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In this paper, we consider data driven control of Hammerstein systems. For such systems a common control structure is a transfer function followed by a static output nonlinearity that tries to cancel the input nonlinearity of the system, which is modeled as a polynomial or piece-wise linear function. The linear part of the controller is used to achieve desired disturbance rejection and tracking properties. To design a linear part of the controller, we propose a weighted average risk criterion with the risk being the average of the squared L2 tracking error. Here the average is with respect to the observations used in the controller and the weighting is with respect to how important it is to have good control for different impulse responses. This criterion corresponds to the average risk criterion leading to the Bayes estimator and we therefore call this approach Bayes control. By parametrizing the weighting function and estimating the corresponding hyperparameters we tune the weighting function to the information regarding the true impulse response contained in the data set available to the user for the control design. The numerical results show that the proposed methods result in stable controllers with performance comparable to the optimal controller, designed using the true input nonlinearity and true plant.

In this paper, we consider data driven control of Hammerstein systems. For such systems a common control structure is a transfer function followed by a static output nonlinearity that tries to cancel the input nonlinearity of the system, which is modeled as a polynomial or piece-wise linear function. The linear part of the controller is used to achieve desired disturbance rejection and tracking properties. To design a linear part of the controller, we propose a weighted average risk criterion with the risk being the average of the squared L2 tracking error. Here the average is with respect to the observations used in the controller and the weighting is with respect to how important it is to have good control for different impulse responses. This criterion corresponds to the average risk criterion leading to the Bayes estimator and we therefore call this approach Bayes control. By parametrizing the weighting function and estimating the corresponding hyperparameters we tune the weighting function to the information regarding the true impulse response contained in the data set available to the user for the control design. The numerical results show that the proposed methods result in stable controllers with performance comparable to the optimal controller, designed using the true input nonlinearity and true plant.

In this paper, we consider data driven control of Hammerstein systems. For such systems a common control structure is a transfer function followed by a static output nonlinearity that tries to cancel the input nonlinearity of the system, which is modeled as a polynomial or piece-wise linear function. The linear part of the controller is used to achieve desired disturbance rejection and tracking properties. To design a linear part of the controller, we propose a weighted average risk criterion with the risk being the average of the squared L2 tracking error. Here the average is with respect to the observations used in the controller and the weighting is with respect to how important it is to have good control for different impulse responses. This criterion corresponds to the average risk criterion leading to the Bayes estimator and we therefore call this approach Bayes control. By parametrizing the weighting function and estimating the corresponding hyperparameters we tune the weighting function to the information regarding the true impulse response contained in the data set available to the user for the control design. The numerical results show that the proposed methods result in stable controllers with performance comparable to the optimal controller, designed using the true input nonlinearity and true plant.

In this paper, we consider data driven control of Hammerstein systems. For such systems a common control structure is a transfer function followed by a static output nonlinearity that tries to cancel the input nonlinearity of the system, which is modeled as a polynomial or piece-wise linear function. The linear part of the controller is used to achieve desired disturbance rejection and tracking properties. To design a linear part of the controller, we propose a weighted average risk criterion with the risk being the average of the squared L2 tracking error. Here the average is with respect to the observations used in the controller and the weighting is with respect to how important it is to have good control for different impulse responses. This criterion corresponds to the average risk criterion leading to the Bayes estimator and we therefore call this approach Bayes control. By parametrizing the weighting function and estimating the corresponding hyperparameters we tune the weighting function to the information regarding the true impulse response contained in the data set available to the user for the control design. The numerical results show that the proposed methods result in stable controllers with performance comparable to the optimal controller, designed using the true input nonlinearity and true plant.

In this paper, we consider data driven control of Hammerstein systems. For such systems a common control structure is a transfer function followed by a static output nonlinearity that tries to cancel the input nonlinearity of the system, which is modeled as a polynomial or piece-wise linear function. The linear part of the controller is used to achieve desired disturbance rejection and tracking properties. To design a linear part of the controller, we propose a weighted average risk criterion with the risk being the average of the squared L2 tracking error. Here the average is with respect to the observations used in the controller and the weighting is with respect to how important it is to have good control for different impulse responses. This criterion corresponds to the average risk criterion leading to the Bayes estimator and we therefore call this approach Bayes control. By parametrizing the weighting function and estimating the corresponding hyperparameters we tune the weighting function to the information regarding the true impulse response contained in the data set available to the user for the control design. The numerical results show that the proposed methods result in stable controllers with performance comparable to the optimal controller, designed using the true input nonlinearity and true plant.

Several estimation methods have been proposed for identifying errors-in-variables systems, where both input and output measurements are corrupted by noise. One of the more interesting approaches is the Frisch scheme. The method can be applied using either time or frequency domain representations. This paper investigates the general mathematical and geometrical aspects of the Frisch scheme, illustrating the analogies and the differences between the time and frequency domain formulations.

This paper describes a new approach for the blind identification of a two-channel FIR system from a finite number of output measurements, in the presence of additive and uncorrelated white noise. The proposed approach is based on frequency domain data and, as a major novelty, it enables the estimation to be frequency selective. The features of the proposed method are analyzed by means of Monte Carlo simulations. The benefits of filtering the data and using only part of the frequency domain are highlighted by means of a numerical example.

Several estimation methods have been proposed for identifying errors-in-variables systems, where both input and output measurements are corrupted by noise. One of the more interesting approaches is the Frisch scheme. The method can be applied using either time or frequency domain representations. This paper investigates the general mathematical and geometrical aspects of the Frisch scheme, illustrating the analogies and the differences between the time and frequency domain formulations.

This paper describes a new approach for the blind identification of a two-channel FIR system from a finite number of output measurements, in the presence of additive and uncorrelated white noise. The proposed approach is based on frequency domain data and, as a major novelty, it enables the estimation to be frequency selective. The features of the proposed method are analyzed by means of Monte Carlo simulations. The benefits of filtering the data and using only part of the frequency domain are highlighted by means of a numerical example.

Several estimation methods have been proposed for identifying errors-in-variables systems, where both input and output measurements are corrupted by noise. One of the more interesting approaches is the Frisch scheme. The method can be applied using either time or frequency domain representations. This paper investigates the general mathematical and geometrical aspects of the Frisch scheme, illustrating the analogies and the differences between the time and frequency domain formulations.

This paper describes a new approach for the blind identification of a two-channel FIR system from a finite number of output measurements, in the presence of additive and uncorrelated white noise. The proposed approach is based on frequency domain data and, as a major novelty, it enables the estimation to be frequency selective. The features of the proposed method are analyzed by means of Monte Carlo simulations. The benefits of filtering the data and using only part of the frequency domain are highlighted by means of a numerical example.

Several estimation methods have been proposed for identifying errors-in-variables systems, where both input and output measurements are corrupted by noise. One of the more interesting approaches is the Frisch scheme. The method can be applied using either time or frequency domain representations. This paper investigates the general mathematical and geometrical aspects of the Frisch scheme, illustrating the analogies and the differences between the time and frequency domain formulations.

This paper describes a new approach for the blind identification of a two-channel FIR system from a finite number of output measurements, in the presence of additive and uncorrelated white noise. The proposed approach is based on frequency domain data and, as a major novelty, it enables the estimation to be frequency selective. The features of the proposed method are analyzed by means of Monte Carlo simulations. The benefits of filtering the data and using only part of the frequency domain are highlighted by means of a numerical example.

Several estimation methods have been proposed for identifying errors-in-variables systems, where both input and output measurements are corrupted by noise. One of the more interesting approaches is the Frisch scheme. The method can be applied using either time or frequency domain representations. This paper investigates the general mathematical and geometrical aspects of the Frisch scheme, illustrating the analogies and the differences between the time and frequency domain formulations.

This paper describes a new approach for the blind identification of a two-channel FIR system from a finite number of output measurements, in the presence of additive and uncorrelated white noise. The proposed approach is based on frequency domain data and, as a major novelty, it enables the estimation to be frequency selective. The features of the proposed method are analyzed by means of Monte Carlo simulations. The benefits of filtering the data and using only part of the frequency domain are highlighted by means of a numerical example.

A B S T R A C T Radio frequency interference (RFI) mitigation and radar echo recovery are critically important for the proper functioning of ultra-wideband (UWB) radar systems using one-bit sampling techniques. We re-cently introduced a technique for one-bit UWB radar, which first uses a majorization-minimization method for RFI parameter estimation followed by a sparse method for radar echo recovery. However, this technique suffers from high computational complexity due to the need to estimate the parameters of each RFI source separately and iteratively. In this paper, we present a computationally efficient joint RFI mitigation and radar echo recovery framework to greatly reduce the computational cost. Specifically, we exploit the sparsity of RFI in the fast-frequency domain and the sparsity of radar echoes in the fast -time domain to design a one-bit weighted SPICE (SParse Iterative Covariance-based Estimation) based framework for the joint RFI mitigation and radar echo recovery of one-bit UWB radar. Both simulated and experimental results are presented to show that the proposed one-bit weighted SPICE framework can not only reduce the computational cost but also outperform the existing approach for decoupled RFI mitigation and radar echo recovery of one-bit UWB radar.(c) 2021 Elsevier B.V. All rights reserved.

In the present paper, we focus on the doubling of closed invariant curves associated with quasiperiodic dynamics. We consider a 5D map derived from a hybrid model originating from systems biology and containing a continuous part with time delay and pulse-modulated feedback. Using numerical bifurcation analysis, we show that doubling bifurcation takes place on a closed 2D invariant manifold. We explain how such a configuration of the phase space can be created and highlight the role of delay.

This paper deals with the identification of Volterra models that capture the dynamics of smooth pursuit eye movements recorded by an eye tracker. The framework is motivated by neurological applications but can also be useful in biometrics. In healthy subjects, ocular dynamics are predominantly linear, while neurological conditions inflict nonlinearity on smooth pursuit eye movements. Besides overparameterization, Volterra models may also exhibit functional dependence among the model coefficients. A combination of sparse estimation and Principal Component Analysis is shown to be instrumental in estimating parsimonious Volterra models from eye-tracking data. The efficacy of the approach is demonstrated on experimental data collected from Parkinsonian patients as well as healthy controls.

Approaches to the estimation of the full state vector of a larger epidemiological model for the spread of Covid-19 in Sweden at the initial time instant from available data and with a simplified dynamical model are proposed and evaluated. The larger epidemiological model is based on a time-continuous Markov chain and captures the demographic composition of and the transport flows between the counties of Sweden. Its intended use is to predict the outbreak development in temporal and spatial coordinates as well as across the demographic groups. It can also support evaluations and comparisions of prospective intervention strategies in terms of, e.g., lockdown in certain areas or isolation of specific age groups. The simplified model is a discrete time-invariant linear system that has cumulative infectious incidence, infected population, asymptomatic population, exposed population, and infectious pressure as the state variables. Since the system matrix of the model depends on a number of transition rates, structural properties of the model are investigated for suitable parameter ranges. It is concluded that the model becomes unobservable for some parameter values. Two contrasting approaches to the initial state estimation are considered. One is a version of Rauch Tung Striebel smoother and another is based on solving a batch nonlinear optimization problem. The benefits and shortcomings of the considered estimation techniques are analyzed and compared.

Deep learning is a topic of considerable interest today. Since it deals with estimating - or learning - models, there are connections to the area of System Identification developed in the Automatic Control community. Such connections are explored and exploited in this contribution. It is stressed that common deep nets such as feedforward and cascadeforward nets are nonlinear ARX (NARX) models, and can thus be easily incorporated in System Identification code and practice. The case of LSTM nets is an example of NonLinear State-Space (NLSS) models., Koen Tiels: "Was with the dept in Uppsala. Now at Dept of Mechanical Engineering, Eindhoven University of Technology"

Structural identifiablity of a third-order continuous time-invariant linear plant under an intrinsic pulse-modulated feedback is analyzed. The model represents a biomedical system, where the input signal to the continuous plant is immeasurable and the feedback modulation functions have to be identified along with the continuous dynamics. It is shown that two eigenvalues of the continuous plant system matrix (i.e. time constants), along with the times and weights of impulses occurring during a finite time interval, are identifiable from the measurement of one continuous system state over the interval in question. When an infinite time horizon is considered, all parameters are identifiable, up to gain scaling and linear block permutations.

Structural identifiablity of a third-order continuous time-invariant linear plant under an intrinsic pulse-modulated feedback is analyzed. The model represents a biomedical system, where the input signal to the continuous plant is immeasurable and the feedback modulation functions have to be identified along with the continuous dynamics. It is shown that two eigenvalues of the continuous plant system matrix (i.e. time constants), along with the times and weights of impulses occurring during a finite time interval, are identifiable from the measurement of one continuous system state over the interval in question. When an infinite time horizon is considered, all parameters are identifiable, up to gain scaling and linear block permutations.

Approaches to the estimation of the full state vector of a larger epidemiological model for the spread of Covid-19 in Sweden at the initial time instant from available data and with a simplified dynamical model are proposed and evaluated. The larger epidemiological model is based on a time-continuous Markov chain and captures the demographic composition of and the transport flows between the counties of Sweden. Its intended use is to predict the outbreak development in temporal and spatial coordinates as well as across the demographic groups. It can also support evaluations and comparisions of prospective intervention strategies in terms of, e.g., lockdown in certain areas or isolation of specific age groups. The simplified model is a discrete time-invariant linear system that has cumulative infectious incidence, infected population, asymptomatic population, exposed population, and infectious pressure as the state variables. Since the system matrix of the model depends on a number of transition rates, structural properties of the model are investigated for suitable parameter ranges. It is concluded that the model becomes unobservable for some parameter values. Two contrasting approaches to the initial state estimation are considered. One is a version of Rauch Tung Striebel smoother and another is based on solving a batch nonlinear optimization problem. The benefits and shortcomings of the considered estimation techniques are analyzed and compared.

Deep learning is a topic of considerable interest today. Since it deals with estimating - or learning - models, there are connections to the area of System Identification developed in the Automatic Control community. Such connections are explored and exploited in this contribution. It is stressed that common deep nets such as feedforward and cascadeforward nets are nonlinear ARX (NARX) models, and can thus be easily incorporated in System Identification code and practice. The case of LSTM nets is an example of NonLinear State-Space (NLSS) models., Koen Tiels: "Was with the dept in Uppsala. Now at Dept of Mechanical Engineering, Eindhoven University of Technology"

Structural identifiablity of a third-order continuous time-invariant linear plant under an intrinsic pulse-modulated feedback is analyzed. The model represents a biomedical system, where the input signal to the continuous plant is immeasurable and the feedback modulation functions have to be identified along with the continuous dynamics. It is shown that two eigenvalues of the continuous plant system matrix (i.e. time constants), along with the times and weights of impulses occurring during a finite time interval, are identifiable from the measurement of one continuous system state over the interval in question. When an infinite time horizon is considered, all parameters are identifiable, up to gain scaling and linear block permutations.

Deep learning is a topic of considerable interest today. Since it deals with estimating - or learning - models, there are connections to the area of System Identification developed in the Automatic Control community. Such connections are explored and exploited in this contribution. It is stressed that common deep nets such as feedforward and cascadeforward nets are nonlinear ARX (NARX) models, and can thus be easily incorporated in System Identification code and practice. The case of LSTM nets is an example of NonLinear State-Space (NLSS) models., Koen Tiels: "Was with the dept in Uppsala. Now at Dept of Mechanical Engineering, Eindhoven University of Technology"

Approaches to the estimation of the full state vector of a larger epidemiological model for the spread of Covid-19 in Sweden at the initial time instant from available data and with a simplified dynamical model are proposed and evaluated. The larger epidemiological model is based on a time-continuous Markov chain and captures the demographic composition of and the transport flows between the counties of Sweden. Its intended use is to predict the outbreak development in temporal and spatial coordinates as well as across the demographic groups. It can also support evaluations and comparisions of prospective intervention strategies in terms of, e.g., lockdown in certain areas or isolation of specific age groups. The simplified model is a discrete time-invariant linear system that has cumulative infectious incidence, infected population, asymptomatic population, exposed population, and infectious pressure as the state variables. Since the system matrix of the model depends on a number of transition rates, structural properties of the model are investigated for suitable parameter ranges. It is concluded that the model becomes unobservable for some parameter values. Two contrasting approaches to the initial state estimation are considered. One is a version of Rauch Tung Striebel smoother and another is based on solving a batch nonlinear optimization problem. The benefits and shortcomings of the considered estimation techniques are analyzed and compared.

Approaches to the estimation of the full state vector of a larger epidemiological model for the spread of Covid-19 in Sweden at the initial time instant from available data and with a simplified dynamical model are proposed and evaluated. The larger epidemiological model is based on a time-continuous Markov chain and captures the demographic composition of and the transport flows between the counties of Sweden. Its intended use is to predict the outbreak development in temporal and spatial coordinates as well as across the demographic groups. It can also support evaluations and comparisions of prospective intervention strategies in terms of, e.g., lockdown in certain areas or isolation of specific age groups. The simplified model is a discrete time-invariant linear system that has cumulative infectious incidence, infected population, asymptomatic population, exposed population, and infectious pressure as the state variables. Since the system matrix of the model depends on a number of transition rates, structural properties of the model are investigated for suitable parameter ranges. It is concluded that the model becomes unobservable for some parameter values. Two contrasting approaches to the initial state estimation are considered. One is a version of Rauch Tung Striebel smoother and another is based on solving a batch nonlinear optimization problem. The benefits and shortcomings of the considered estimation techniques are analyzed and compared.

Structural identifiablity of a third-order continuous time-invariant linear plant under an intrinsic pulse-modulated feedback is analyzed. The model represents a biomedical system, where the input signal to the continuous plant is immeasurable and the feedback modulation functions have to be identified along with the continuous dynamics. It is shown that two eigenvalues of the continuous plant system matrix (i.e. time constants), along with the times and weights of impulses occurring during a finite time interval, are identifiable from the measurement of one continuous system state over the interval in question. When an infinite time horizon is considered, all parameters are identifiable, up to gain scaling and linear block permutations.

Deep learning is a topic of considerable interest today. Since it deals with estimating - or learning - models, there are connections to the area of System Identification developed in the Automatic Control community. Such connections are explored and exploited in this contribution. It is stressed that common deep nets such as feedforward and cascadeforward nets are nonlinear ARX (NARX) models, and can thus be easily incorporated in System Identification code and practice. The case of LSTM nets is an example of NonLinear State-Space (NLSS) models., Koen Tiels: "Was with the dept in Uppsala. Now at Dept of Mechanical Engineering, Eindhoven University of Technology"

Structural identifiablity of a third-order continuous time-invariant linear plant under an intrinsic pulse-modulated feedback is analyzed. The model represents a biomedical system, where the input signal to the continuous plant is immeasurable and the feedback modulation functions have to be identified along with the continuous dynamics. It is shown that two eigenvalues of the continuous plant system matrix (i.e. time constants), along with the times and weights of impulses occurring during a finite time interval, are identifiable from the measurement of one continuous system state over the interval in question. When an infinite time horizon is considered, all parameters are identifiable, up to gain scaling and linear block permutations.

Deep learning is a topic of considerable interest today. Since it deals with estimating - or learning - models, there are connections to the area of System Identification developed in the Automatic Control community. Such connections are explored and exploited in this contribution. It is stressed that common deep nets such as feedforward and cascadeforward nets are nonlinear ARX (NARX) models, and can thus be easily incorporated in System Identification code and practice. The case of LSTM nets is an example of NonLinear State-Space (NLSS) models., Koen Tiels: "Was with the dept in Uppsala. Now at Dept of Mechanical Engineering, Eindhoven University of Technology"

Approaches to the estimation of the full state vector of a larger epidemiological model for the spread of Covid-19 in Sweden at the initial time instant from available data and with a simplified dynamical model are proposed and evaluated. The larger epidemiological model is based on a time-continuous Markov chain and captures the demographic composition of and the transport flows between the counties of Sweden. Its intended use is to predict the outbreak development in temporal and spatial coordinates as well as across the demographic groups. It can also support evaluations and comparisions of prospective intervention strategies in terms of, e.g., lockdown in certain areas or isolation of specific age groups. The simplified model is a discrete time-invariant linear system that has cumulative infectious incidence, infected population, asymptomatic population, exposed population, and infectious pressure as the state variables. Since the system matrix of the model depends on a number of transition rates, structural properties of the model are investigated for suitable parameter ranges. It is concluded that the model becomes unobservable for some parameter values. Two contrasting approaches to the initial state estimation are considered. One is a version of Rauch Tung Striebel smoother and another is based on solving a batch nonlinear optimization problem. The benefits and shortcomings of the considered estimation techniques are analyzed and compared.