Nonsmooth programming techniques for controller design
- controller structure/architecture is important
- plant has large size
- multiple plants/specifications should be accounted for
- classical linear methods are conservative or inappropriate
In the past decade, we have developed specialized nonsmooth optimization techniques for control system design and tuning. These techniques aim at solving challenging control problems which often are classified as NP hard. In essence, the proposed techniques can only provide local solutions of these difficult synthesis problems. This might appear restrictive but turns out very satisfactory according to extensive testing as well as in numerous industrial applications in the aerospace sector and beyond. Nonsmooth techniques are typically very fast compared to LMI based methods. Moreover, they can deal with problems where LMIs, Riccati and the like are non longer operational. The case of practical arbitrary structured controllers is what we have in mind. These new tools hinfstruct and systune have capability to directly handle problems as posed in practice to engineers. This includes controller complexity, multiple performance and robustness constraints together with family of certain or uncertain models.
In design problems where
Potentials and flexibility of these tools are discussed in the papers below. Refer to the software section for details on related computational techniques.
2025
P. Apkarian and D. NollMinimizing transients via the Kreiss system norm
Journal of the Franklin Institute, Elsevier, 2025.
2021
P. Apkarian and D. NollMixed L1/ H∞-synthesis for L∞-stability
International Journal of Robust and Nonlinear Control, 2021.
P. Apkarian and D. NollOptimization-based control design techniques and tools
Encyclopedia of Systems and Control 2021. Baillieul, John; Samad, Tariq (Eds.). Springer Nature, Switzerland, 2021.
2020
P. Apkarian and D. NollOptimizing the Kreiss constant
SIAM J. Control and Optimization, 58(6):2020,3342-3362.
P. Apkarian and D. NollBoundary feedback control of an anti-stable wave equation
IMA Journal of Mathematical Control and Information, 37(2020),1367-1399.
P. Apkarian and D. NollBoundary control of partial differential equations using frequency domain optimization techniques
Systems and Control Letters, vol 135, 2020, 1045-1077.
2019
P. Apkarian and D. NollOptimization-based control design techniques and tools
Encyclopedia of Systems and Control 2019. Baillieul, John; Samad, Tariq (Eds.).
2018
P. Apkarian and D. NollStructured H∞ control of infinite-dimensional systems
Int. Journal of Robust & Nonlinear Control, vol. 28, no. 9, pp 3212-3238, 2018
P. Apkarian, D. Noll and L. RavanbodNon-smooth optimization for robust control of infinite-dimensional systems
Set-value and variational analysis, vol. 26, no. 2, pp. 406-429, 2018
Y. Shi, H.D. Tuan, P. Apkarian and A. SavkineGlobal optimal power flow over large scale transmission networks
Systems & Control Letters, pp 16-21, 2018
R.S.S. de Aguiar, P. Apkarian, and D. NollStructured Robust Control Against Mixed Uncertainty
IEEE Trans. on Control Systems Technology, vol. 26, no. 5, pp. 1771-1781, 2018
2017
E. Chambon, L. Burlion, and P. ApkarianDetermination de matrice semblable Metzler par optimisation non lisse
Journal Européen des Systèmes Automatisés, Vol.50(1-2), pp.75-94, 2017
Y. Shi, H.D. Tuan, and P. ApkarianNonconvex Spectral Optimization Algorithms for Reduced-Order H∞ LPV-LFT controllers
Int. Journal of Robust & Nonlinear Control, 27:4421-4442, 2017
L. Ravanbod, D. Noll and P. ApkarianBranch and bound algorithm with applications to robust stability
Journal of Global Optimization, vol. 67, no. 3, pp. 553 - 579, 2017
L. Hewing, S. Leonhardt, P. Apkarian and B. MisgeldH∞ optimal controller design with closed-loop positive real constraints
Journal of Dynamic Systems, Measurement, and Control, 139(9), 094502 / 1 - 8
P. Apkarian and D. NollThe H∞ problem is solved
Journal Aerospace Lab, issue 13, september 2017.
DOI: 10.12762/2017.AL13-01
2016
P. Apkarian and D. NollWorst-case stability and performance with mixed parametric and dynamic uncertainties
International Journal of Robust and Nonlinear Control, 27(8), 1284-1301
P. Apkarian, D. Noll, and L. RavanbodNonsmooth bundle trust-region algorithm with applications to robust stability
Set-Valued and Variational Analysis, 24(1), pp 115-148, 2016.
E. Chambon, L. Burlion, and P. ApkarianTime-response shaping using Output to Input Saturation Transformation
Submitted, 2016
E. Chambon, L. Burlion, and P. ApkarianOverview of LTI interval observer design: towards a non-smooth optimisation-based approach
IET Control Theory & Applications , 10(11), pp. 1258-1268, 2016
2015
L. Ravanbod, D. Noll, and P. ApkarianBranch and bound algorithm for the robustness analysis of uncertain systems
Proc. 16th IFAC Workshop on Control Applications of Optimization, 2015.
P. Apkarian, Minh Ngoc Dao, and D. NollParametric robust structured control design
IEEE TAC, vol. 60(7), pp. 1857 - 1869, 2015
P. Apkarian, D. Noll, L. RavanbodComputing the structured distance to instability
SIAM Conference on Control and Its Applications (CT15), 2015
Minh Ngoc Dao, D. Noll, P. ApkarianRobust eigenstructure clustering by non-smooth optimisation
International Journal of Control, vol. 88(8), pp. 1441-1455, 2015
2014
P. Apkarian, P. Gahinet, P. BuhrMulti-model, multi-objective tuning of fixed-structure controllers
European Control Conference (ECC), 2014 , pp.856,861, 24-27 June 2014
P. Apkarian, D. NollOptimization-Based Control Design Techniques and Tools
Encyclopedia of Systems and Control, Springer London, 2014 , pp. 1-12, 2014
2013
P. Gahinet, P. ApkarianAutomated tuning of gain-scheduled control systems
Conference on Decision and Control, pp. 2740-2745, 10-13 Dec. 2013
P. ApkarianTuning controllers against multiple design requirements
American Control Conference (ACC), 2013, pp. 3888-3893, 17-19 June 2013
Jingwen Yang; F. Hamelin,P. Apkarian,D. SauterMixed H-/ H∞ fault detection observer design for multi model systems via nonsmooth optimization approach
Conference on Control and Fault-Tolerant Systems (SysTol), pp.164,171, 9-11 Oct. 2013
2012
P. Gahinet, P. ApkarianFrequency-domain tuning of fixed-structure control systems
2012 UKACC International Conference on Control, pp.178-183, 3-5 Sept. 2012
2011
A. M. Simoes, P. Apkarian, D. Alazard, D.NollLateral flight control design for a highly flexible aircraft using nonsmooth optimization
Aerospace Science and Technology, Volume 15, Issue 4, June 2011, pp. 314-322
P. ApkarianNonsmooth μ synthesis
International Journal of Robust and Nonlinear Control, vol. 21(8), pp. 1493-1508, 2011.
P. Apkarian, L. Ravanbod-Hosseini, D. NollTime domain constrained H-∞-synthesis
International Journal of Robust and Nonlinear Control, vol. 21, no. 2, pp. 197-217, 2011.
J-M. Biannic and P. ApkarianAnti-windup design via nonsmooth multi-objective H∞ optimization
Submitted to American Control Conference, San Francisco 2011.
2010
2009
A. M. Simoes,Synthèse de compensateurs structurés par l' optimisation non lisse
PhD. Thesis, ONERA & ISAE, 24 juin 2009.
A. Simoes, P. Apkarian, D. NollNonsmooth multi-objective synthesis with applications
Control Engineering Practice, vol. 17, no. 11, pp. 1338-1348, 2009.
A. M. Simoes, Diego C. Savelli, P. C. Pellanda, N. Martins and P. ApkarianRobust Design of a TCSC Oscillation Damping Controller in a Weak 500-kV Interconnection
Considering Multiple Power Flow Scenarios and External Disturbances
IEEE Trans. on Power Systems, vol. 24, no. 1, pp.226-236, 2009.
P. Apkarian, D. Noll and A. SimoesTime-domain control design: a nonsmooth approach
IEEE Trans. on Control Systems Technology, vol. 17, no. 6, pp. 1439-1445, 2009.
P. Apkarian, D. Noll and O. ProtA proximity control algorithm to minimize nonsmooth and nonconvex
semi-infinite maximum eigenvalue functions
Journal of Convex Analysis, vol. 16, no. 3 & 4, pp. 641-666, 2009.
2008
N. V. Q. Hung, H. D. Tuan, T. Narikiyo and P. ApkarianA Lyapunov variable-free KYP lemma for SISO continuous systems
IEEE Trans. on Automatic Control, vol. 53, no. 11, pp. 2669-2673, 2009.
N. V. Q. Hung, H. D. Tuan, T. Narikiyo and P. ApkarianAdaptive control for nonlinearly parameterized uncertainties in robot manipulators
IEEE Trans. on Control Systems Technology, vol.16, no. 3, pp. 458-468, 2008.
A. Simoes, P. Apkarian and D. NollMulti-scenario time-domain control design using a nonsmooth approach
VIII Int. Conference, Identification & Control Problems, SICPRO 2009.
V. Bompart, P. Apkarian and D.
NollControl design in the time- and frequency domain using nonsmooth techniques
Syst. and Control Letters, vol. 57, 3, pp. 271-282, 2008.
A. Simoes, P. Apkarian and D.
NollA nonsmooth progress function algorithm for frequency shaping control design
IET Control Theory & Applications, vol. 2, 4, pp. 323-336, April, 2008.
A. Simoes, P. Apkarian and D.
NollNonsmooth frequency shaping control design with an application
IFAC World Congress, Seoul, Korea, 2008.
P. Apkarian, D. Noll and O. ProtA Trust region spectral bundle method for nonconvex eigenvalue optimization
SIAM J. on Optimization, vol. 19,1, pp. 281-306, 2008.
P. Apkarian, D. Noll and A. RondepierreMixed H2/H∞ control via nonsmooth optimization
SIAM J. on Control and Optimization, 47(3), pp. 1516-1546, 2008.
2007
P. Apkarian, V. Bompart and D. NollNonsmooth optimization techniques for structured controller design
Int. Conference nonconvex programming: Local and Global Approaches
Theory, Algorithms and Applications, Rouen, France, Decembre 2007.
talk
V. Bompart,Optimisation non lisse pour la commande des systemes de l'Aeronautique
PhD. Thesis, ONERA & Institut de Math\351matiques, UPS, November 2007.
V. Bompart, P. Apkarian and D.
NollSecond-order nonsmooth optimization for H∞ synthesis
Numerische Mathematik, vol. 107, no. 3, pp. 433-454, 2007.
V. Bompart, P. Apkarian and D.
NollNonsmooth technique for stabilizing linear systems
ACC 2007
O. Prot, P. Apkarian and D. NollA nonsmooth IQC method for robust synthesis
CDC 2007.
P. Apkarian, D. Noll and A.
RondepierreNonsmooth optimization algorithm for mixed H2/H∞ synthesis
CDC 2007
P. Apkarian and D. Noll Nonsmooth Optimization for Multiband Frequency Domain Control Design.
Automatica Journal, vol. 43, no. 4, pp. 724-731, 2007.
P. Apkarian, V. Bompart and D.
NollNonsmooth Structured Control Design with Application to PID Loop-Shaping of a Process
International Journal of Robust and Nonlinear Control, vol. 17, no. 14, pp. 1320-1342, 2007.
2006
P. C. Pellanda, P. Apkarian and N.
MartinsTuning Structurally Constrained Stabilizers for Large Power Systems via Nonsmooth Multi-Directional Search
XII Latin-American Congress on Automatic Control, Oct.3-6, 2006.
P. Apkarian and D. Noll IQC analysis and synthesis via nonsmooth optimization
Systems and Control Letters, vol. 55, no. 12, pp. 971-981, 2006.
V. Bompart, D. Noll and P. ApkarianSecond-order nonsmooth optimization for H∞ synthesis
5th IFAC Symposium on Robust Control Design, Toulouse, 2006.
P. Apkarian and D. Noll Nonsmooth Optimization for Multidisk H∞ Synthesis
European Journal of Control, vol. 12, no. 3, pp. 229-244, 2006.
P. Apkarian and D. Noll Nonsmooth H∞ synthesis
IEEE TAC. vol. 51, no. 1, pp. 71-86, Jan. 2006.
P. Apkarian and D. Noll Controller design via nonsmooth multi-directional search
2nd IFAC Symposium on System, Structure and Control, Oaxaca, Mexico, 2004.
SIAM J. on Control and Optimization, vol. 44, 6, pp. 1923-1949 2006.
2005
P. Apkarian D. Noll and P. PellandaNonsmooth H∞ synthesis (paper)
Nonsmooth H∞ synthesis (slides)
WCSMO6, 6th World Congress on Structural and Multidisciplinary Optimization, Rio de Janeiro, Brazil, May 2005.
J. B. Thevenet , P. Apkarian and D. NollReduced-order output feedback control design with specSDP, a code for linear / nonlinear SDP problems.
ICCA05, Budapest, 2005
D. Noll and P. ApkarianSpectral bundle methods for non-convex maximum eigenvalue functions. Part 2: second-order methods
Maths. Prog. Series B., vol. 104, no. 2, pp. 729-747, Nov. 2005.
D. Noll and P. Apkarian
Spectral
bundle methods for non-convex
maximum eigenvalue functions. Part 1: first-order methods
Maths. Prog. Series B., vol. 104, no. 2, pp. 701-727, Nov. 2005.
2004
J. B. Thevenet , D. Noll and P. ApkarianNonlinear spectral SDP method for BMI-constrained problems: Applications to control design.
Informatics in Control, Automation and Robotics, Kluwer Academic Publishers, 2004
J.B.
Thevenet and D. Noll and P. ApkarianNonlinear spectral SDP method for BMI constrained problems: Application to control design
ICINCO proceedings, 1:237-248, Portugal, 2004.
P. Apkarian and D. Noll and J.B. Thevenet
H.D. Tuan
A spectral quadratic-SDP method with applications to fixed-order H2 and H∞ synthesis
Asian Control Conference, Melbourne, Australia, 2004.
European J. of Control, vol. 10(6), pp. 527-538, 2004.
D. Noll and M. Torki and P. Apkarian
Partially Augmented Lagrangian Method for Matrix Inequality Constraints
SIAM Journal on Optimization, vol. 15, 1, pp. 161-184, 2004.
...2003
P. Apkarian and D. Noll and H.D. Tuan
Fixed-Order H∞ Control Design via a Partially Augmented Lagrangian Method
International Journal of Robust and Nonlinear Control., vol. 13, no. 12, pp. 1137-1148, 2003.
B. Fares and D. Noll and P. Apkarian
Robust
Control via Sequential Semidefinite Programming
SIAM Journal on Control and Optimization, vol. 40, no. 6, pp.
1791-1820,
2002.
B. Fares, P. Apkarian, D. Noll
An
Augmented Lagrangian Method for a Class of LMI-Constrained Problems in
Robust Control Theory
International Journal of Control, vol.74, no.4, pp.348-360, 2001.
B. Fares, P. Apkarian, D. Noll
An
Augmented
Lagrangian Method for a Class of LMI-Constrained Problems in Robust
Control
Theory
American Control Conference, pp. 3702-3705, 2000.
