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  • 1.
    Müller, Matias
    KTH, School of Electrical Engineering and Computer Science (EECS), Automatic Control.
    Regret and Risk Optimal Design in Control2019Licentiate thesis, monograph (Other academic)
    Abstract [en]

    Engineering sciences deal with the problem of optimal design in the face of uncertainty. In particular, control engineering is concerned about designing policies/laws/algorithms that sequentially take decisions given unreliable data.

    This thesis addresses two particular instances of optimal sequential decision making for two different problems. The first problem is known as the H-norm (or l2-gain, for LTI systems) estimation problem, which is a fundamental quantity in control design through the small gain theorem. Given an unknown system, the goal is to find the maximum l2-gain which, in a model-free approach, involves solving a sequential input design problem. The H-norm estimation problem (or simply "gain estimation problem") is cast as the composition of a multi-armed bandit problem generating data, and an optimal estimation problem given that data. It is shown that the separation of the gain estimation problem into these two sub-problems is optimal in a mean-square sense, as the expected estimation error asymptotically matches the Cramér-Rao lower bound.

    In the second part of the thesis, we address the problem of risk-coherent optimal control design for disturbance rejection under uncertainty, where optimality is studied from an H2 and an H sense. We consider a parametric model for the plant and the noise spectrum, where the modeling error between the model and the real system is uncertain. This uncertainty is condensed in a probability density function over the different realizations of the parameters defining the model. We use this information to design a controller that minimizes the risk of falling into poor closed-loop performance within a financial theory of risk framework. A systematic approach for the design of H2- and H-optimal controllers is proposed in terms of a quadratically-constrained linear program and a semi-definite program, respectively. An interesting application to H2-optimal design under covert attacks is also developed.

  • 2.
    Müller, Matias I.
    et al.
    KTH, School of Electrical Engineering and Computer Science (EECS), Automatic Control.
    Milosevic, Jezdimir
    KTH, School of Electrical Engineering and Computer Science (EECS), Automatic Control.
    Sandberg, Henrik
    KTH, School of Electrical Engineering and Computer Science (EECS), Automatic Control.
    Rojas, Cristian R.
    KTH, School of Electrical Engineering and Computer Science (EECS), Automatic Control.
    A Risk-Theoretical Approach to H2-Optimal Control under Covert Attacks2018In: 57th IEEE Conference on Decision and Control, IEEE , 2018, p. 4553-4558Conference paper (Refereed)
    Abstract [en]

    We consider the control design problem of optimizing the H-2 performance of a closed-loop system despite the presence of a malicious covert attacker. It is assumed that the attacker has incomplete knowledge on the true process we are controlling. To account for this uncertainty, we employ different measures of risk from the so called family of coherent measures of risk. In particular, we compare the closed-loop performance when a nominal value is used, with three different measures of risk: average risk, worst-case scenario and conditional valueat- risk (CVaR). Additionally, applying the approach from a previous work, we derive a convex formulation for the control design problem when CVaR is employed to quantify the risk. A numerical example illustrates the advantages of our approach.

  • 3.
    Müller, Matias I.
    et al.
    KTH, School of Electrical Engineering and Computer Science (EECS), Automatic Control.
    Rojas, Cristian R.
    KTH, School of Electrical Engineering and Computer Science (EECS), Automatic Control.
    A Markov Chain Approach to Compute the ℓ2-gain of Nonlinear Systems2018Conference paper (Refereed)
    Abstract [en]

    In this work the problem of computing the maximum gain of non-linear systems, also known as its ℓ2-gain, from input-output data is studied. From an input design perspective, this problem reduces to find an optimal input sequence, of bounded norm, maximizing the norm gain of the output, where our target estimation corresponds to the ratio of these quantities. The novelty of this approach lies on the fact that the input signal is a realization of a stationary process with finite memory whose range is a finite set of values. Based on recent developents on input design for nonlinear systems, our approach leads to a linear program whose optimal cost gives an approximation of the ℓ2-gain of the system. An illustrative example shows how well the algorithm performs compared to other methods approximating this quantity.

  • 4.
    Müller, Matias I.
    et al.
    KTH, School of Electrical Engineering and Computer Science (EECS), Automatic Control.
    Rojas, Cristian R.
    KTH, School of Electrical Engineering and Computer Science (EECS), Automatic Control.
    Gain estimation of linear dynamical systems using Thompson Sampling2019In: Proceedings of Machine Learning Research / [ed] Kamalika Chaudhuri, Masashi Sugiyama, 2019, Vol. 89, p. 1535-1543Conference paper (Refereed)
  • 5.
    Müller, Matias I.
    et al.
    KTH, School of Electrical Engineering and Computer Science (EECS), Intelligent systems, Decision and Control Systems (Automatic Control).
    Rojas, Cristian R.
    KTH, School of Electrical Engineering and Computer Science (EECS), Intelligent systems, Decision and Control Systems (Automatic Control).
    Risk-Coherent H-optimal Filter Design Under Model Uncertainty with Applications to MISO Control2019In: 2019 18th European Control Conference, ECC 2019, Institute of Electrical and Electronics Engineers (IEEE), 2019, p. 1461-1466, article id 8795947Conference paper (Refereed)
    Abstract [en]

    This work presents a framework to address the problem of designing discrete-time LTI (linear and time-invariant) multiple-input and multiple-output (MIMO) filters, aiming to optimize the performance of a system when model uncertainty is considered. Additionally, we present an interesting application to control design for disturbance rejection under model uncertainty. To account for this uncertainty we employ coherent measures of risk, which are a family of measures in theory of risk. We particularly discuss which measures are suitable by comparing the conditional value-at-risk (CVaR) to other three common designs. Using a scenario approach, we derive a convex optimization problem based on linear matrix inequalities (LMIs), whose solution minimizes the risk of falling into poor mathcal{H}{ infty} performance. Finally, we present an application to multiple-input and single-output (MISO) control design under model uncertainty in the auto-covariance function of the output noise, comparing approaches minimizing different notions of risk.

  • 6.
    Müller, Matias I.
    et al.
    KTH, School of Electrical Engineering (EES), Automatic Control.
    Valenzuela, Patricio Esteban
    KTH, School of Electrical Engineering (EES), Automatic Control.
    Proutiere, Alexandre
    KTH, School of Electrical Engineering (EES), Automatic Control.
    Rojas, Cristian R.
    KTH, School of Electrical Engineering (EES), Automatic Control.
    A stochastic multi-armed bandit approach to nonparametric H-norm estimation2017In: 56th IEEE Conference on Decision and Control, Institute of Electrical and Electronics Engineers (IEEE), 2017, p. 4632-4637Conference paper (Refereed)
    Abstract [en]

    We study the problem of estimating the largest gain of an unknown linear and time-invariant filter, which is also known as the H norm of the system. By using ideas from the stochastic multi-armed bandit framework, we present a new algorithm that sequentially designs an input signal in order to estimate this quantity by means of input-output data. The algorithm is shown empirically to beat an asymptotically optimal method, known as Thompson Sampling, in the sense of its cumulative regret function. Finally, for a general class of algorithms, a lower bound on the performance of finding the H-infinity norm is derived.

  • 7.
    Müller, Matias I.
    et al.
    KTH, School of Electrical Engineering and Computer Science (EECS), Automatic Control.
    Valenzuela, Patricio Esteban
    KTH, School of Electrical Engineering and Computer Science (EECS), Automatic Control.
    Rojas, Cristian R.
    KTH, School of Electrical Engineering and Computer Science (EECS), Automatic Control.
    Risk-coherent H2-optimal disturbance rejection under model uncertainty2017In: 20th IFAC World Congress, Elsevier, 2017, Vol. 50, no 1, p. 15530-15535Conference paper (Refereed)
    Abstract [en]

    A control design procedure for disturbance rejection, when the disturbance model is uncertain, is proposed. We use the probabilistic information about the process disturbance model to design a controller to account for the uncertainty by using a risk-theoretical approach. By introducing the notion of coherent measures of risk, we analyze standard approaches to account for this uncertainty, and we intend to show that the conditional value-at-risk (CVaR) is an appropriate function to measure the uncertainty in the disturbance model. We also derive a convex formulation for the controller design problem when the Youla parameter is linearly parametrized. A numerical example illustrates the main discussion of this article.

  • 8.
    Ramírez-Chavarría, Roberto G.
    et al.
    Universidad Nacional Autónoma de México.
    Müller, Matias I.
    KTH, School of Electrical Engineering and Computer Science (EECS), Automatic Control.
    Mattila, Robert
    KTH, School of Electrical Engineering and Computer Science (EECS), Automatic Control.
    Quintana-Carapia, Gustavo
    Vrije Universiteit Brussel.
    Sánchez-Pérez, Celia
    Universidad Nacional Autónoma de México.
    A framework for high-resolution frequency response measurement and parameter estimation in microscale impedance applications2019In: Measurement, ISSN 0263-2241, Vol. 148, article id 106913Article in journal (Refereed)
    Abstract [en]

    Electrical impedance spectroscopy (EIS) is a tool for characterizing the electrical behavior of matter. Nevertheless, most of the work is focused on purely experimental results, leading aside alternative measurement and estimation techniques. In this paper, we introduce a framework for spectral measurements and parameter estimation applied to EIS. There are two methods in the proposal running independently: frequency response function based non-parametric estimation, and parametric recursive estimation. The former provides consistent estimates even in the presence of noise and works with batches of data. Whilst the latter gives consistent parametric estimates under the right model structure. The proposed platform is designed around a reconfigurable device, which comprises minimal hardware design and digital signal processing. We test the system with a multisine signal by measuring calibration circuits and colloidal samples at microscale. Results show that this method outperforms the state-of-the-art techniques for impedance measurement applications, exhibiting low uncertainty and physical interpretation.

  • 9.
    Ramírez-Chavarría, Roberto G.
    et al.
    Universidad Nacional Autónoma de México.
    Quintana-Carapia, Gustavo
    Vrije Universiteit Brussel.
    Müller, Matias I.
    KTH, School of Electrical Engineering and Computer Science (EECS), Automatic Control.
    Mattila, Robert
    KTH, School of Electrical Engineering and Computer Science (EECS), Automatic Control.
    Matatagui, Daniel
    Universidad Nacional Autónoma de México.
    Sánchez-Pérez, Celia
    Universidad Nacional Autónoma de México.
    Bioimpedance Parameter Estimation using Fast Spectral Measurements and Regularizaton2018In: IFAC-PapersOnLine, IFAC Papers Online, 2018, Vol. 51, no 15, p. 521-526Conference paper (Refereed)
    Abstract [en]

    This work proposes an alternative framework for parametric bioimpedance estimation as a powerful tool to characterize biological media. We model the bioimpedance as an electrical network of parallel RC circuits, and transform the frequency-domain estimation problem into a time constant domain estimation problem by means of the distribution of relaxation times (DRT) method. The Fredholm integral equation of the first kind is employed to pose the problem in a regularized least squares (RLS) form. We validate the proposed methodology by numerical simulations for a synthetic biological electrical circuit, by using a multisine signal in the frequency range of 1kHz to 853kHz and considering an error in variables (EIV) problem. Results show that the proposed method outperforms the state-of-the-art techniques for spectral bioimpedance analysis. We also illustrates its potentiality in terms of accurate spectral measurements and precise data interpretation, for further usage in biological applications.

  • 10.
    Rojas, Cristian R.
    et al.
    KTH, School of Electrical Engineering and Computer Science (EECS), Automatic Control.
    Müller, Matias I.
    KTH, School of Electrical Engineering and Computer Science (EECS), Automatic Control.
    Algorithms for data-driven H-norm estimation2019In: DATA-DRIVEN FILTER AND CONTROL DESIGN: Methods and applications / [ed] Carlo Novara and Simone Formentin, IET Digital Library, 2019, p. 145-163Chapter in book (Refereed)
    Abstract [en]

    In this chapter, the problem of estimating in a model-free manner the H norm of a linear dynamic system is discussed at a tutorial level. Two recently developed methods for addressing this problem are presented, namely the power iterations method and a class of multi-armed bandit (MAB) algorithms. Due to reasons of space, many details are omitted, but references are provided to complement this exposition.

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