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Application of a Linear PEM Estimator to a Stochastic Wiener-Hammerstein Benchmark Problem⁎

IFAC-PapersOnLine 2018年第15期51卷 784-789页

作者： Abdalmoaty, Mohamed Rasheed Hjalmarsson, Håkan Automatic Control Lab and ACCESS Linnaeus Center KTH Royal institute of Technology Stockholm Sweden

The estimation problem of stochastic Wiener-Hammerstein models is recognized to be challenging, mainly due to the analytical intractability of the likelihood function. In this contribution, we apply a computationally attractive prediction error method estimator to a real-data stochastic Wiener-Hammerstein benchmark problem. The estimator is defined using a deterministic predictor that is nonlinear in the input. The prediction error method results in tractable expressions, and Monte Carlo approximations are not necessary. This allows us to tackle several issues considered challenging from the perspective of the current mainstream approach. Under mild conditions, the estimator can be shown to be consistent and asymptotically normal. The results of the method applied to the benchmark data are presented and discussed. © 2018

关键词： Benchmarking Error analysis Identification (control systems) Monte Carlo methods Nonlinear systems Stochastic models Stochastic systems Bench mark problems Benchmark data Estimation problem Likelihood functions Monte carlo approximations Prediction error method Wiener Hammerstein Wiener hammerstein models

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Simulated Pseudo Maximum Likelihood Identification of Nonlinear Models

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IFAC-PapersOnLine 2017年第1期50卷 14058-14063页

作者： Abdalmoaty, Mohamed Rasheed Hjalmarsson, Håkan Automatic Control Department ACCESS Linnaeus Center KTH Royal institute of Technology Stockholm Sweden

Nonlinear stochastic parametric models are widely used in various fields. However, for these models, the problem of maximum likelihood identification is very challenging due to the intractability of the likelihood function. Recently, several methods have been developed to approximate the analytically intractable likelihood function and compute either the maximum likelihood or a Bayesian estimator. These methods, albeit asymptotically optimal, are computationally expensive. In this contribution, we present a simulation-based pseudo likelihood estimator for nonlinear stochastic models. It relies only on the first two moments of the model, which are easy to approximate using Monte-Carlo simulations on the model. The resulting estimator is consistent and asymptotically normal. We show that the pseudo maximum likelihood estimator, based on a multivariate normal family, solves a prediction error minimization problem using a parameterized norm and an implicit linear predictor. In the light of this interpretation, we compare with the predictor defined by an ensemble Kalman filter. Although not identical, simulations indicate a close relationship. The performance of the simulated pseudo maximum likelihood method is illustrated in three examples. They include a challenging state-space model of dimension 100 with one output and 2 unknown parameters, as well as an application-motivated model with 5 states, 2 outputs and 5 unknown parameters. © 2017

关键词： Stochastic models Identification (control systems) Intelligent systems Maximum likelihood estimation Monte Carlo methods Nonlinear systems State space methods Stochastic systems Asymptotically optimal Ensemble Kalman Filter Likelihood functions Maximum likelihood estimator Maximum likelihood methods Nonlinear stochastic model Prediction error minimizations State space models

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Identification of a Class of Nonlinear Dynamical Networks⁎

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IFAC-PapersOnLine 2018年第15期51卷 868-873页

作者： Abdalmoaty, Mohamed R.H. Rojas, Cristian R. Hjalmarsson, Håkan Automatic Control Department and ACCESS Linnaeus Center KTH Royal institute of Technology Stockholm Sweden

Identification of dynamic networks has attracted considerable interest recently. So far the main focus has been on linear time-invariant networks. Meanwhile, most real-life systems exhibit nonlinear behaviors; consider, for example, two stochastic linear time-invariant systems connected in series, each of which has a nonlinearity at its output. The estimation problem in this case is recognized to be challenging, due to the analytical intractability of both the likelihood function and the optimal one-step ahead predictors of the measured nodes. In this contribution, we introduce a relatively simple prediction error method that may be used for the estimation of nonlinear dynamical networks. The estimator is defined using a deterministic predictor that is nonlinear in the known signals. The estimation problem can be defined using closed-form analytical expressions in several non-trivial cases, and Monte Carlo approximations are not necessarily required. We show, that this is the case for some block-oriented networks with no feedback loops and where all the nonlinear modules are polynomials. Consequently, the proposed method can be applied in situations considered challenging by current approaches. The performance of the estimation method is illustrated on a numerical simulation example. © 2018

关键词： Nonlinear analysis Estimation Identification (control systems) Invariance Linear systems Numerical methods Real time systems Stochastic models Stochastic systems Time varying control systems Analytical expressions Block oriented model Dynamical networks Likelihood functions Linear time invariant networks Linear time invariant systems Monte carlo approximations Prediction error method

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On Re-weighting, Regularization Selection, and Transient in Nuclear Norm based Identification

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IFAC-PapersOnLine 2015年第28期48卷 92-97页

作者： Abdalmoaty, Mohamed Hjalmarsson, Håkan Automatic Control Department and ACCESS Linnaeus Center KTH Royal institute of Technology Stockholm Sweden

In this contribution, we consider the classical problem of estimating an Output Error model given a set of input-output measurements. First, we develop a regularization method based on the re-weighted nuclear norm heuristic. We show that the re-weighting improves the estimate in terms of better fit. Second, we suggest an implementation method that helps in eliminating the regularization parameters from the problem by introducing a constant based on a validation criterion. Finally, we develop a method for considering the effect of the transient when the initial conditions are unknown. A simple numerical example is used to demonstrate the proposed method in comparison to classical and another recent method based on the nuclear norm heuristic. © 2015

关键词： Heuristic methods Numerical methods Least Square Nuclear norms Output error identification Rank estimations regularization

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A Least Squares Method for Identification of Feedback Cascade Systems

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IFAC-PapersOnLine 2015年第28期48卷 98-103页

作者： Galrinho, Miguel Rojas, Cristian R. Hjalmarsson, Håkan Department of Automatic Control and ACCESS Linnaeus Center School of Electrical Engineering KTH - Royal Institute of Technology SE-100 44 Stockholm Sweden

The problem of identification of systems in dynamic networks is considered. Although the prediction error method (PEM) can be applied to the overall system, the non-standardmodel structure requires solving a non-convex optimization problem. Alternative methods have been proposed, such as instrumental variables and indirect PEM. In this paper, we first consider acyclic cascade systems, and argue that these methods have different ranges of applicability. Then, for a network with feedback connection, we propose an approach to deal with the fact that indirect PEM yields a non-convex problem in that case. A numerical simulation may indicate that this approach is competitive with other existing methods. © 2015

关键词： Least squares approximations Convex optimization Error analysis Feedback Identification (control systems) Numerical methods Closed loop identification Feed back loop Feed forward network Identification of systems Instrumental variables Least squares algorithm Nonconvex optimization Prediction error method

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Energy and CO2 efficient scheduling of smart appliances in active houses equipped with batteries

Energy and CO2 efficient scheduling of smart appliances in a...

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2014 IEEE International Conference on Automation Science and Engineering, CASE 2014

作者： Paridari, Kaveh Parisio, Alessandra Sandberg, Henrik Johansson, Karl Henrik ACCESS Linnaeus Center and the Automatic Control Lab School of Electrical Engineering KTH Royal Institute of Technology Sweden

In this paper, we present a novel method for scheduling smart appliances and batteries, in order to reduce both the electricity bill and the CO2 emissions. Mathematically, the scheduling problem is posed as a multi-objective Mixed Integer Linear Programming (MILP), which can be solved by using standard algorithms. A case study is performed to assess the performance of the proposed scheduling framework. Numerical results show that the new formulation can decrease both the CO2 emissions and the electricity bill. Furthermore, a survey of studies that deal with scheduling of smart appliances is provided. These papers use methods based on MILP, Dynamic Programming (DP), and Minimum Cut Algorithm (MCA) for solving the scheduling problem. We discuss their performance in terms of computation time and optimality versus time discretization and number of appliances. © 2014 IEEE.

关键词： Scheduling

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Randomized optimal consensus of multi-agent systems

Randomized optimal consensus of multi-agent systems

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作者： Shi, Guodong Johansson, Karl Henrik Automatic Control Lab ACCESS Linnaeus Centre School of Electrical Engineering Stockholm 100 44 Sweden

In this paper, we formulate and solve a randomized optimal consensus problem for multi-agent systems with stochastically time-varying interconnection topology. The considered multi-agent system with a simple randomized iterating rule achieves an almost sure consensus meanwhile solving the optimization problem minz∈Rd∑i=1nfi(z), in which the optimal solution set of objective function fi can only be observed by agent i itself. At each time step, simply determined by a Bernoulli trial, each agent independently and randomly chooses either taking an average among its neighbor set, or projecting onto the optimal solution set of its own optimization component. Both directed and bidirectional communication graphs are studied. Connectivity conditions are proposed to guarantee an optimal consensus almost surely with proper convexity and intersection assumptions. The convergence analysis is carried out using convex analysis. We compare the randomized algorithm with the deterministic one via a numerical example. The results illustrate that a group of autonomous agents can reach an optimal opinion by each node simply making a randomized trade-off between following its neighbors or sticking to its own opinion at each time step. © 2012 Elsevier Ltd. All rights reserved.

关键词： Multi agent systems

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A generalized utility maximization problem with outage constraints in CDMA networks

A generalized utility maximization problem with outage const...

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作者： Fischione, Carlo D'Angelo, Massimiliano Automatic Control Lab. ACCESS Linnaeus Centre KTH Royal Institute of Technology Sweden Italy

ISBN: (纸本)9783902661821

The problem of maximizing a utility function while limiting the outage probability below an appropriate threshold is investigated. A coded-division multi access wireless network under mixed Nakagami-lognormal fading is considered. Solving such a utility maximization problem is difficult because the problem is non-convex and non-geometric with mixed integer and real decision variables and no explicit functions of the constraints are available. In this paper, two methods to the solution of the utility maximization problem are proposed. By the first method, a simple explicit outage approximation is used and the constraint that rates are integers is relaxed yielding a standard convex programming optimization that can be solved quickly but at the price of a reduced accuracy. The second method uses a more accurate outage approximation, which allows one solving the utility maximization problem by the Lagrange duality for non-convex problems and contraction mapping theory. Numerical results show that the first method performs well for average values of the outage requirements, whereas the second one is always more accurate, but is also more computationally expensive. © 2010 IFAC.

关键词： Outages

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Bayesian kernel-based system identification with quantized output data

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IFAC-PapersOnLine 2015年第28期48卷 455-460页

作者： Bottegal, Giulio Pillonetto, Gianluigi Hjalmarsson, Håkan Automatic Control Lab and ACCESS Linnaeus Centre School of Electrical Engineering KTH Royal Institute of Technology Stockholm Sweden Department of Information Engineering University of Padova Padova Italy

In this paper we introduce a novel method for linear system identification with quantized output data. We model the impulse response as a zero-mean Gaussian process whose covariance (kernel) is given by the recently proposed stable spline kernel, which encodes information on regularity and exponential stability. This serves as a starting point to cast our system identification problem into a Bayesian framework. We employ Markov Chain Monte Carlo (MCMC) methods to provide an estimate of the system. In particular, we show how to design a Gibbs sampler which quickly converges to the target distribution. Numerical simulations show a substantial improvement in the accuracy of the estimates over state-of-the-art kernel-based methods when employed in identification of systems with quantized data. © 2015

关键词： Monte Carlo methods Impulse response Linear systems Markov processes Numerical methods Religious buildings Bayesian frameworks Identification of systems Kernel based methods Markov chain Monte Carlo method Spline kernels State of the art System identification problems Zero mean Gaussian process

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Networked control under time-synchronization errors

Networked control under time-synchronization errors

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作者： Seuret, Alexandre Johansson, Karl H. NeCS Team Automatic Control Department of Grenoble GIPSA-Lab UMR CNRS 5216 France ACCESS Linnaeus Center Royal Institute of Technology Stockholm Sweden

ISBN: (纸本)9783902661678

A robust controller is derived for networked control systems with uncertain plant dynamics. The link between the nodes is disturbed by time-varying communication delays, samplings and time-synchronization. A stability criterion for a robust control is presented in terms of LMIs based on Lyapunov-Krasovskii techniques. A second-order system example is considered and the relation between the admissive bounds of the synchronization error and the size of the uncertainties is computed. Copyright © IFAC 2009.

关键词： Stability criteria

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