization of all stabilizing feedback controllers, which relies on the existence of coprime factorizations of the plant model. This parametrization and spectral factorization methods for solving model-matching problems are described within the context of impulse-response energy and worst-case energy-gain measures of controller performance.

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Bibliography

  • Ball JA, Ran ACM (1987) Optimal Hankel norm model reductions and Wiener-Hopf factorization I: the canonical case. SIAM J Control Optim 25(2):362–382

    Article  MathSciNet  MATH  Google Scholar 

  • Ball JA, Helton JW, Verma M (1991) A factorization principle for stabilization of linear control systems. Int J Robust Nonlinear Control 1(4):229–294

    Article  MATH  Google Scholar 

  • Boyd SP, Barratt CH (1991) Linear controller design: limits of performance. Prentice Hall, Englewood Cliffs

    MATH  Google Scholar 

  • Curtain RF, Zwart HJ (1995) An introduction to infinite-dimensional linear systems theory. Volume 21 of texts in applied mathematics. Springer, New York

    Google Scholar 

  • Dahleh MA, Diaz-Bobillo IJ (1995) Control of uncertain systems: a linear programming approach. Prentice Hall, Upper Saddle River

    MATH  Google Scholar 

  • DeSantis RM, Saeks R, Tung LJ (1978) Basic optimal estimation and control problems in Hilbert space. Math Syst Theory 12(1):175–203

    Article  MathSciNet  Google Scholar 

  • Desoer C, Liu R-W, Murray J, Saeks R (1980) Feedback system design: the fractional representation approach to analysis and synthesis. IEEE Trans Autom Control 25(3):399–412

    Article  MathSciNet  MATH  Google Scholar 

  • Feintuch A (1998) Robust control theory in Hilbert space. Applied mathematical sciences. Spinger, New York

    Book  MATH  Google Scholar 

  • Francis BA (1987) A course in H ∞ control theory. Lecture notes in control and information sciences. Springer, Berlin/New York

    Google Scholar 

  • Francis BA, Doyle JC (1987) Linear control theory with an H ∞ optimality criterion. SIAM J Control Optim 25(4):815–844

    Article  MathSciNet  MATH  Google Scholar 

  • Glover K, Limebeer DJN, Doyle JC, Kasenally EM, Safonov MG (1991) A characterization of all solutions to the four block general distance problem. SIAM J Control Optim 29(2):283–324

    Article  MathSciNet  MATH  Google Scholar 

  • Green M, Glover K, Limebeer DJN, Doyle JC (1990) A J-spectral factorization approach to \(\mathcal{H}_{\infty }\) control. SIAM J Control Optim 28(6):1350–1371

    Article  MathSciNet  MATH  Google Scholar 

  • Kailath T (1980) Linear systems. Prentice-Hall, Englewood Cliffs

    MATH  Google Scholar 

  • Kimura H (1989) Conjugation, interpolation and model-matching in H ∞ . Int J Control 49(1):269–307

    MATH  Google Scholar 

  • Kimura H (1997) Chain-scattering approach to H ∞ control. Systems & control. Birkhäuser, Boston

    Book  MATH  Google Scholar 

  • Kucera V (1975) Stability of discrete linear control systems. In: 6th IFAC world congress, Boston. Paper 44.1

    Google Scholar 

  • Qi X, Salapaka MV, Voulgaris PG, Khammash M (2004) Structured optimal and robust control with multiple criteria: a convex solution. IEEE Trans Autom Control 49(10):1623–1640

    Article  MathSciNet  Google Scholar 

  • Quadrat A (2006) On a generalization of the Youla–Kučera parametrization. Part II: the lattice approach to MIMO systems. Math Control Signals Syst 18(3):199–235

    Article  MathSciNet  MATH  Google Scholar 

  • Vidyasagar M (1985) Control system synthesis: a factorization approach. Signal processing, optimization and control. MIT, Cambridge

    Google Scholar 

  • Youla D, Jabr H, Bongiorno J (1976) Modern Wiener-Hopf design of optimal controllers – Part II: the multivariable case. IEEE Trans Autom Control 21(3):319–338

    Article  MathSciNet  MATH  Google Scholar 

  • Zhou K, Doyle JC, Glover K (1996) Robust and optimal control. Prentice Hall, Upper Saddle River

    MATH  Google Scholar 

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Authors and Affiliations

  1. University of Melbourne, 3010, Parkville, Australia

    Michael Cantoni

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  1. Michael Cantoni
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Correspondence to Michael Cantoni .

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Editors and Affiliations

  1. Electrical and Computer Engineering, Boston University, Boston, Massachusetts, USA

    John Baillieul

  2. Automation and Control Solutions, Honeywell, Golden Valley, Minnesota, USA

    Tariq Samad

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© 2014 Springer-Verlag London

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Cantoni, M. (2014). Optimal Control via Factorization and Model Matching. In: Baillieul, J., Samad, T. (eds) Encyclopedia of Systems and Control. Springer, London. https://doi.org/10.1007/978-1-4471-5102-9_206-1

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  • DOI: https://doi.org/10.1007/978-1-4471-5102-9_206-1

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  • Online ISBN: 978-1-4471-5102-9

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Chapter history

  1. Latest

    Optimal Control via Factorization and Model Matching
    Published:
    07 November 2019

    DOI: https://doi.org/10.1007/978-1-4471-5102-9_206-2

  2. Original

    Optimal Control via Factorization and Model Matching
    Published:
    02 October 2014

    DOI: https://doi.org/10.1007/978-1-4471-5102-9_206-1

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