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  • 1.
    Böling, Jari M.
    et al.
    Department of Engineering, Åbo Akademi.
    Mäkilä, Pertti
    Luleå University of Technology, Department of Computer Science, Electrical and Space Engineering, Signals and Systems.
    On control relevant criteria in H∞ identification1998In: IEEE Transactions on Automatic Control, ISSN 0018-9286, E-ISSN 1558-2523, Vol. 43, no 5, p. 694-700Article in journal (Refereed)
    Abstract [en]

    This paper proposes a technique for using control relevant criteria in H∞ identification. The work reported here has its background in a desire to understand the closed-loop versus open-loop issue in control relevant identification. The proposed technique has some features in common with the iterative closed-loop Schrama scheme, but is constructed so as to be able to obtain control relevant reduced complexity models also directly from open-loop data (for stable systems). It is demonstrated that the proposed technique solves, with the initial open-loop data only, the examples treated earlier in the literature using the iterative closed-loop Schrama scheme

  • 2. Fischer, Britta
    et al.
    Gotthold, Daniel
    Mäkilä, Pertti
    Luleå University of Technology, Department of Computer Science, Electrical and Space Engineering, Signals and Systems.
    Control relevant identification in hinf: adaptive information and experiment design1996In: Proceedings of the 13th World Congress: International Federation of Automatic Control : San Francisco, USA, 30th June - 5th July 1996 ; (in 18 volumes) / [ed] Janos J. Gertler, Oxford: Pergamon Press, 1996, Vol. 1, p. 115-120Conference paper (Refereed)
  • 3. Fischer, Britta
    et al.
    Gotthold, Daniel
    Mäkilä, Pertti
    Luleå University of Technology, Department of Computer Science, Electrical and Space Engineering, Signals and Systems.
    Control relevant identification in hinf: adaptive information and experiment design1996In: Elsevier IFAC Publications / IFAC Proceedings series, ISSN 1474-6670, Vol. 29, no 1, p. 4046-4051Article in journal (Refereed)
    Abstract [en]

    Joint issues of modelling and control design are studied in a frequency domain setup. Stable systems with monotone Bode plots are chosen as the basis of the study presented in this work. Such dynamics is typical for plants in industrial process control. Adaptive information is considered and both open-loop and closed-loop experimental conditions are included. For systems with monotone Bode plots the information typically required for successful control design consists of a small part of the frequency response only. This can be exploited in experiment design.

  • 4. Gotthold, Daniel
    et al.
    Fischer, Britta
    Mäkilä, Pertti
    Luleå University of Technology, Department of Computer Science, Electrical and Space Engineering, Signals and Systems.
    Control relevant identification i H -adaptive experiment design for systems with monotone bode plots1996In: Reglermöte '96: [preprints], Luleå: Högskolan i Luleå , 1996, p. 201-205Conference paper (Other academic)
  • 5. Gustafsson, T.K.
    et al.
    Mäkilä, Pertti
    Luleå University of Technology, Department of Computer Science, Electrical and Space Engineering, Signals and Systems.
    Modelling of uncertain systems via linear programming1993In: Automatic control : world congress: proceedings of the 12th Triennial World Congress of the International Federation of Automatic Control / [ed] Graham Clifford Goodwin ; R.J. Evans, Oxford: Pergamon Press, 1993, p. 293-298Conference paper (Refereed)
  • 6.
    Gustafsson, T.K.
    et al.
    Åbo Akademi University, Department of Engineering.
    Mäkilä, Pertti
    Luleå University of Technology, Department of Computer Science, Electrical and Space Engineering, Signals and Systems.
    Modelling of uncertain systems via linear programming1996In: Automatica, ISSN 0005-1098, E-ISSN 1873-2836, Vol. 32, no 3, p. 319-335Article in journal (Refereed)
    Abstract [en]

    Real plants are, in general, time-varying and uncertain. Yet most industrial control loops are designed using linear time-invariant (LTI) plant models. The present work formalizes the problem of best approximate LTI modelling of BIBO-stable linear time-varying (LTV) systems in a way that is compatible with the notion of induced l∞ norm used in robust l1 control. This setup is closely associated with certain identification methods and controlmotivated model validation/invalidation procedures that can be efficiently implemented with special-purpose linear programming (LP) techniques. Results are given for approximate modelling of BIBO-stable LTV and LTI systems using LTI models, especially BIBO-stable fixed-pole state-space model parametrizations. It is shown that such parametrizations are satisfactory from an approximate modelling point of view, and can be used in output-error-type LP identification techniques and in LP model validation procedures. Various useful constraints on model parameters etc. can be included, as long as they are linear in the unknown parameters, and both insensitive (statistically robust) and sensitive criteria can be used in identification and model validation. Simulation examples are included to illustrate that such techniques indeed give good results and can be used to solve problems of realistic size.

  • 7. Gustafsson, Tore K.
    et al.
    Mäkilä, Pertti
    Luleå University of Technology, Department of Computer Science, Electrical and Space Engineering, Signals and Systems.
    On system identification and model validation via linear programming1993In: Proceedings of the 32nd IEEE Conference on Decision and Control, IEEE Communications Society, 1993, Vol. 3, p. 2087-2092Conference paper (Refereed)
    Abstract [en]

    Linear programming methods for discrete l1 approximation are used to provide solutions to problems of approximate identification with state space models and to problems of model validation for stable uncertain systems. Choice of model structure is studied via Kolmogorov n-width concept and a related n-width concept for state space models. Several results are given for FIR, Laguerre and Kautz models concerning their approximation properties in the space of bounded-input bounded-output (BIBO) stable systems. A robust convergence result is given for a modified least sum of absolute deviations identification algorithm for BIBO stable linear discrete-time systems. A simulation example with identification of Kautz models and subsequent model validation is given

  • 8.
    Mäkilä, Pertti
    Luleå University of Technology, Department of Computer Science, Electrical and Space Engineering, Signals and Systems.
    Robust identification of uncertain systems1994In: Colloquium on Identification of Uncertain Systems: on Tuesday, 26 April 1994, London: IEEE Communications Society, 1994, p. 1-4Conference paper (Refereed)
    Abstract [en]

    In this paper an overview is given of some of the current research activities on robust identification of uncertain systems. This field deals with identification of nominal models, estimation of uncertainty models, and validation of uncertainty models for the purpose of robust control design. Special attention is given to issues of black-box estimation of uncertainty models

  • 9.
    Mäkilä, Pertti
    et al.
    Luleå University of Technology, Department of Computer Science, Electrical and Space Engineering, Signals and Systems.
    Gotthold, Daniel
    Fischer, Britta
    Modelling and validation for control design: uncertain systems, monotone bode plots and process control1997In: Mathematical Modelling of Systems, ISSN 1381-2424, Vol. 3, no 1, p. 3-26Article in journal (Refereed)
    Abstract [en]

    The interplay between modelling and control design is studied in the context of typical plant dynamics in industrial process control. An abstract way of summarizing the plant dynamics in most examples in textbooks on process control and in many applications is provided by the concept of stable models with monotone Bode plots. It is shown that for this class of systems approximate knowledge of a small part of the plant frequency response provides sufficient information for successful control design from experimental data. The role of adaptive information is studied in experimental modelling of systems with monotone Bode plots for control design. Frequency domain data is considered in the present tutorial style paper only. Both open-loop and closed-loop experimental conditions are included. In fact, it turns out that a strong form of adaptive information can be useful, reminescent of dual control where the input signal is to guarantee a learning property, too. Furthermore, the role of uncertain systems, model validation and control design validation are discussed

  • 10.
    Mäkilä, Pertti
    et al.
    Luleå University of Technology, Department of Computer Science, Electrical and Space Engineering, Signals and Systems.
    Gustafsson, T.K.
    Robust identification and model validation via linear programming1994In: Systems and Networks: mathematical theory and applications; proceedings of the International Symposium MTNS '93 held in Regensburg, Germany, August 2 - 6, 1993 / [ed] Uwe Helmke, Berlin: Akademie Verlag, 1994Conference paper (Refereed)
  • 11.
    Mäkilä, Pertti
    et al.
    Luleå University of Technology, Department of Computer Science, Electrical and Space Engineering, Signals and Systems.
    Partington, J. R.
    School of Mathematics, University of Leeds.
    Gustafsson, T.K.
    Faculty of Chemical Engineering, Åbo Akademi.
    Worst-case control-relevant identification1995In: Automatica, ISSN 0005-1098, E-ISSN 1873-2836, Vol. 31, no 12, p. 1799-1819Article in journal (Refereed)
    Abstract [en]

    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 ℓ1 are covered including algorithms, convergence and divergence results, worst-case estimation of uncertainty models, model validation and control relevancy issues.

  • 12.
    Mäkilä, Pertti
    et al.
    Luleå University of Technology, Department of Computer Science, Electrical and Space Engineering, Signals and Systems.
    Partington, J.R.
    An essay on identification of feedback systems1994In: The modeling of uncertainty in control systems: Proceedings of the 1992 Santa Barbara Workshop / [ed] Roy S. Smith; Mohammed Dahleh, London: Encyclopedia of Global Archaeology/Springer Verlag, 1994, p. 11-13Conference paper (Refereed)
  • 13.
    Mäkilä, Pertti
    et al.
    Luleå University of Technology, Department of Computer Science, Electrical and Space Engineering, Signals and Systems.
    Partington, J.R.
    Identification of feedback systems from time series1994In: The modeling of uncertainty in control systems: Proceedings of the 1992 Santa Barbara Workshop / [ed] R.S. Smith; M. Dahleh, Encyclopedia of Global Archaeology/Springer Verlag, 1994, p. 117-126Conference paper (Refereed)
  • 14.
    Mäkilä, Pertti
    et al.
    Luleå University of Technology, Department of Computer Science, Electrical and Space Engineering, Signals and Systems.
    Partington, J.R.
    School of Mathematics, University of Leeds.
    On bounded-error identification of feedback systems1995In: International journal of adaptive control and signal processing (Print), ISSN 0890-6327, E-ISSN 1099-1115, Vol. 9, no 1, p. 47-61Article in journal (Refereed)
    Abstract [en]

    This paper studies identification of linear feedback systems from closed loop time series. Unfalsified approximate bounded error identification is shown to result in a control-relevant identification methodology for robustness optimization under BIBO-stable coprime factor uncertainty. Furthermore, well-posedness (continuity) of the robustness optimization method for controller synthesis is established

  • 15.
    Mäkilä, Pertti
    et al.
    Luleå University of Technology, Department of Computer Science, Electrical and Space Engineering, Signals and Systems.
    Partington, J.R.
    Luleå tekniska universitet.
    Robust approximate modelling of stable linear systems1993In: International Journal of Control, ISSN 0020-7179, E-ISSN 1366-5820, Vol. 58, no 3, p. 665-683Article in journal (Refereed)
    Abstract [en]

    Robust approximation and worst-case approximate modelling of stable shift-invariant systems from corrupted transfer function estimates are studied in the H[]∞ sense. Connections between the problem formulations of the present work and certain problems of worst-case system identification, notably the Helmicki-Jacobson-Nett problem formulation for identification in H[]∞, are established. Issues of model set selection are addressed using the n-width concept: a concrete result establishes a priori knowledge for which a certain rational model set is optimal in the n-width sense. A notion of robust convergence is defined so that any untuned approximation method satisfying it has a generic well-posedness property for systems in the disk algebra

  • 16.
    Mäkilä, Pertti
    et al.
    Luleå University of Technology, Department of Computer Science, Electrical and Space Engineering, Signals and Systems.
    Partington, J.R.
    Gustafsson, T.
    Robust identification1995In: System identification: a postprint volume from the IFAC symposium, Copenhagen, Denmark, 4 - 6 July 1994 / SYSID '94 / [ed] M. Blanke; Torsten Söderström, New York: Published for the International Federation of Automatic Control by Pergamon , 1995, p. 45-63Conference paper (Refereed)
    Abstract [en]

    This paper introduces the reader to several recent developments in robust 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 l1 are covered; including algorithms, convergence and divergence results, control relevancy issues, and objective worst case estimation of uncertainty models

  • 17.
    Mäkilä, Pertti
    et al.
    Luleå University of Technology, Department of Computer Science, Electrical and Space Engineering, Signals and Systems.
    Partington, J.R.
    University of Leeds, School of Mathematics.
    Gustafsson, T.K.
    Åbo Akademi University, Department of Chemical Engineering.
    Robust identification1994In: Elsevier IFAC Publications / IFAC Proceedings series, ISSN 1474-6670, Vol. 27, no 8, p. 45-63Article in journal (Refereed)
    Abstract [en]

    This paper introduces the reader to several recent developments in robust 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 l1 are covered; including algorithms, convergence and divergence results, control relevancy issues, and objective worst case estimation of uncertainty models

  • 18.
    Mäkilä, Pertti
    et al.
    Luleå University of Technology, Department of Computer Science, Electrical and Space Engineering, Signals and Systems.
    Partington, J.R.
    Leeds University.
    Norlander, Torbjörn
    Bounded power signal spaces for robust control and modeling1999In: SIAM Journal of Control and Optimization, ISSN 0363-0129, E-ISSN 1095-7138, Vol. 37, no 1, p. 92-117Article in journal (Refereed)
    Abstract [en]

    The nonlinear space of signals allowing Wiener's generalized harmonic analysis (GHA), the linear bounded power signal spaces of Beurling, Marcinkiewicz, and Wiener, and a new linear bounded power space are studied from a control and systems theory perspective. Specifically, it is shown that the system power gain is given by the $H_\infty$ norm of the system transfer function in each of these spaces for a large class of (power) stable finite and infinite dimensional systems. The GHA setup is shown to possess several limitations for the purpose of robustness analysis which motivates the use of the other more general (nonstationary) signal spaces. The natural double-sided time axis versions of bounded power signal spaces are shown to break the symmetry between Hardy space $H_\infty$ methods and bounded power operators; e.g., the system transfer function being in $H_\infty$ does not imply that a causal-linear time-invariant (LTI) system is bounded as an operator on any of the double-sided versions of the studied bounded power signal spaces.

  • 19. Norlander, Torbjörn
    et al.
    Mäkilä, Pertti
    Luleå University of Technology, Department of Computer Science, Electrical and Space Engineering, Signals and Systems.
    A sampled-data theory for fixed structure LQ controller design2000Report (Other academic)
    Abstract [en]

    The fixed structure sampled-data LQ-optimal control problem is discussed. A method is presented to design a discrete controller with fixed structure and order that minimizes a continuous quadratic loss function. The transition from continuous time signals to discrete time signals includes an averaging sampler, in order to circumvent the difficulties of sampling white noise signals. Some examples using the proposed method are also presented.

  • 20.
    Norlander, Torbjörn
    et al.
    Luleå University of Technology, Department of Computer Science, Electrical and Space Engineering, Signals and Systems.
    Mäkilä, Pertti
    Defragilization in optimal control design1999In: Proceedings of the 38th IEEE Conference on Decision and Control :: December 7 - 10, 1999, Crowne Plaza Hotel & Resort, Phoenix, Arizona, USA, Piscataway, NJ: IEEE Communications Society, 1999, p. 875-876Conference paper (Refereed)
    Abstract [en]

    We present a general methodology to address the fragility issue in optimization based modern control systems design

  • 21.
    Norlander, Torbjörn
    et al.
    Luleå University of Technology, Department of Computer Science, Electrical and Space Engineering, Signals and Systems.
    Mäkilä, Pertti
    Luleå University of Technology, Department of Computer Science, Electrical and Space Engineering, Signals and Systems.
    Defragilization in optimal design and its application to fixed structure LQ controller design2001In: IEEE Transactions on Control Systems Technology, ISSN 1063-6536, E-ISSN 1558-0865, Vol. 9, no 4, p. 590-598Article in journal (Refereed)
    Abstract [en]

    In this work, we present a general methodology to address the recently debated fragility issue in optimization-based modern control systems design. Based on this methodology we have developed a defragilization procedure which is applied to fixed structure linear quadratic (LQ) control design. Issues regarding computational efficiency of the procedure and the relationship between controller fragility and controller parameterization are discussed via two examples taken from practical applications. The first example is based on a rotary cement kiln control application and the latter example on a wing flutter control application. The procedure could also be used in design problems with specifications which are related to controller nonfragility requirements, e.g., so as to allow some degree of controller online tuning.

  • 22. Norlander, Torbjörn
    et al.
    Mäkilä, Pertti
    Luleå University of Technology, Department of Computer Science, Electrical and Space Engineering, Signals and Systems.
    Parametric linear quadratic control and random delays2000In: IET Control Theory & Applications, ISSN 1751-8644, E-ISSN 1751-8652, Vol. 147, no 6, p. 641-647Article in journal (Refereed)
    Abstract [en]

    The authors derive the design equations for parametric linear quadratic control of continuous-time systems with random delays. This problem motivates a more general setup that is utilised for the development of efficient numerical algorithms. Systems with random delays are important in control problems over communication networks. The generalised setup allows robustness issues against modelling errors and statistically varying disturbances to be addressed. The results are illustrated with examples

  • 23.
    Norlander, Torbjörn
    et al.
    Luleå University of Technology, Department of Computer Science, Electrical and Space Engineering, Signals and Systems.
    Mäkilä, Pertti
    Sampled-data design of fixed structure LQ controllers1998In: Proceedings of the 37th IEEE Conference on Decision and Control: December 16 - 18, 1998, Hyatt Regency Westshore, Tampa, Florida, Piscataway, NJ: IEEE Communications Society, 1998, p. 837-840Conference paper (Refereed)
    Abstract [en]

    A method to design an output feedback sampled-data controller with fixed structure that minimizes a continuous quadratic loss function, thus accounting for intersample behavior, is presented. The method involves three steps, first a continuous Linear Quadratic optimal control problem is formulated, then the discrete equivalent problem is found and finally this problem is reformulated as a parametric optimization problem which is solved using the loss increment technique. In the feedback we have used an averaging sampler to pre-filter the measured signals, thus circumvent the problems of sampling white noise

  • 24.
    Partington, J.R.
    et al.
    School of Mathematics, University of Leeds.
    Mäkilä, Pertti
    Luleå University of Technology, Department of Computer Science, Electrical and Space Engineering, Signals and Systems.
    Analysis of linear methods for robust identification in l11995In: Automatica, ISSN 0005-1098, E-ISSN 1873-2836, Vol. 31, no 5, p. 755-758Article in journal (Refereed)
    Abstract [en]

    We consider worst-case analysis of system identification by means of the linear algorithms such as least-squares. We provide estimates for worst-case and average errors, showing that worst-case robust convergence cannot occur in the l1 identification problem. The case of periodic inputs is also analysed. Finally a pseudorandomness assumption is introduced that allows more powerful convergence results in a deterministic framework.

  • 25.
    Partington, J.R.
    et al.
    School of Mathematics, University of Leeds.
    Mäkilä, Pertti
    Luleå University of Technology, Department of Computer Science, Electrical and Space Engineering, Signals and Systems.
    Modeling of linear fading memory systems1996In: IEEE Transactions on Automatic Control, ISSN 0018-9286, E-ISSN 1558-2523, Vol. 41, no 6, p. 899-903Article in journal (Refereed)
    Abstract [en]

    Motivated by questions of approximate modeling and identification, we consider various classes of linear time-varying bounded-input-bounded output (BIBO) stable fading memory systems and prove some characterizations of them. These include fading memory systems, in general, almost periodic systems, and asymptotically periodic systems. We also show that norm and strong convergence coincide for BIBO stable causal fading memory systems

  • 26.
    Partington, J.R.
    et al.
    School of Mathematics, University of Leeds.
    Mäkilä, Pertti
    Luleå University of Technology, Department of Computer Science, Electrical and Space Engineering, Signals and Systems.
    Worst-case analysis of identification: BIBO robustness for closed loop data1994In: IEEE Transactions on Automatic Control, ISSN 0018-9286, E-ISSN 1558-2523, Vol. 39, no 10, p. 2171-2176Article in journal (Refereed)
    Abstract [en]

    This paper deals with the worst-case analysis of identification of linear shift-invariant (possibly) infinite-dimensional systems. A necessary and sufficient input richness condition for the existence of robustly convergent identification algorithms in l1 is given. A closed-loop identification setting is studied to cover both stable and unstable (but BIBO stabilizable) systems. Identification (or modeling) error is then measured by distance functions which lead to the weakest convergence notions for systems such that closed-loop stability, in the sense of BIBO stability, is a robust property. Worst-case modeling error bounds in several distance functions are included

  • 27.
    Partington, J.R.
    et al.
    School of Mathematics, University of Leeds.
    Mäkilä, Pertti
    Luleå University of Technology, Department of Computer Science, Electrical and Space Engineering, Signals and Systems.
    Worst-case analysis of the least-squares method and related identification methods1995In: Systems & control letters (Print), ISSN 0167-6911, E-ISSN 1872-7956, Vol. 24, no 3, p. 193-200Article in journal (Refereed)
    Abstract [en]

    We consider worst-case analysis of system identification under less restrictive assumptions on the noise than the l∞ bounded error condition. It is shown that the least-squares method has a robust convergence property in l2 identification, but lacks a corresponding property in l1 identification (as well as in all other non-Hilbert space settings). The latter result is in stark contrast with typical results in asymptotic stochastic analysis of the least-squares method. Furthermore, it is shown that the Khintchine inequality is useful in the analysis of least lp identification methods

  • 28.
    Wahlberg, B.
    et al.
    S3 — Automatic Control, Royal Institute of Technology.
    Mäkilä, Pertti
    Luleå University of Technology, Department of Computer Science, Electrical and Space Engineering, Signals and Systems.
    On approximation of stable linear dynamical systems using Laguerre and Kautz functions1996In: Automatica, ISSN 0005-1098, E-ISSN 1873-2836, Vol. 32, no 5, p. 693-708Article in journal (Refereed)
    Abstract [en]

    Approximation of stable linear dynamical systems by means of so-called Laguerre and Kautz functions, which are the Laplace transforms of a class of orthonormal exponentials, is studied. Since the impulse response of a stable finite dimensional linear dynamical system can be represented by a sum of exponentials (times polynomials), it seems reasonable to use basis functions of the same type. Assuming that the transfer function of a system is bounded and analytic outside a given disc, it is shown that Laguerre basis functions are optimal in a mini-max sense. This result is extended to the "two-parameter" Kautz functions which can have complex poles, while the poles of Laguerre functions are restricted to the real axis. By conformal mapping techniques the "two-parameter" Kautz approximation problem is recast as two Laguerre approximation problems. Thus, the well-developed theory of Laguerre functions can be applied to analyze Kautz approximations. Unilateral shifts are used to further develop the connection between Laguerre functions and Kautz functions. Results on H2 and H∞ approximation using Kautz models are given. Furthermore, the weighted L2 Kautz approximation problem is shown to be equivalent to solving a block Toeplitz matrix equation

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