Abstract
Structured output feedback controller synthesis is an exciting recent concept in modern control design, which bridges between theory and practice in so far as it allows for the first time to apply sophisticated mathematical design paradigms like H∞- or H2-control within control architectures preferred by practitioners. The new approach to structured H∞-control, developed by the authors during the past decade, is rooted in a change of paradigm in the synthesis algorithms. Structured design is no longer based on solving algebraic Riccati equations or matrix inequalities. Instead, optimization-based design techniques are required. In this essay we indicate why structured controller synthesis is central in modern control engineering. We explain why non-smooth optimization techniques are needed to compute structured control laws, and we point to software tools which enable practitioners to use these new tools in high-technology applications.
This is a preview of subscription content, log in via an institution.
Bibliography
Apkarian P (2013) Tuning controllers against multiple design requirements. In: American control conference (ACC), pp 3888–3893
Apkarian P, Noll D (2006a) Controller design via nonsmooth multi-directional search. SIAM J Control Optim 44(6):1923–1949
Apkarian P, Noll D (2006b) Nonsmooth H∞ synthesis. IEEE Trans Aut Control 51(1):71–86
Apkarian P, Noll D (2006c) Nonsmooth optimization for multidisk H∞ synthesis. Eur J Control 12(3):229–244
Apkarian P, Noll D (2007) Nonsmooth optimization for multiband frequency domain control design. Automatica 43(4):724–731
Apkarian P, Noll D (2018) Structured H∞-control of infinite dimensional systems. Int J Robust Nonlinear Control 28(9):3212–3238
Apkarian P, Noll D (2019) Boundary control of partial differential equations using frequency domain optimization techniques. arXiv:1905.06786v1, pp 1–22
Apkarian P, Noll D, Thevenet JB, Tuan HD (2003) A spectral quadratic-SDP method with applications to fixed-order H2 and H∞ synthesis. Eur J Control 10(6):527–538
Apkarian P, Noll D, Rondepierre A (2007) Mixed H2∕H∞ control via nonsmooth optimization. In: Proceedings of the 46th IEEE conference on decision and control, New Orleans, pp 4110–4115
Apkarian P, Noll D, Prot O (2008) A trust region spectral bundle method for nonconvex eigenvalue optimization. SIAM J Optim 19(1):281–306
Apkarian P, Dao MN, Noll D (2015a) Parametric robust structured control design. IEEE Trans Auto Control 60(7):1857–1869
Apkarian P, Noll D, Ravanbod L (2015b) Computing the structured distance to instability. In: SIAM conference on control and its applications, pp 423–430. https://doi.org/10.1137/1.9781611974072.58
Apkarian P, Noll D, Ravanbod L (2016) Nonsmooth bundle trust-region algorithm with applications to robust stability. Set-Valued Var Anal 24(1):115–148
Apkarian P, Noll D, Ravanbod L (2018) Non-smooth optimization for robust control of infinite-dimensional systems. Set-Valued Var Anal 26(2):405–429
Benner P, Sima V, Voigt M (2012) L∞-norm computation for continuous-time descriptor systems using structured matrix pencils. IEEE Trans Aut Control 57(1):233–238
Boyd S, Balakrishnan V, Kabamba P (1989) A bisection method for computing the H∞ norm of a transfer matrix and related problems. Math Control Signals Syst 2(3):207–219
Bresch-Pietri D, Krstic M (2014) Output-feedback adaptive control of a wave PDE with boundary anti-damping. Automatica 50(5):1407–1415
Burke J, Lewis A, Overton M (2005) A robust gradient sampling algorithm for nonsmooth, nonconvex optimization. SIAM J Optim 15:751–779
DeQueiroz M, Rahn CD (2002) Boundary control of vibrations and noise in distributed parameter systems: an overview. Mech Syst Signal Process 16(1):19–38
Falcoz A, Pittet C, Bennani S, Guignard A, Bayart C, Frapard B (2015) Systematic design methods of robust and structured controllers for satellites. Application to the refinement of Rosetta’s orbit controller. CEAS Space J 7:319–334. https://doi.org/ 10.1007/ s12567- 015- 0099-8
Fares B, Apkarian P, Noll D (2001) An augmented Lagrangian method for a class of LMI-constrained problems in robust control theory. Int J Control 74(4):348–360
Fares B, Noll D, Apkarian P (2002) Robust control via sequential semidefinite programming. SIAM J Control Optim 40(6):1791–1820
Fridman E (2014) Introduction to time-delay systems. Systems and control, foundations and applications. Birkhuser, Basel
Gahinet P, Apkarian P (2011) Structured H∞ synthesis in MATLAB. In: Proceedings of IFAC world congress, Milan, pp 1435–1440
Ganet-Schoeller M, Desmariaux J, Combier C (2017) Structured control for future european launchers. AeroSpaceLab 13:2–10
Kocvara M, Stingl M (2003) A code for convex nonlinear and semidefinite programming. Optim Methods Softw 18(3):317–333
Kolda TG, Lewis RM, Torczon V (2003) Optimization by direct search: new perspectives on some classical and modern methods. SIAM Rev 45(3):385–482
Lemaréchal C (1975) An extension of Davidson’s methods to nondifferentiable problems. In: Balinski ML, Wolfe P (eds) Nondifferentiable optimization. Mathematical programming study, Springer, Berlin, Heidelberg, vol 3, pp 95–109
Lemaréchal C, Oustry F (2000) Nonsmooth algorithms to solve semidefinite programs. In: El Ghaoui L, Niculescu S-I (ed) SIAM advances in linear matrix inequality methods in control Series, SIAM, pp 57–77
Lieslehto J (2001) PID controller tuning using evolutionary programming. In: American control conference, vol 4, pp 2828–2833
Moelja AA, Meinsma G (2003) Parametrization of stabilizing controllers for systems with multiple i/o delays. IFAC Proc Vol 36(19):351–356. 4th IFAC workshop on time delay systems (TDS 2003), Rocquencourt, 8–10 Sept 2003
Noll D (2007) Local convergence of an augmented Lagrangian method for matrix inequality constrained programming. Optim Methods Softw 22(5):777–802
Noll D, Apkarian P (2005) Spectral bundle methods for nonconvex maximum eigenvalue functions: first-order methods. Math Prog Ser B 104(2):701–727
Noll D, Torki M, Apkarian P (2004) Partially augmented Lagrangian method for matrix inequality constraints. SIAM J Optim 15(1):161–184
Noll D, Prot O, Rondepierre A (2008) A proximity control algorithm to minimize nonsmooth and nonconvex functions. Pac J Optim 4(3):571–604
Noll D, Prot O, Apkarian P (2009) A proximity control algorithm to minimize nonsmooth and nonconvex semi-infinite maximum eigenvalue functions. J Convex Anal 16(3 & 4):641–666
Oi A, Nakazawa C, Matsui T, Fujiwara H, Matsumoto K, Nishida H, Ando J, Kawaura M (2008) Development of PSO-based PID tuning method. In: International conference on control, automation and systems, pp 1917–1920
Ravanbod L, Noll D, Apkarian P (2017) Branch and bound algorithm with applications to robust stability. J Glob Optim 67(3):553–579
Robust Control Toolbox 42 (2012) The MathWorks Inc. Natick, MA
Saldivar B, Mondié S, Loiseau J, Rasvan V (2013) Suppressing axial-torsional vibrations in drillstrings. J Control Eng Appl Inf, SRAIT 14:3–10
Shamma JF, Athans M (1990) Analysis of gain scheduled control for nonlinear plants. IEEE Trans Aut Control 35(8):898–907
Smyshlyaev A, Krstic M (2009) Boundary control of an anti-stable wave equation with anti-damping on the uncontrolled boundary. Syst Control Lett 58: 617–623
Stein G, Doyle J (1991) Beyond singular values and loopshapes. AIAA J Guid Control 14:5–16
Zhou K, Doyle JC, Glover K (1996) Robust and optimal control. Prentice Hall, Upper Saddle River
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Section Editor information
Rights and permissions
Copyright information
© 2019 Springer-Verlag London Ltd., part of Springer Nature
About this entry
Cite this entry
Apkarian, P., Noll, D. (2019). Optimization-Based Control Design Techniques and Tools. In: Baillieul, J., Samad, T. (eds) Encyclopedia of Systems and Control. Springer, London. https://doi.org/10.1007/978-1-4471-5102-9_144-2
Download citation
DOI: https://doi.org/10.1007/978-1-4471-5102-9_144-2
Published:
Publisher Name: Springer, London
Print ISBN: 978-1-4471-5102-9
Online ISBN: 978-1-4471-5102-9
eBook Packages: Springer Reference EngineeringReference Module Computer Science and Engineering
Publish with us
Chapter history
-
Latest
Optimization-Based Control Design Techniques and Tools- Published:
- 09 December 2019
DOI: https://doi.org/10.1007/978-1-4471-5102-9_144-2
-
Original
Optimization-Based Control Design Techniques and Tools- Published:
- 22 March 2014
DOI: https://doi.org/10.1007/978-1-4471-5102-9_144-1