| 1. |
- Abdalmoaty, Mohamed, 1986-
(författare)
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Learning Stochastic Nonlinear Dynamical Systems Using Non-stationary Linear Predictors
- 2017
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Licentiatavhandling (övrigt vetenskapligt/konstnärligt)abstract
- The estimation problem of stochastic nonlinear parametric models is recognized to be very challenging due to the intractability of the likelihood function. Recently, several methods have been developed to approximate the maximum likelihood estimator and the optimal mean-square error predictor using Monte Carlo methods. Albeit asymptotically optimal, these methods come with several computational challenges and fundamental limitations.The contributions of this thesis can be divided into two main parts. In the first part, approximate solutions to the maximum likelihood problem are explored. Both analytical and numerical approaches, based on the expectation-maximization algorithm and the quasi-Newton algorithm, are considered. While analytic approximations are difficult to analyze, asymptotic guarantees can be established for methods based on Monte Carlo approximations. Yet, Monte Carlo methods come with their own computational difficulties; sampling in high-dimensional spaces requires an efficient proposal distribution to reduce the number of required samples to a reasonable value.In the second part, relatively simple prediction error method estimators are proposed. They are based on non-stationary one-step ahead predictors which are linear in the observed outputs, but are nonlinear in the (assumed known) input. These predictors rely only on the first two moments of the model and the computation of the likelihood function is not required. Consequently, the resulting estimators are defined via analytically tractable objective functions in several relevant cases. It is shown that, under mild assumptions, the estimators are consistent and asymptotically normal. In cases where the first two moments are analytically intractable due to the complexity of the model, it is possible to resort to vanilla Monte Carlo approximations. Several numerical examples demonstrate a good performance of the suggested estimators in several cases that are usually considered challenging.
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| 2. |
- Risuleo, Riccardo Sven, 1986-, et al.
(författare)
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Semi-parametric kernel-based identification of Wiener systems
- 2018
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Ingår i: 2018 IEEE Conference on Decision and Control (CDC). - Piscataway, NJ : Institute of Electrical and Electronics Engineers (IEEE). - 9781538613955 ; , s. 3874-3879
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Konferensbidrag (refereegranskat)abstract
- We present a technique for kernel-based identification of Wiener systems. We model the impulse response of the linear block with a Gaussian process. The static nonlinearity is modeled with a combination of basis functions. The coefficients of the static nonlinearity are estimated, together with the hyperparameters of the covariance function of the Gaussian process model, using an iterative algorithm based on the expectation-maximization method combined with elliptical slice sampling to sample from the posterior distribution of the impulse response given the data. The same sampling method is then used to find the posterior-mean estimate of the impulse response. We test the proposed algorithm on a benchmark of randomly-generated Wiener systems.
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| 3. |
- Abdalmoaty, Mohamed R., 1986-, et al.
(författare)
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Application of a Linear PEM Estimator to a Stochastic Wiener-Hammerstein Benchmark Problem⁎
- 2018
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Ingår i: IFAC-PapersOnLine. - : Elsevier B.V.. - 2405-8963. ; 51:15, s. 784-789
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Tidskriftsartikel (refereegranskat)abstract
- 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.
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| 4. |
- Abdalmoaty, Mohamed Rasheed, 1986-, et al.
(författare)
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Consistent Estimators of Stochastic MIMO Wiener Models based on Suboptimal Predictors
- 2018
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Ingår i: 2018 IEEE Conference on Decision and Control (CDC). - : IEEE. - 9781538613955 - 9781538613948 - 9781538613962 ; , s. 3842-3847
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Konferensbidrag (refereegranskat)abstract
- We consider a parameter estimation problem in a general class of stochastic multiple-inputs multiple-outputs Wiener models, where the likelihood function is, in general, analytically intractable. When the output signal is a scalar independent stochastic process, the likelihood function of the parameters is given by a product of scalar integrals. In this case, numerical integration may be efficiently used to approximately solve the maximum likelihood problem. Otherwise, the likelihood function is given by a challenging multidimensional integral. In this contribution, we argue that by ignoring the temporal and spatial dependence of the stochastic disturbances, a computationally attractive estimator based on a suboptimal predictor can be constructed by evaluating scalar integrals regardless of the number of outputs. Under some conditions, the convergence of the resulting estimators can be established and consistency is achieved under certain identifiability hypothesis. We highlight the relationship between the resulting estimators and a recently proposed prediction error method estimator. We also remark that the method can be used for a wider class of stochastic nonlinear models. The performance of the method is demonstrated by a numerical simulation example using a 2-inputs 2-outputs model with 9 parameters.
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| 5. |
- Abdalmoaty, Mohamed R., 1986-, et al.
(författare)
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Identification of a Class of Nonlinear Dynamical Networks⁎
- 2018
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Ingår i: IFAC-PapersOnLine. - : Elsevier B.V.. - 2405-8963. ; 51:15, s. 868-873
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Tidskriftsartikel (refereegranskat)abstract
- 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.
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| 6. |
- Abdalmoaty, Mohamed, 1986-, et al.
(författare)
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Simulated Pseudo Maximum Likelihood Identification of Nonlinear Models
- 2017
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Ingår i: The 20th IFAC World Congress. - : Elsevier. ; 50:1, s. 14058-14063
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Konferensbidrag (refereegranskat)abstract
- 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.
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| 7. |
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| 8. |
- Bombois, Xavier, et al.
(författare)
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Optimal identification experiment design for the interconnection of locally controlled systems
- 2018
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Ingår i: Automatica. - : Elsevier. - 0005-1098 .- 1873-2836. ; 89, s. 169-179
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Tidskriftsartikel (refereegranskat)abstract
- This paper considers the identification of the modules of a network of locally controlled systems (multi-agent systems). Its main contribution is to determine the least perturbing identification experiment that will nevertheless lead to sufficiently accurate models of each module for the global performance of the network to be improved by a redesign of the decentralized controllers. Another contribution is to determine the experimental conditions under which sufficiently informative data (i.e. data leading to a consistent estimate) can be collected for the identification of any module in such a network.
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| 9. |
- Briat, C., et al.
(författare)
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The Conservation of Information, Towards an Axiomatized Modular Modeling Approach to Congestion Control
- 2015
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Ingår i: IEEE/ACM Transactions on Networking. - 1063-6692 .- 1558-2566. ; 23:3, s. 851-865
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Tidskriftsartikel (refereegranskat)abstract
- We derive a modular fluid-flow network congestion control model based on a law of fundamental nature in networks: the conservation of information. Network elements such as queues, users, and transmission channels and network performance indicators like sending/acknowledgment rates and delays are mathematically modeled by applying this law locally. Our contributions are twofold. First, we introduce a modular metamodel that is sufficiently generic to represent any network topology. The proposed model is composed of building blocks that implement mechanisms ignored by the existing ones, which can be recovered from exact reduction or approximation of this new model. Second, we provide a novel classification of previously proposed models in the literature and show that they are often not capable of capturing the transient behavior of the network precisely. Numerical results obtained from packet-level simulations demonstrate the accuracy of the proposed model.
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| 10. |
- Ebadat, Afrooz, 1986-
(författare)
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Experiment Design for Closed-loop System Identification with Applications in Model Predictive Control and Occupancy Estimation
- 2017
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Doktorsavhandling (övrigt vetenskapligt/konstnärligt)abstract
- The objective of this thesis is to develop algorithms for application-oriented input design. This procedure takes the model application into account when designing experiments for system identification.This thesis is divided into two parts. The first part considers the theory of application-oriented input design, with special attention to Model Predictive Control (MPC). We start by studying how to find a convex approximation of the set of models that result in acceptable control performance using analytical methods when controllers with no closed-form control law, for e.g., MPC are employed. The application-oriented input design is formulated in time domain to enable handling of signals constraints. The framework is extended to closed-loop systems where two cases are considered i.e., when the plant is controlled by a general but known controller and for the case of MPC. To this end, an external stationary signal is designed via graph theory. Different sources of uncertainty in application-oriented input design are investigated and a robust application-oriented input design framework is proposed.The second part of this thesis is devoted to the problem of estimating the number of occupants based on the information available to HVAC systems in buildings. The occupancy estimation is first formulated as a two-tier problem. In the first tier, the room dynamic is identified using temporary measurements of occupancy. In the second tier, the identified model is employed to formulate the problem as a fused-lasso problem. The proposed method is further developed to be used as a multi-room estimator using a physics-based model. However, since it is not always possible to collect measurements of occupancy, we proceed by proposing a blind identification algorithm which estimates the room dynamic and occupancy, simultaneously. Finally, the application-oriented input design framework is employed to collect data that is informative enough for occupancy estimation purposes.
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