| 1. |
- Elton, Augustus, et al.
(författare)
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Blind Nonparametric Estimation of SISO Continuous-time Systems
- 2023
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Ingår i: IFAC-PapersOnLine. - : Elsevier BV. ; , s. 4222-4227
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Konferensbidrag (refereegranskat)abstract
- Blind system identification is aimed at finding parameters of a system model when the input is inaccessible. In this paper, we propose a blind system identification method that delivers a single-input single-output, continuous-time model in a nonparametric kernel form. We take advantage of the representer theorem to form a joint maximum a posteriori estimator of the input and system impulse response. The identified system model and input are optimised in sequence to overcome the blind problem with generalised cross validation used to select appropriate hyperparameters given some fixed input sequence. We demonstrate via Monte Carlo simulations the accuracy of the method in terms of estimating the input.
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| 2. |
- Müller, Matias I.
(författare)
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Learning Sequential Decision Rules in Control Design: Regret-Optimal and Risk-Coherent Methods
- 2021
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Doktorsavhandling (övrigt vetenskapligt/konstnärligt)abstract
- 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, in general, ℓ2-gain for nonlinear systems) estimation problem, which is a fundamental quantity in control design through, e.g., 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 multi-armed bandit problem generating data, and an optimal estimation problem given that data. The problem of generating data is a sequential input-design problem in which, at every round, the decision-maker chooses one (or many) frequencies to sample from the unknown frequency response of the system under study. We show that Thompson Sampling (TS), a classical bandit algorithm, is optimal within the class of algorithms that chooses only one frequency per round. Additionally, we introduce Weighted Thompson Sampling (WTS), which is a TS-based algorithm that can sample many frequencies at every round. In this thesis, we prove that WTS is an optimal bandit policy within the class of algorithms that can sample many frequencies simultaneously. On the other hand, the problem of estimating the H∞-norm of the system using the data provided by the bandit algorithm is also discussed. In particular, we show that the expected estimation error of the gain of the system asymptotically matches the Cramér-Rao lower bound for a proposed estimator, and for every bandit policy in a wide class of algorithms.In the second part, 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. When the parameters in the plant are not known with sufficient accuracy for control purposes, we introduce a framework that allows us to tackle the joint-stabilization problem by means of sequential convex relaxations, each of them leading to a semi-definite program. On the other hand, when the noise spectrum is uncertain, we propose a systematic scenario approach for designing H2- and H∞-optimal controllers in terms of quadratically-constrained linear programs and sequential semi-definite programming, respectively. Simulations show that, from a risk-theoretical perspective, exploiting the information encoded in the probability density function of the parameters defining the models better balances the risk of falling into poor closed-loop performances.
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| 3. |
- Oomen, Tom, et al.
(författare)
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Analyzing Iterations in Identification with Application to Nonparametric H∞-Norm Estimation
- 2011
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Ingår i: Proceedings of the 18th World Congress, The International Federation of Automatic Control, Milano (Italy) August 28 - September 2, 2011. - : IFAC Papers Online. ; , s. 9972-9977
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Konferensbidrag (refereegranskat)abstract
- In the last decades, many iterative approaches in the field of system identification for control have been proposed. Many successful implementations have been reported, despite the lack of a solid analysis with respect to the convergence and value of these iterations. The aim of this paper is to present a thorough analysis of a specific iterative algorithm that involves nonparametric H-infinity-norm estimation. The pursued approach involves a novel frequency domain approach that appropriately deals with additive stochastic disturbances and input normalization. The results of the novel convergence analysis are twofold: i) the presence of additive disturbances introduces a bias in the estimation procedure, and ii) the iterative procedure can be interpreted as experiment design for H-infinity-norm estimation, revealing the value of iterations and limits of accuracy in terms of the Fisher information matrix. The results are confirmed by means of a simulation example.
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| 4. |
- Oomen, Tom, et al.
(författare)
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Iterative Data-Driven H-infinity Norm Estimation of Multivariable Systems With Application to Robust Active Vibration Isolation
- 2014
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Ingår i: IEEE Transactions on Control Systems Technology. - 1063-6536 .- 1558-0865. ; 22:6, s. 2247-2260
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Tidskriftsartikel (refereegranskat)abstract
- This paper aims to develop a new data-driven H-infinity norm estimation algorithm for model-error modeling of multivariable systems. An iterative approach is presented that requires significantly a fewer prior assumptions on the true system, hence it provides stronger guarantees in a robust control design. The iterative estimation algorithm is embedded in a robust control design framework with a judiciously selected uncertainty structure to facilitate high control performance. The approach is experimentally implemented on an industrial active vibration isolation system.
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| 5. |
- Oomen, Tom, et al.
(författare)
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Reset-free data-driven gain estimation : Power iteration using reversed-circulant matrices
- 2024
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Ingår i: Automatica. - : Elsevier BV. - 0005-1098 .- 1873-2836. ; 161
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Tidskriftsartikel (refereegranskat)abstract
- A direct data-driven iterative algorithm is developed to accurately estimate the H∞ norm of a linear time-invariant system from continuous operation, i.e., without resetting the system. The main technical step involves a reversed-circulant matrix that can be evaluated in a model-free setting by performing experiments on the real system.
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| 6. |
- Oomen, Tom, et al.
(författare)
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Sparse Iterative Learning Control (SPILC) : When to Sample for Resource-Efficiency?
- 2018
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Ingår i: 2018 IEEE 15TH INTERNATIONAL WORKSHOP ON ADVANCED MOTION CONTROL (AMC). - : IEEE. - 9781538619469 ; , s. 497-502
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Konferensbidrag (refereegranskat)abstract
- Iterative learning control enables the determination of optimal command inputs by learning from measured data of previous tasks. The aim of this paper is to address the negative impact of trial-varying disturbances that contaminate these measurements, both in terms of resource-efficient implementations and performance degradation. The proposed method is an optimal framework for ILC that enforces sparsity and related structure on the command signal. This is achieved through a convex relaxation relying on l(1) regularization. The approach is demonstrated on a benchmark motion system, confirming substantial extensions compared to earlier results.
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| 7. |
- Oomen, Tom, et al.
(författare)
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Sparse iterative learning control with application to a wafer stage : Achieving performance, resource efficiency, and task flexibility
- 2017
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Ingår i: Mechatronics (Oxford). - : PERGAMON-ELSEVIER SCIENCE LTD. - 0957-4158 .- 1873-4006. ; 47, s. 134-147
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Tidskriftsartikel (refereegranskat)abstract
- Trial-varying disturbances are a key concern in Iterative Learning Control (ILC) and may lead to inefficient and expensive implementations and severe performance deterioration. The aim of this paper is to develop a general framework for optimization-based ILC that allows for enforcing additional structure, including sparsity. The proposed method enforces sparsity in a generalized setting through convex relaxations using el norms. The proposed ILC framework is applied to the optimization of sampling sequences for resource efficient implementation, trial-varying disturbance attenuation, and basis function selection. The framework has a large potential in control applications such as mechatronics, as is confirmed through an application on a wafer stage.
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| 8. |
- Rallo, Gianmarco, et al.
(författare)
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Data-driven H-infinity-norm estimation via expert advice
- 2017
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Ingår i: 2017 IEEE 56TH ANNUAL CONFERENCE ON DECISION AND CONTROL (CDC). - : Institute of Electrical and Electronics Engineers (IEEE). - 9781509028733 ; , s. 1560-1565
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Konferensbidrag (refereegranskat)abstract
- H-infinity-norm estimation is usually an important aspect of robust control design. The aim of this paper is to develop a data-driven estimation method exploiting iterative input design, without requiring parametric modeling. More specifically, the estimation problem is formulated as a sequential game, whose solution is derived within the prediction with expert advice framework. The proposed method is shown to be competitive with the state-of-the-art techniques.
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| 9. |
- Rojas, Cristian R., et al.
(författare)
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Analyzing iterations in identification with application to nonparametric H-infinity-norm estimation
- 2012
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Ingår i: Automatica. - : Elsevier BV. - 0005-1098 .- 1873-2836. ; 48:11, s. 2776-2790
-
Tidskriftsartikel (refereegranskat)abstract
- Many iterative approaches in the field of system identification for control have been developed. Although successful implementations have been reported, a solid analysis with respect to the convergence of these iterations has not been established. The aim of this paper is to present a thorough analysis of a specific iterative algorithm that involves nonparametric H ∞- norm estimation. The pursued methodology involves a novel frequency domain approach that addresses both additive stochastic disturbances and input normalization. The results of the convergence analysis are twofold: (1) the presence of additive disturbances introduces a bias in the estimation procedure, and (2) the iterative procedure can be interpreted as experiment design for H ∞-norm estimation, revealing the value of iterations and limits of accuracy in terms of the Fisher information matrix. The results are confirmed by means of a simulation example.
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