Prof. Dr. Achim Ilchmann

Besuchsanschrift:
Weimarer Str. 25
Curiebau, Raum C 232
98693 Ilmenau

Postanschrift:
Postfach 10 05 65
98684 Ilmenau

E-Mail

+49 3677 69-3623

photophanie

Seit April 2022 emeritiert.

Forschung

Prof. Dr. Achim Ilchmann leitete von 2000 bis 2022, nach sechs Jahren in Exeter (UK), die Fachabteilung "Analysis und Systemtheorie" am Institut für Mathematik der Technischen Universität Ilmenau. Von 2003 bis 2020 organisierte er federführend den jährlichen Elgersburg Workshop zur Mathematischen Systemtheorie. Seine Forschungsgebiete sind die adaptive Regelung (nichtlinearer) Systeme, die Untersuchung struktureller Eigenschaften differentiell-algebraischer Systeme und die algebraische Behandlung zeitvarianter linearer Systeme. Insbesondere entwickelte er gemeinsam mit Professor Ryan (Bath, UK) das Konzept der funnel-Regelung. Regelmäßig hielt und hält er Seminare zu philosophischen Problemen der Mathematik, und er hat drei Bücher zur Rokoko-Architektur verfasst.

Publications

Latest publications

A. Ilchmann
Das Rokoko in der Herzogin Anna Amalia Bibliothek
Harrassowitz Verlag, Wiesbaden 2023
A. A. Mazzotti and A. Ilchmann
A method for recognising oval forms. The case study of a copperplate engraving of the Bibliotheca Wolfenbüttel 1705/23
Nexus Network Journal. Architecture and Mathematics 25(3): 685-712, 2023
A. Ilchmann, J.Kirchhoff
Relative genericity of controllability and stabilizability
Maths. of Control, Signals, and Systems 35:45-76, 2023
T. Berger, A. Ilchmann, St.Trenn
Quasi feedback forms for differential-algebraic systems
IMA J of Control 39(2) 533-563, 2022

T. Berger, D. Dennstädt, A. Ilchmann, K. Worthmann
Funnel MPC for nonlinear systems with relative degree one
SIAM J. on Control and Opt. 60(6):3358-3383, 2022

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Mandy Neuendorf

T. Berger, A. Ilchmann, St.Trenn
Quasi feedback forms for differential-algebraic systems,
to appear in IMA, 2021 [PDF]
A. Ilchmann, J.Kirchhoff
Differential-algebraic systems are generically controllable and stabilizable,
MCSS (2021) 33:359–377 [PDF]
A. Ilchmann, J. Witschel, K. Worthmann
Model predictive control for singular differential-algebraic equations
to appear in International Journal of Control, 2021 [PDF]
A. Ilchmann, L. Leben, J. Witschel, K. Worthmann
Optimal control of differential-algebraic equations from an ordinary differential equation perspective
Optimal Control, Applications and Methods, 40:351-366, 2019 [PDF]
A. Ilchmann, T. Reis
Outer transfer functions of differential-algebraic systems
ESAIM: Control, Opt. and Calculus of Variations 23(2) (2017) 391-425 [pdf]
Th. Berger, A. Ilchmann and T. Reis
Funnel control for nonlinear functional differential-algebraic systems
MTNS, Groningen pp. 46-53 (2014) [pdf]
Th. Berger, A. Ilchmann and T. Reis
Normal forms, high-gain and funnel control for linear differential-algebraic systems
pp. 127-164 in "Control and Optimization with Differential-Algebraic Constraints", Eds.: L. Biegler, S.L. Campbell, V. Mehrmann; SIAM, Philadelphia (2012) [pdf]
Th. Berger, A. Ilchmann and T. Reis
Zero dynamics and funnel control of linear differential-algebraic systems
Mathematics of Control, Signals and Systems 24(3) (2012) 219-263 [pdf]
Th. Berger and A. Ilchmann
On stability of time-varying linear differential-algebraic equations
Int. J. of Control 86(6) (2013) 1060–1076 [pdf]
Th. Berger and A. Ilchmann
On the standard canonical form of time-varying linear DAEs
Quarterly of Applied Mathematics 71 (2013) 69-87 [pdf]
Th. Berger, A. Ilchmann and St. Trenn
The quasi-Weierstraß form for regular matrix pencils
Linear Algebra and its Appl. 436 (2012) 4052-4069 [pdf]
A. Ilchmann and V. Mehrmann
A behavioural approach to time-varying linear systems, Part 2: Descriptor systems
SIAM J. of Control and Optimization 44 (2005) 1748-1765 [pdf]
A. Ilchmann and V. Mehrmann
A behavioural approach to time-varying linear systems, Part 1: General theory
SIAM J. of Control and Optimization 44 (2005) 1725-1747 [pdf]
A. Ilchmann
Algebraic theory of time-varying linear systems: a survey
in `Selected Plenaries, Milestones and Surveys' Eds.: P. Horacek, M. Simandl, P. Zitek; Prague, Czech Republic (2005) 312-318 [pdf]
M.d.R. De Pinho and A. Ilchmann
Weak maximum principle for optimal problems with mixed constraints
Nonlinear Analysis 48 (2002) 1179-1196 [pdf]
A. Ilchmann
Time-varying linear systems and invariants of system equivalence
Int. J. Control 42 (1985) 759-790 [pdf]
A. Ilchmann, I. Nürnberger and W. Schmale
Time-varying polynomial matrix systems
Int. J. Control 40 (1984) 329-362 [pdf]

Th. Berger, A. Ilchmann and F. Wirth
Zero dynamics and stabilization for analytic linear systems
Acta Applicandae Mathematicae 138(1) (2015) 17-57
B. D. O. Anderson, A. Ilchmann and F. R. Wirth
Stabilizability of linear time-varying systems
Systems and Control Letters 62(9) (2013) 747–755
Th. Berger and A. Ilchmann
Zero dynamics of time-varying linear systems
Preprint 10-05 (2010)
A. Ilchmann and Adrian T. Hill
Exponential stability of time-varying linear systems
IMA Journal of Numerical Analysis 31(3) (2011) 865-885
A. Ilchmann and P.H.A. Ngoc
On positivity and stability of linear time-varying Volterra equations
Positivity 13(4) (2009) 671-681
A. Ilchmann and M. Mueller
Time-varying linear systems: relative degree and normal form
IEEE Trans. Aut. Control 52 (2007) 840-851
H. Crauel, T. Damm and A. Ilchmann
Stabilization of linear systems by rotation
J. of Differential Equations 234 (2007) 412-438
L. H. Duc, A. Ilchmann, S. Siegmund and P. Taraba
On stability of linear time-varying second-order differential equations
Quarterly of Appl. Maths. 64 (2006) 137-151
A. Ilchmann and I.M.Y. Mareels
On stability radii of slowly time-varying systems
Advances in Mathematical Systems Theory, Eds.:F. Colonius, U. Helmke, D. Prätzel-Wolters, F.Wirth, Birkhäuser Verlag, Boston (2000) 55-75
A. Ilchmann and B.Werner
Characterization of the stability radius via bifurcation techniques
Applicable Analysis 52 (1994) 231-246
D. Hinrichsen, A. Ilchmann and A. J. Pritchard
A stability radius for time-varying linear systems
The Mathematics of Control Theory, Eds.: N. K. Nichols and D. H. Owens, Oxford University Press, Oxford (1992) 281-290
D. Hinrichsen , A. Ilchmann and A. J. Pritchard
Robustness of stability of time-varying linear systems
J. of Differential Equations 82 (1989) 219-250
A. Ilchmann and G. Kern
Stabilizability of systems with exponential dichotomy
Systems & Control Lett. 8 (1987) 211-220
A. Ilchmann, D. H. Owens and D. Prätzel-Wolters
Sufficient conditions for stability of linear time-varying systems
Systems & Control Lett. 9 (1987) 157-163

T. Berger, D. Dennstädt, A. Ilchmann, K. Worthmann
Funnel MPC for nonlinear systems with relative degree one
submitted to SICON, 2021 [PDF]
T. Berger, A. Ilchmann, E. P. Ryan
Funnel control of nonlinear systems
to appear in MCSS, 2021 [PDF]
Th. Berger, A. Ilchmann and T. Reis
Funnel control for nonlinear functional differential-algebraic systems
MTNS Groningen, The Netherlands (2014) 46--53
A. Ilchmann, T. Selig, C. Trunk
The Byrnes-Isidori form for infinite-dimensional systems
SIAM J. Control and Opt. 54(3):1504-1534, (2016)
Th. Berger, A. Ilchmann and T. Reis
Normal forms, high-gain and funnel control for linear differential-algebraic systems
pp. 127-164 in "Control and Optimization with Differential-Algebraic Constraints", Eds.: L. Biegler, S.L. Campbell, V. Mehrmann; SIAM, Philadelphia (2012)
Th. Berger, A. Ilchmann and T. Reis
Zero dynamics and funnel control of linear differential-algebraic systems
Mathematics of Control, Signals and Systems 24(3) (2012) 219-263
A. Ilchmann
Decentralized tracking of interconnected systems
in: Knut Hüper and Jochen Trumpf (eds.), Mathematical System Theory - Festschrift in Honor of Uwe Helmke on the Occasion of his Sixtieth Birthday, CreateSpace (2013) 229-245
C. Hackl, N. Hopfe, A. Ilchmann, M. Mueller and S. Trenn
Funnel Control for systems with relative degree two
SIAM J. of Control and Optimization 51(2):(2013) 965–995
A. Ilchmann, H. Logemann and E. P. Ryan
Tracking with prescribed transient performance for hysteretic systems
SIAM J. of Control and Optimization 48(7):(2010) 4731-4752
N. Hopfe, A. Ilchmann and E. P. Ryan
Funnel control with saturation: nonlinear SISO systems
IEEE Trans. Automatic Control 55(9):(2010) 2177-2182
N. Hopfe, A. Ilchmann and E. P. Ryan
Funnel control with saturation: linear MIMO systems
IEEE Trans. Automatic Control 55(2): (2010) 532-538
A. Ilchmann and M. Mueller
Robustness of funnel control in the gap metric
SIAM J. of Control and Optimization 47(5): (2009) 2724-2744
A. Ilchmann and E. P. Ryan
Performance funnels and tracking control
Int. J. of Control 82(10): (2009) 1828-1840
A. Ilchmann and H. Schuster
PI-funnel control for two mass systems
IEEE Trans. Automatic Control 54 (2009) 918-923
A. Ilchmann, E. P. Ryan and P. Townsend
Tracking with prescribed transient behaviour for nonlinear systems of known relative degree
SIAM J. of Control and Optimization 46 (2007) 210-230
A. Ilchmann and E. P. Ryan
Asymptotic tracking with prescribed transient behaviour for linear systems
Int. J. Control 79 (2006) 910-917
A. Ilchmann, E. P. Ryan and P. Townsend
Tracking control with prescribed transient behaviour for systems of known relative degree
Systems & Control Lett. 55 (2006) 396-406
A. Ilchmann, E.P. Ryan and S. Trenn
Tracking control: performance funnels and prescribed transient behaviour
Systems & Control Lett. 54 (2005) 655-670
A. Ilchmann and S. Trenn
Input constrained funnel control with applications to chemical reactor models
Systems & Control Lett. 53 (2004) 361-375
A. Ilchmann, E.P. Ryan and C.J. Sangwin
Tracking with prescribed transient behaviour
ESAIM: Control, Optimisation and Calculus of Variations 7 (2002) 471-493

M. French, A. Ilchmann and E. P. Ryan
Robustness in the graph topology of a common adaptive controller
SIAM J. of Control and Optimization 45 (2006) 1736-1757
A. Ilchmann, S. Townley and M. Thuto
Adaptive sampled-data tracking for input constrained exothermic chemical reaction models
Systems & Control Lett. 54 (2005) 1149-1161
A. Ilchmann and E.P. Ryan
On tracking and disturbance rejection by adaptive control
Systems & Control Lett. 52 (2004) 137-147
A. Ilchmann and E.P. Ryan
On gain adaptation in adaptive control
IEEE Trans. Aut. Control 48 (2003) 895-899
A. Ilchmann and A. Isidori
Adaptive dynamic output feedback stabilisation of nonlinear systems
Asian Journal of Control 4 (2002) 1-9
P. Georgieva, A. Ilchmann and M.-F. Weirig
Modelling and adaptive control of aerobic continuous stirred tank reactors
European J. of Control 7 (2001) 476-491
I.M.Y.Mareels, S. Van Gils, J.W. Polderman and A. Ilchmann
Asymptotic dynamics in adaptive gain control
Advances in Control, Highlights of ECC '99, Ed.: P.M. Frank, Springer-Verlag, London (1999) 29-63
A. Ilchmann and S. Townley
Adaptive sampling control of high-gain stabilizable systems
IEEE Trans. Autom. Control 44 (1999) 1961-1966
A. Ilchmann
Universal adaptive control of nonlinear systems
Dynamics and Control 7 (1997) 199-213
A. Ilchmann
Adaptive stabilization
EncyclopaediaofMathematics, First Supplement, Managing Ed.:M.Hazewinkel,KluwerAcademic Publishers, Dordrecht, Boston (1997) 28-29 [pdf]
H. Logemann and A. Ilchmann
An adaptive servomechanism for a class of infinite-dimensional systems
SIAM J. on Control and Opt. 32 (1994) 917-936
A. Ilchmann
Adaptive controllers and root-loci of minimum phase systems
Dynamics and Control 4 (1994) 203-226
A. Ilchmann and S. Townley
Simple adaptive stabilization of high-gain stabilizable systems
Systems & Control Lett. 20 (1993) 189-198
A. Ilchmann and D.H. Owens
Adaptive exponential tracking for nonlinearly perturbed minimum phase systems
Control-Theory and Advanced Technology 9 (1993) 353-379
A. Ilchmann and H. Logemann
High-gain adaptive tabilization of multivariable linear systems - revisited
Systems & Control Lett. 18 (1992) 355-364
A. Ilchmann and D. H. Owens
Exponential stabilization using non-differential gain adaptation
IMA J. of Math. Control and Inf. 7 (1991) 339-349
A. Ilchmann and D. H. Owens
Threshold switching functions in high-gain adaptive control
IMA J. of Math. Control and Inf. 8 (1991) 409-429
A. Ilchmann
Robust adaptive stabilization of discrete first order systems
Automatica 27 (1991) 829-835
A. Ilchmann and D. H. Owens
Adaptive stabilization with exponential decay
Systems & Control Lett. 14 (1990) 437-443
D. Prätzel-Wolters, D. H. Owens and A. Ilchmann
Robust adaptive stabilization by high gain and switching
Int. J. Control 49 (1989) 1861-1868
A. Ilchmann, D. H. Owens and D. Prätzel-Wolters
High gain robust adaptive controllers for multivariable systems
Systems & Control Lett. 8 (1987) 397-404
D. H. Owens, D. Prätzel-Wolters and A. Ilchmann
Positive real structure and high gain adaptive stabilization
IMA J. of Math. Control and Inf. 4 (1987) 167-181

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Prof. Dr. Achim Ilchmann