Anders Lindquist
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View article: A general solution to the simultaneous stabilization problem by analytic interpolation
A general solution to the simultaneous stabilization problem by analytic interpolation Open
In this paper, we tackle the significant challenge of simultaneous stabilization in control systems engineering, where the aim is to employ a single controller to ensure stability across multiple systems. We delve into both scalar and mult…
View article: Distribution Steering for Discrete-Time Uncertain Ensemble Systems
Distribution Steering for Discrete-Time Uncertain Ensemble Systems Open
Ensemble systems appear frequently in many engineering applications and, as a result, they have become an important research topic in control theory. These systems are best characterized by the evolution of their underlying state distribut…
View article: Multivariable simultaneous stabilization: A modified Riccati approach
Multivariable simultaneous stabilization: A modified Riccati approach Open
Simultaneous stabilization problem arises in various systems and control applications. This paper introduces a new approach to addressing this problem in the multivariable scenario, building upon our previous findings in the scalar case. T…
View article: General Discrete-Time Fokker-Planck Control by Power Moments
General Discrete-Time Fokker-Planck Control by Power Moments Open
In this paper, we address the so-called general Fokker-Planck control problem for discrete-time first-order linear systems. Unlike conventional treatments, we don't assume the distributions of the system states to be Gaussian. Instead, we …
View article: Quantitative Error Analyses of Spectral Density Estimators Using Covariance Lags
Quantitative Error Analyses of Spectral Density Estimators Using Covariance Lags Open
Spectral density estimation is a core problem of system identification, which is an important research area of system control and signal processing. There have been numerous results on the design of spectral density estimators. However to …
View article: A parameterized solution to the simultaneous stabilization problem
A parameterized solution to the simultaneous stabilization problem Open
In a series of fundamental papers BK Ghosh reduced the simultaneous stabilization problem to a NevanlinnaPick interpolation problem. In this paper we generalize some of these results allowing for derivative constraints. Moreover, we apply …
View article: General Distribution Steering: A Sub-Optimal Solution by Convex Optimization
General Distribution Steering: A Sub-Optimal Solution by Convex Optimization Open
General distribution steering is intrinsically an infinite-dimensional problem, when the continuous distributions to steer are arbitrary. We put forward a moment representation of the primal system for control in [42]. However, the system …
View article: Density Steering by Power Moments
Density Steering by Power Moments Open
This paper considers the problem of steering an arbitrary initial probability density function to an arbitrary terminal one, where the system dynamics is governed by a first-order linear stochastic difference equation. It is a generalizati…
View article: A Non-Gaussian Bayesian Filter Using Power and Generalized Logarithmic Moments
A Non-Gaussian Bayesian Filter Using Power and Generalized Logarithmic Moments Open
In this paper, we aim to propose a consistent non-Gaussian Bayesian filter of which the system state is a continuous function. The distributions of the true system states, and those of the system and observation noises, are only assumed Le…
View article: A Multivariate Non-Gaussian Bayesian Filter Using Power Moments
A Multivariate Non-Gaussian Bayesian Filter Using Power Moments Open
In this paper, we extend our results on the univariate non-Gaussian Bayesian filter using power moments to the multivariate systems, which can be either linear or nonlinear. Doing this introduces several challenging problems, for example a…
View article: Group Steering: Approaches Based on Power Moments
Group Steering: Approaches Based on Power Moments Open
This paper considers the problem of steering a vast group of agents of which the dynamics are governed by a discrete-time first-order linear system. The group of agents are characterized as a probability density function and an occupation …
View article: Density Steering by Power Moments
Density Steering by Power Moments Open
This paper considers the problem of steering an arbitrary initial probability density function to an arbitrary terminal one, where the system dynamics is governed by a first-order linear stochastic difference equation. It is a generalizati…
View article: Non-Gaussian Bayesian Filtering by Density Parametrization Using Power Moments
Non-Gaussian Bayesian Filtering by Density Parametrization Using Power Moments Open
Non-Gaussian Bayesian filtering is a core problem in stochastic filtering. The difficulty of the problem lies in parameterizing the state estimates. However the existing methods are not able to treat it well. We propose to use power moment…
View article: A Non-Classical Parameterization for Density Estimation Using Sample Moments
A Non-Classical Parameterization for Density Estimation Using Sample Moments Open
Probability density estimation is a core problem of statistics and signal processing. Moment methods are an important means of density estimation, but they are generally strongly dependent on the choice of feasible functions, which severel…
View article: Identification of Low Rank Vector Processes
Identification of Low Rank Vector Processes Open
We study modeling and identification of stationary processes with a spectral density matrix of low rank. Equivalently, we consider processes having an innovation of reduced dimension for which Prediction Error Methods (PEM) algorithms are …
View article: Modeling of Low Rank Time Series
Modeling of Low Rank Time Series Open
Rank-deficient stationary stochastic vector processes are present in many problems in network theory and dynamic factor analysis. In this paper we study hidden dynamical relations between the components of a discrete-time stochastic vector…
View article: On analytic interpolation with non-classical constraints for solving problems in robust control
On analytic interpolation with non-classical constraints for solving problems in robust control Open
In this work we consider robust stabilization of uncertain dynamical systems and show that this can be achieved by solving a non-classically constrained analytic interpolation problem. In particular, this non-classical constraint confines …
View article: On a Fejér–Riesz factorization of generalized trigonometric polynomials
On a Fejér–Riesz factorization of generalized trigonometric polynomials Open
Function theory on the unit disc proved key to a range of problems in statistics, probability theory, signal processing literature, and applications, and in this, a special place is occupied by trigonometric functions and the Fejer-Riesz t…
View article: The Covariance Extension Equation: A Riccati-type Approach to Analytic Interpolation
The Covariance Extension Equation: A Riccati-type Approach to Analytic Interpolation Open
Analytic interpolation problems with rationality and derivative constraints are ubiquitous in systems and control. This paper provides a new method for such problems, both in the scalar and matrix case, based on a non-standard Riccati-type…
View article: Spectral Rank, Feedback, Causality and the Indirect Method for CARMA Identification
Spectral Rank, Feedback, Causality and the Indirect Method for CARMA Identification Open
Building on a recent paper by Georgiou and Lindquist [1] on the problem of rank deficiency of spectral densities and hidden dynamical relations after sampling of continuous-time stochastic processes, this paper is devoted to understanding …
View article: Multivariable analytic interpolation with complexity constraints: A modified Riccati approach
Multivariable analytic interpolation with complexity constraints: A modified Riccati approach Open
Analytic interpolation problems with rationality and derivative constraints occur in many applications in systems and control. In this paper we present a new method for the multivariable case, which generalizes our previous results on the …
View article: Lower Bounds on the Maximum Delay Margin by Analytic Interpolation
Lower Bounds on the Maximum Delay Margin by Analytic Interpolation Open
We study the delay margin problem in the context of recent works by T. Qi, J.\nZhu, and J. Chen, where a sufficient condition for the maximal delay margin is\nformulated in terms of an interpolation problem obtained after introducing a\nra…
View article: A modified Riccati approach to analytic interpolation with applications to system identification and robust control
A modified Riccati approach to analytic interpolation with applications to system identification and robust control Open
This paper provides a new method to solve analytic interpolation problems with rationality and derivative constraints, occurring in many applications to system and control. It is based on the covariance extension equation previously propos…
View article: Dynamic Relations in Sampled Processes
Dynamic Relations in Sampled Processes Open
Linear dynamical relations that may exist in continuous-time, or at some natural sampling rate, are not directly discernable at reduced observational sampling rates. Indeed, at reduced rates, matricial spectral densities of vectorial time …
View article: Multidimensional Rational Covariance Extension with Approximate Covariance Matching
Multidimensional Rational Covariance Extension with Approximate Covariance Matching Open
In our companion paper "Multidimensional rational covariance extension with applications to spectral estimation and image compression" we discussed the multidimensional rational covariance extension problem (RCEP), which has important appl…
View article: Partial Realization Theory and System Identification Redux
Partial Realization Theory and System Identification Redux Open
Some twenty years ago we introduced a nonstandard matrix Riccati equation to solve the partial stochastic realization problem. In this paper we provide a new derivation of this equation in the context of system identification. This allows …
View article: Optimal Estimation With Missing Observations via Balanced Time-Symmetric Stochastic Models
Optimal Estimation With Missing Observations via Balanced Time-Symmetric Stochastic Models Open
We consider data fusion for the purpose of smoothing and interpolation based on observation records with missing data. Stochastic processes are generated by linear stochastic models. The paper begins by drawing a connection between time re…
View article: Likelihood Analysis of Power Spectra and Generalized Moment Problems
Likelihood Analysis of Power Spectra and Generalized Moment Problems Open
We develop an approach to spectral estimation that has been advocated by Ferrante, Masiero and Pavon and, in the context of the scalar-valued covariance extension problem, by Enqvist and Karlsson. The aim is to determine the power spectrum…