Worst-case control-relevant identification

Abstract This paper introduces the reader to several recent developments in worst-case identification motivated by various issues of modelling of systems from data for the purpose of robust control design. Many aspects of identification in H ∞ and l 1 are covered including algorithms, convergence and divergence results, worst-case estimation of uncertainty models, model validation and control relevancy issues.

[1]  I. P. Natanson Constructive function theory , 1964 .

[2]  D.J.N. Limebeer,et al.  System identification for H/sup infinity / control , 1992, [1992] Proceedings of the 31st IEEE Conference on Decision and Control.

[3]  R. Tempo,et al.  Optimal algorithms theory for robust estimation and prediction , 1985 .

[4]  E. Fogel System identification via membership set constraints with energy constrained noise , 1979 .

[5]  P. Khargonekar,et al.  Linear and nonlinear algorithms for identification in H∞ with error bounds , 1991, 1991 American Control Conference.

[6]  Arthur J. Helmicki,et al.  Identification in H ∞ : linear algorithms , 1990 .

[7]  C. Jacobson,et al.  Worst case system identification in l 1 ne-equation> 1 : optimal algorithms and error bounds , 1992 .

[8]  G. Zames,et al.  Uncertainty Principles and Identification n-Widths for LTI and Slowly Varying Systems , 1992, 1992 American Control Conference.

[9]  Jonathan R. Partington,et al.  On bounded‐error identification of feedback systems , 1995 .

[10]  Guoxiang Gu,et al.  Identification in ℋ∞ with nonuniformly spaced frequency response measurements , 1994 .

[11]  Ruud J. P. Schrama Accurate identification for control: the necessity of an iterative scheme , 1992 .

[12]  Roy S. Smith Model validation and parameter identification for systems in H∞ and l1 , 1992, 1992 American Control Conference.

[13]  C. Jacobson,et al.  Worst Case System Identification in l1: Optimal Algorithms and Error Bounds , 1991, 1991 American Control Conference.

[14]  Ruud J.P. Schrama,et al.  An iterative scheme for identification and control design based on coprime factorizations , 1992, 1992 American Control Conference.

[15]  Jonathan R. Partington,et al.  Analysis of linear methods for robust identification in ℓ1 , 1995, Autom..

[16]  J. Tsitsiklis,et al.  The sample complexity of worst-case identification of FIR linear systems , 1993, Proceedings of 32nd IEEE Conference on Decision and Control.

[17]  Antonio Vicino,et al.  Information-Based Complexity and Nonparametric Worst-Case System Identification , 1993, J. Complex..

[18]  Er-Wei Bai,et al.  A Linear Robustly Convergent Interpolatory Algorithm For System Identification , 1992, 1992 American Control Conference.

[19]  K. Poolla,et al.  On the time complexity of worst-case system identification , 1994, IEEE Trans. Autom. Control..

[20]  Graham C. Goodwin,et al.  Estimation of Model Quality , 1994 .

[21]  K. Poolla,et al.  A time-domain approach to model validation , 1994, IEEE Trans. Autom. Control..

[22]  Pramod Khargonekar,et al.  A Time-Domain Approach to Model Validation , 1992, 1992 American Control Conference.

[23]  J. Partington Robust identification in H , 1992 .

[24]  N. Young An Introduction to Hilbert Space , 1988 .

[25]  Mario Milanese,et al.  Worst-Case l1 Identification , 1996 .

[26]  J. Partington Robust identification and interpolation in H , 1991 .

[27]  George Zames Adaptive feedback, identification and complexity: an overview , 1993, Proceedings of 32nd IEEE Conference on Decision and Control.

[28]  Bruce A. Francis,et al.  Feedback Control Theory , 1992 .

[29]  Arthur J. Helmicki,et al.  Least squares methods for H∞ control-oriented system identification , 1993, IEEE Trans. Autom. Control..

[30]  Jie Chen,et al.  The Caratheodory-Fejer problem and H∞/l1 identification: a time domain approach , 1995, IEEE Trans. Autom. Control..

[31]  P M M Akil WORST-CASE INPUT-OUTPUT IDENTIFICATION , 1992 .

[32]  Lennart Ljung,et al.  Information contents in identification data from closed-loop operation , 1993, Proceedings of 32nd IEEE Conference on Decision and Control.

[33]  Kameshwar Poolla,et al.  Sample Complexity for Worst-Case System Identification Problems , 1993, 1993 American Control Conference.

[34]  T. Georgiou,et al.  Optimal robustness in the gap metric , 1990 .

[35]  H. Woxniakowski Information-Based Complexity , 1988 .

[36]  Lennart Ljung System Identification in a MIC Perspective , 1994 .

[37]  Sandor M. Veres,et al.  Identification by parameter bounds in adaptive control , 1995 .

[38]  A. Helmicki,et al.  Identification in H∞: a robustly convergent, nonlinear algorithm , 1990, 1990 American Control Conference.

[39]  B. Francis,et al.  A Course in H Control Theory , 1987 .

[40]  Jonathan R. Partington,et al.  Robust identification from partial frequency data , 1994, Proceedings of 1994 33rd IEEE Conference on Decision and Control.

[41]  J. Leblond,et al.  Identification for control: closing the loop gives more accurate controllers , 1994, Proceedings of 1994 33rd IEEE Conference on Decision and Control.

[42]  Roy S. Smith,et al.  Towards a Methodology for Robust Parameter Identification , 1990, 1990 American Control Conference.

[43]  Paul M. J. Van den Hof,et al.  Identification and control - Closed-loop issues , 1995, Autom..

[44]  G. Lorentz Approximation of Functions , 1966 .

[45]  Jie Chen,et al.  Worst Case Identification of Continuous time Systems via Interpolation , 1993 .

[46]  P. Mäkilä Robust identification and Galois sequences , 1991 .

[47]  Paul M.J. Van den Hof,et al.  Frequency domain curve fitting with maximum amplitude criterion and guaranteed stability , 1994 .

[48]  Jonathan R. Partington,et al.  Robust approximate modelling of stable linear systems , 1993 .

[49]  Håkan Hjalmarsson Aspects on Incomplete Modeling in System Identification , 1993 .

[50]  Okko H. Bosgra,et al.  Modelling Linear Dynamical Systems through Generalized Orthonormal Basis Functions , 1993 .

[51]  Hidenori Kimura,et al.  Time domain identification for robust control , 1993 .

[52]  Sandor M. Veres,et al.  Predictive self-tuning control by parameter bounding and worst-case design , 1993, Autom..

[53]  P. Khargonekar,et al.  Robust convergence of two-stage nonlinear algorithms for identification in H ∞ , 1992 .

[54]  Carl N. Nett,et al.  Control oriented system identification: a worst-case/deterministic approach in H/sub infinity / , 1991 .

[55]  Antonio Vicino,et al.  Strongly optimal algorithms and optimal information in estimation problems , 1986, J. Complex..

[56]  Yakov Z. Tsypkin,et al.  Robust identification , 1980, Autom..

[57]  John Doyle,et al.  Model validation: a connection between robust control and identification , 1992 .

[58]  P. Mäkilä,et al.  Worst-case analysis of the least-squares method and related identification methods , 1995 .

[59]  Guoxiang Gu,et al.  Identification in H∞ with nonuniformly spaced frequency response measurements , 1992, 1992 American Control Conference.

[60]  Antonio Vicino,et al.  Optimal estimation theory for dynamic systems with set membership uncertainty: An overview , 1991, Autom..

[61]  J. Partington An introduction to Hankel operators , 1988 .

[62]  Mario Milanese,et al.  H∞ identification and model structure selection , 1996 .

[63]  R.J.P. Schrama,et al.  Approximate Identification and Control Design: With application to a mechanical system , 1992 .

[64]  A. Helmicki,et al.  H∞ identification of stable LSI systems: a scheme with direct application to controller design , 1989, 1989 American Control Conference.

[65]  Robert L. Kosut System Identification for Robust Control Design. , 1996 .

[66]  R. G. Hakvoort,et al.  System identification for rubust process control. Nominal models and error bounds , 1994 .

[67]  Mario Milanese,et al.  Properties of Least Squares Estimates in Set Membership Identification , 1994 .

[68]  Yeung Yam,et al.  A criterion for joint optimization of identification and robust control , 1992 .

[69]  Keith Glover,et al.  Robust control design using normal-ized coprime factor plant descriptions , 1989 .

[70]  M. Milanese,et al.  Estimation theory and uncertainty intervals evaluation in presence of unknown but bounded errors: Linear families of models and estimators , 1982 .

[71]  Guoxiang Gu,et al.  A class of algorithms for identification in H∞ , 1992, Autom..

[72]  Pertti Mäkilä,et al.  Modelling of uncertain systems via linear programming , 1993, Autom..

[73]  Er-Wei Bai,et al.  Stochastic and worst case system identification are not necessarily incompatible , 1994, Autom..

[74]  Harry L. Trentelman,et al.  Essays on control : perspectives in the theory and its applications , 1993 .

[75]  Graham C. Goodwin,et al.  Estimated Transfer Functions with Application to Model Order Selection , 1992 .

[76]  Jonathan R. Partington,et al.  Robust identification in the disc algebra using rational wavelets and orthonormal basis functions , 1996 .

[77]  W. Kautz Transient synthesis in the time domain , 1954 .

[78]  B. Ninness,et al.  A unifying construction of orthonormal bases for system identification , 1994, Proceedings of 1994 33rd IEEE Conference on Decision and Control.

[79]  Bo Wahlberg,et al.  Applications of Kautz Models in System Identification , 1993 .

[80]  J. P. Norton,et al.  Identification and Application of Bounded-Parameter Models , 1985 .

[81]  Jonathan R. Partington,et al.  Worst-case identification in Banach spaces , 1992 .

[82]  Petre Stoica,et al.  Decentralized Control , 2018, The Control Systems Handbook.

[83]  R. G. Hakvoort,et al.  Worst-case system identification in l/sub 1/: error bounds, optimal models and model reduction , 1992, [1992] Proceedings of the 31st IEEE Conference on Decision and Control.

[84]  Jie Chen,et al.  Worst-case system identification in H∞: validation of apriori information, essentially optimal algorithms, and error bounds , 1992, 1992 American Control Conference.

[85]  G. Belforte,et al.  Optimal input design for worst-case system identification in l 1 /l 2 /l ∞ , 1993 .

[86]  Pramod P. Khargonekar,et al.  The least squares algorithm, parametric system identification and bounded noise , 1993, Autom..

[87]  Guoxiang Gu,et al.  Worst Case Identification of Continuous time Systems via Interpolation , 1993, 1993 American Control Conference.

[88]  Robert Kosut,et al.  Closed-Loop Identification via the Fractional Representation: Experiment Design , 1989, 1989 American Control Conference.

[89]  Jie Chen,et al.  Optimal nonparametric identification from arbitrary corrupt finite time series , 1995, IEEE Trans. Autom. Control..

[90]  Jonathan R. Partington,et al.  Worst-case analysis of identification-BIBO robustness for closed-loop data , 1994, IEEE Trans. Autom. Control..

[91]  Jonathan R. Partington,et al.  Robust identification of strongly stabilizable systems , 1992 .

[92]  B. Ninness,et al.  Stochastic and Deterministic Approaches to Estimation in H 1 , 1993 .

[93]  Jonathan R. Partington,et al.  Interpolation in Normed Spaces from the Values of Linear Functionals , 1994 .

[94]  Munther A. Dahleh,et al.  Controller design for plants with structured uncertainty , 1993, Autom..

[95]  P. Mäkilä Worst-case input-output identification , 1992 .

[96]  Arthur J. Helmicki,et al.  Worst-case/deterministic identification in H/sub infinity /: the continuous-time case , 1992 .

[97]  Guoxiang Gu,et al.  Identification in H/sub infinity / using Pick's interpolation , 1992, [1992] Proceedings of the 31st IEEE Conference on Decision and Control.

[98]  Håkan Hjalmarson,et al.  A Unifying View of Disturbances in Identification , 1994 .

[99]  G. Zames,et al.  Fast identification n-widths and uncertainty principles for LTI and slowly varying systems , 1994, IEEE Trans. Autom. Control..

[100]  Lennart Ljung,et al.  Identifiability implies robust identifiability , 1993, Proceedings of 32nd IEEE Conference on Decision and Control.

[101]  Eric Walter,et al.  Characterizing Sets Defined By Inequalities , 1994 .

[102]  R. Tempo,et al.  Optimality of central and projection algorithms for bounded uncertainty , 1986 .

[103]  Michel Gevers,et al.  Towards a Joint Design of Identification and Control , 1993 .

[104]  Karl Johan Åström,et al.  Matching Criteria for Control and Identification , 1993 .

[105]  Brian D. O. Anderson,et al.  On Adaptive Robust Control and Control-Relevant System Identification , 1992, 1992 American Control Conference.

[106]  Richard G. Hakvoort,et al.  Worst-Case System Identification in H∞: Error Bounds and Optimal Models , 1993 .

[107]  Hüseyin Akçay,et al.  The Least-Squares Identification of Fir Systems Subject to Worst-Case Noise , 1994 .

[108]  C. A. Jacobson,et al.  Least squares methods for H∞ control-oriented system identification , 1992, 1992 American Control Conference.

[109]  Jonathan R. Partington,et al.  Algorithms for identification in H∞ with unequally spaced function measurements , 1993 .

[110]  Jan C. Willems,et al.  From time series to linear system - Part III: Approximate modelling , 1987, Autom..

[111]  Er-Wei Bai,et al.  Robust system identification with noisy experimental data: Projection operator and linear algorithms , 1994, Autom..

[112]  L. Ljung,et al.  Hard frequency-domain model error bounds from least-squares like identification techniques , 1992 .

[113]  J. Tsitsiklis,et al.  Optimal asymptotic identification under bounded disturbances , 1991, [1991] Proceedings of the 30th IEEE Conference on Decision and Control.

[114]  Bo Wahlberg,et al.  On approximation of stable linear dynamical systems using Laguerre and Kautz functions , 1996, Autom..